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	<title>Roger Marjoribanks &#187; Structural Geology</title>
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		<title>Drill Core Orientation Tools &#8211; A Review</title>
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		<comments>https://rogermarjoribanks.info/drill-core-orientation-tools/#comments</comments>
		<pubDate>Wed, 24 Jan 2024 02:40:38 +0000</pubDate>
		<dc:creator><![CDATA[Roger Marjoribanks]]></dc:creator>
				<category><![CDATA[Diamond Drilling]]></category>
		<category><![CDATA[Structural Geology]]></category>

		<guid isPermaLink="false">http://rogermarjoribanks.info/?p=2165</guid>
		<description><![CDATA[<p>An oriented drill hole is one where the inclination and azimuth of all sectors of the hole axis are known, usually by means of a special down-hole survey. This data provides the inclination and azimuth of the longitudinal axis (the Core Axis, CA) of the cylindrical core of rock that [&#8230;]</p><p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/drill-core-orientation-tools/">Drill Core Orientation Tools &#8211; A Review</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></description>
				<content:encoded><![CDATA[<p style="text-align: center;">An <b><i>oriented drill hol</i>e</b> is one where the inclination and azimuth of all sectors of the hole axis are known, usually by means of a special down-hole survey. This data provides the inclination and azimuth of the longitudinal axis (the Core Axis, <b><i>CA</i></b>) of the cylindrical core of rock that has been extracted from the hole. However, extracted core is not fully oriented because it is always rotated by some unknown amount about the core axis and the attitude of structures within it cannot therefore be measured.</p>
<p>In fully <b><i>oriented drill core</i></b>, an additional survey procedure, called a core orientation survey, has been carried out to determine the line of intersection of the original <b><i>down gravity vector</i></b> across the length of the core. Drillers use special core orientation tools to do this.</p>
<p>Drillers use one of two methods to determine the position of down gravity vector on the surface of the drill core.</p>
<p><b><i>The first method</i></b><i> </i>is to measure <b><i>the orientation of the</i></b> <b><i>core barrel after a run of core has been drilled</i></b>, but before the core is broken free from the ground and brought to surface inside the rod string. The position of the <b><i>down</i></b> gravity vector across the core barrel is determined by an accelerometer built into a tool screwed onto the top of the core barrel (this is the same technology as used to orient the screen on your smart phone or tablet). The data is stored in a memory against a time stamp. After the barrel with its contained core has been pulled to surface, the barrel orientation during <i>the time interval between core drilling and core extraction</i> is recovered by means of an LCD readout and transferred to the last piece of core to be drilled, which, at this stage, is the piece of core gripped by the core lifter.</p>
<p>The idea behind this method of core orientation is that the last-drilled piece of core was attached to Mother Earth at the time the gravity direction across the core barrel was made and recorded. The orientation of the core barrel can be used as a proxy for the orientation of the core. In most cases, this assumption is valid, and the orientation of the barrel (or rather, the core lifter, an integral part of the barrel) is the same as the orientation of this piece of core. The gravity vector shown on the LCD read-out can thus be transferred by making a mark on the core. The whole drilled core run, with the drillers mark at one end, is then extracted from the barrel, placed in core trays, and delivered to the geologist. By matching broken surfaces, the geologist or geology technician then re-assembles the run on a separate channel. This enables the driller&#8217;s end-of-core mark to be transferred as a continuous Bottom Of Hole line along the length of the run.</p>
<p>However, the end piece of core may have broken free from the ground by the turning drill bit and rotated by some unknown amount <b><i>prior</i></b> to its being gripped by the core lifter. This can happen when the core contains fissile surfaces such as bedding or cleavage. Soft, incompetent surfaces such as mudstone or siltstone horizons, or gouge-filled faults, may fail through ductile shear. Surfaces at a high angle to the drill hole are more likely to fail than those at a low angle.</p>
<p>Where this has occurred, the driller’s orientation mark is meaningless and there is no way for the driller, and no easy way for the geologist, to know when this has happened.</p>
<p>Core barrel orientation tools work perfectly every time at orienting core barrels. Accuracies of less than 1 degree are claimed. But the orientation of the barrel is not necessarily the same as the orientation of the core inside the barrel.</p>
<p style="text-align: center;"> <a href="http://rogermarjoribanks.info/wp-content/uploads/2023/07/REFLEX-ACTIII_Op2.jpg" rel="wp-prettyPhoto[2165]"><img class="aligncenter size-medium wp-image-2068" alt="REFLEX-ACTIII_Op2" src="http://rogermarjoribanks.info/wp-content/uploads/2023/07/REFLEX-ACTIII_Op2-300x227.jpg" width="300" height="227" /></a></p>
<p style="text-align: center;"><b><i>Figure 1:</i></b> <i>The Reflex ACT electronic core barrel orientation tool.  The tool is screwed on to the top of the core barrel. The gravity vector across the tool is measured by an accelerometer and recovered by means of a graphical LCD display. Image from the current Reflex website.</i></p>
<p><b><i>The second method</i></b>, and in my opinion a much more reliable one, is to <b>orient the core stub <span style="text-decoration: underline;">before it is drilled</span>. </b>The core stub is the fresh broken rock surface at the bottom of a drill hole which then becomes the top surface of the next drilled run. The match between the orientation tool and the core stub is made by a percussion or wax pencil mark, a shape template, or some combination of these techniques. The gravity vector at the moment of first contact between tool and core stub is recorded by built-in mechanical system (level bubbles) or by an electronic (accelerometer) system similar to that used in core-barrel orientation tools.</p>
<p>In the simplest (and oldest) tool, a narrow but heavy steel rod with a pointed tip (known as a spear) is allowed to slide down the rod string on the end of the wire line after a run of core has been extracted. In angle holes the weight of the spear keeps it in contact with the lower surface of the rods. The spear then impacts the core stub making a mark (percussion or wax pencil) on the <b>lower</b> edge of the stub. The technique is absurdly simple, but in the hands of an experienced driller (he has to control the speed of impact) it generally gave excellent results. Although seldom used nowadays, much legacy drill core was oriented by this technique. The technique fell out of fashion not because of poor results (quite the opposite) but because its use required a separate down hole procedure after each drill run – a procedure which could take 30 minutes or more depending on the depth of the hole.</p>
<p style="text-align: center;"> <a href="http://rogermarjoribanks.info/wp-content/uploads/2024/01/Down-hole-spear_Page_1.jpeg" rel="wp-prettyPhoto[2165]"><img class="aligncenter size-medium wp-image-2163" alt="Down hole spear_Page_1" src="http://rogermarjoribanks.info/wp-content/uploads/2024/01/Down-hole-spear_Page_1-300x198.jpeg" width="300" height="198" /></a></p>
<p style="text-align: center;"><b><i>Figure 2:</i></b><i> Operation of the simple down-hole spear core-stub orientation tool. It is lowered on the wire line after a barrel of core has been extracted to make a mark on the lower edge of the core stub. (Reproduced from Marjoribanks 2016, fig B2, p185).  Down-hole Spears were usually manufactured by drilling companies in their own workshops.</i></p>
<p>More sophisticated core-stub tools operate on the same basic principle as the spear but use a template to record the shape of the stub rather than (or perhaps as well as) making a mark on the core. The template can then be matched to the shape of the stub after it has been drilled and pulled from the ground.</p>
<p style="text-align: center;"> <a href="http://rogermarjoribanks.info/wp-content/uploads/2024/01/Craelius-core-orientation-tool.jpeg" rel="wp-prettyPhoto[2165]"><img class="aligncenter size-medium wp-image-2164" alt="Craelius core orientation tool" src="http://rogermarjoribanks.info/wp-content/uploads/2024/01/Craelius-core-orientation-tool-300x201.jpeg" width="300" height="201" /></a></p>
<p style="text-align: center;"><b><i>Figure 3</i></b><i>: Operation principle of the <b>Craelius</b> simple template core-stub orientation tool. The procedure required a separate operation between each drilled run. This tool is no longer available, but the figure serves to illustrate the basic idea behind core-stub orientation. (Reproduced from Marjoribanks 2016, fig B3 p186).</i></p>
<p style="text-align: center;"> <a href="http://rogermarjoribanks.info/wp-content/uploads/2013/09/EzyMark-Core-Orientation-tool.gif" rel="wp-prettyPhoto[2165]"><img class="aligncenter size-medium wp-image-226" alt="EzyMark Core Orientation tool" src="http://rogermarjoribanks.info/wp-content/uploads/2013/09/EzyMark-Core-Orientation-tool-300x225.gif" width="300" height="225" /></a></p>
<p style="text-align: center;"><b><i>Figure 4: </i></b><i>The pointy end of the EzyMark core-stub orientation tool. This tool fits inside the bottom of the core barrel. The pins and wax pencil record the shape of the core stub. Lockable level bubbles inside the tool record the gravity vector at moment of contact. This all-mechanical tool is no longer available, but a close copy is available from Well Force International (see below). The red plastic block (called an <strong>OriBlock</strong>) containing the pin template and down-gravity mark is extractable from the tool and is intended to be left in the core tray as a permanent orientation record and depth marker – as seen in photo. The OriBlock system (although they don&#8217;t use that term) is also available on the Reflex VertiOri and Well Force Front end tools (see below).</i></p>
<p style="text-align: center;"><i>The image was accessed in 2013 from the 2icAustralia company website</i><i>. </i></p>
<p style="text-align: center;"><b><i> <a href="http://rogermarjoribanks.info/wp-content/uploads/2023/11/REFLEX-VERTO-ORI.png" rel="wp-prettyPhoto[2165]"><img class="aligncenter size-medium wp-image-2142" alt="REFLEX VERTO ORI" src="http://rogermarjoribanks.info/wp-content/uploads/2023/11/REFLEX-VERTO-ORI-300x300.png" width="300" height="300" /></a></i></b></p>
<p><b><i>Figure 5</i></b>: The <b><i>Reflex Verti-Ori</i></b><i> core-stub template tool. It fits within the bottom of the core barrel. Steel pins and wax pencil record the shape of the core stub.  The gravity vector is determined by an inbuilt accelerometer and recovered by means of an electronic user interface.  </i></p>
<p>Core stub tools can fail if mud or disaggregated broken core obscures the core stub, but in my experience, their <span style="text-decoration: underline;">failure rate is less than that of core-barrel tools. But the really important difference between the two systems is</span> this: when core-stub systems fail, that failure is almost always obvious. In other words, results from <b><i>core-stub tools are</i></b> <b><i><span style="text-decoration: underline;">auditable at the point of core recovery</span></i> </b>and no time need be wasted marking up failed runs and making inaccurate measurements from it. And because the ways in which core-stub systems fail are different from the ways in which core-barrel systems fail, core-stub tools can produce accurate orientation in rocks where the core barrel tools fail.</p>
<p><b>Available Core Orientation tools (as of </b><b>October 2023)</b></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2024/12/CORE-ORIENTATION-TOOLS-TABLE-crop.jpeg" rel="wp-prettyPhoto[2165]"><img class="aligncenter size-medium wp-image-2305" alt="CORE ORIENTATION TOOLS TABLE crop" src="http://rogermarjoribanks.info/wp-content/uploads/2024/12/CORE-ORIENTATION-TOOLS-TABLE-crop-300x171.jpeg" width="300" height="171" /></a></p>
<p>The <span style="text-decoration: underline;"><b>core-barrel orientation systems</b></span> that I am aware of are:</p>
<p>BALLMARK was an all-mechanical system, first introduced in the late 1990s but no longer available.  The gravity vector was measured and recorded by the pressing of a steel ball into a soft aluminium disk at the moment of core barrel extraction. This tool (made in Orange, NSW) is the earliest core barrel orientation system that I am aware of. The company that made it may well have been the originator of the core barrel orientation as proxy for actual drill core idea.</p>
<p><i>REFLEX (their ACT™ systems </i><a href="https://reflexnow.com/product/reflex-act-iii"><i>LINK</i></a><i>). Reflex is a subsidiary of IMDEX Corporation</i></p>
<p><i>DEVICO (their DeviCore BCT™ and DeviHead™ systems) </i><a href="https://www.devico.com/product/devihead/"><i>LINK</i></a><i>. Devico is a subsidiary of IMDEX Corporation.</i></p>
<p><i>BOART-LONGYEAR (their Tru-Core™ system) </i><a href="https://www.boartlongyear.com/product/trucore-upix/"><i>LINK</i></a><i>.</i></p>
<p><i>AXIS MINING TECHNOLOGY (their Champ-Ori™ system) </i><a href="https://axisminetech.com/instrumentation/champ-ori"><i>LINK</i></a><i>. Axis is a subsidiary of the ORICA Group.</i></p>
<p><i> </i>There may be other available systems that I am unaware of. As far as I can tell from website description, in their basic method of operation, all the above tools are essentially clones of each other that offer slightly different electronic user interfaces.</p>
<p>The <b>core-stub orientation systems</b> that I am aware of are the Spear (figure 2) the Craelius (figure 3), the EzyMark<sup>TM   </sup>(figure 4), the Reflex VertiOri (figure 5) and the &#8220;<em><strong>front-end orientation tool</strong></em>&#8221; made by WELL FORCE INTERNATIONAL Ltd.</p>
<p>The down-hole <em><strong>Spear</strong> </em>system has fallen out of fashion for the reasons given above, although any drilling company could easily resurrect it.</p>
<p>The <em><strong>Craelius</strong> </em>system is no longer available.</p>
<p><em><strong>EzyMark</strong></em>  was an all-mechanical system, taken over in 2014 by the IMDEX subsidiary Reflex and then marketed the EzyMark as their Reflex Auditor<sup>TM</sup> System. The Auditor tool has now (as far as I can tell) been discontinued and replaced by the Reflex Verti-Ori™ system.</p>
<p>The <em><strong>Verti-Ori</strong> </em>system is a core-stub orientation tool with built in accelerometer and magnetometer that records the gravity vector and magnetic lines of force across the tool (<a href="https://reflexnow.com/product/reflex-verti-ori/">LINK</a>). By providing a magnetic vector, the tool can orient core from very steep-angled to vertical holes where gravity alone is unable to provide accurate orientation data (although EzyMark claimed accuracy for their tool in holes with inclinations of up to 88 degrees). I am informed that there are current availability problems with the Verti-Ori tool.</p>
<p>Well Force International&#8217;s  &#8220;<em><strong>Front End Mechanical Orientation Too</strong></em>l&#8221; (<a title="Well Force International" href="https://wellforceint.com/page/rental-equipment/core-orientation-tools" target="_blank">LINK</a>) is a core stub orientation tool which appears (from their website description) to be a very close copy of the now unavailable EzyMark tool of 2icaustralia.</p>
<p>I am indebted to Sarah Sulway (Imdex) and Olivier Cȏté-Mantha (Agnico Eagle Gold Mines) for some of the details in this post. All expressed opinions are of course mine.</p>
<p>You can read my previous (2013) post on this subject <a title="Core orientation Tools – Which are the best?" href="http://rogermarjoribanks.info/core-orientation-tools-best/">HERE</a></p>
<p><span style="text-decoration: underline;">Reference: </span></p>
<p>Marjoribanks R W 2010. <em>Geological Methods in Mineral Exploration and Mining.</em> Springer pp238. ISBN 978-3-540-74370-5.</p>
<p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/drill-core-orientation-tools/">Drill Core Orientation Tools &#8211; A Review</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></content:encoded>
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		<title>Stereonet validation of structural measurement in oriented drill core</title>
		<link>https://rogermarjoribanks.info/stereonet-validation-structural-measurement-oriented-drill-core/</link>
		<comments>https://rogermarjoribanks.info/stereonet-validation-structural-measurement-oriented-drill-core/#comments</comments>
		<pubDate>Mon, 23 Oct 2023 06:15:26 +0000</pubDate>
		<dc:creator><![CDATA[Roger Marjoribanks]]></dc:creator>
				<category><![CDATA[Diamond Drilling]]></category>
		<category><![CDATA[Sterenet Solutions in structural geology]]></category>
		<category><![CDATA[Structural Geology]]></category>

		<guid isPermaLink="false">http://rogermarjoribanks.info/?p=2105</guid>
		<description><![CDATA[<p>Summary Measuring the attitude of structures in drill core requires fully oriented core. But the tools for orienting core that are currently available to drillers often fail, especially with small core diameters (NQ or less) and where the rock has fissile surfaces within it. As these failures [&#8230;]</p><p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/stereonet-validation-structural-measurement-oriented-drill-core/">Stereonet validation of structural measurement in oriented drill core</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></description>
				<content:encoded><![CDATA[<p><span style="text-decoration: underline;"><strong>Summary</strong></span></p>
<p>Measuring the attitude of structures in drill core requires fully oriented core. But the tools for orienting core that are currently available to drillers often fail, especially with small core diameters (NQ or less) and where the rock has fissile surfaces within it. As these failures are not always apparent at point of core recovery, geologists can make incorrect measurements which are then entered to data bases and become input for computer programs.</p>
<p>This post details how these failures can occur and outlines stereographic techniques which enables these problems to be identified and quantified.</p>
<p><span style="text-decoration: underline;"><strong>How geologists measure Structure in Oriented Drill Core</strong></span></p>
<p><i> </i>The difference between oriented and non-oriented core is graphically illustrated below.</p>
<p style="text-align: center;"> <a href="http://rogermarjoribanks.info/wp-content/uploads/2015/10/NON-OR-Core-cartoon.jpg" rel="wp-prettyPhoto[2105]"><img class="aligncenter size-medium wp-image-828" alt="NON OR Core cartoon" src="http://rogermarjoribanks.info/wp-content/uploads/2015/10/NON-OR-Core-cartoon-300x252.jpg" width="300" height="252" /></a></p>
<p style="text-align: center;"><b><i>Figure 1</i></b><i>: Although the orientation of the core axis may be known, the core has rotated by an unknown amount around that axis. RM, 2015.</i></p>
<p align="center"><a href="http://rogermarjoribanks.info/wp-content/uploads/2015/10/OR-Core-cartoon.jpg" rel="wp-prettyPhoto[2105]"><img class="aligncenter size-medium wp-image-829" alt="OR Core cartoon" src="http://rogermarjoribanks.info/wp-content/uploads/2015/10/OR-Core-cartoon-244x300.jpg" width="244" height="300" /></a></p>
<p style="text-align: center;"><b><i>Figure 2</i></b><i>: The core is now fully oriented in 3D space. RM 2015</i></p>
<p>The most common type of geological structures measured in oriented drill core are planar (bedding, cleavage, veins, joints etc.). Assuming that the core has been correctly oriented (more on this assumption below), the best way to do this – one that produces fewest errors and creates the greatest geological understanding, is by using a geologists’ compass to directly measure structure in core pieces that have been set up in their original orientation by means of a <b><i>Core Orientation Frame </i></b>(for further discussion on this subject see my blog post <a title="Measuring Structures in Oriented Core" href="http://rogermarjoribanks.info/measuring-structures-oriented-core/">HERE</a>)<b><i>.</i></b> However, no doubt because it is quick, easy and involves minimal mental involvement, it is my experience that most geologists today measure and record the attitude of planes in oriented core by the <b><i>Internal Core Angles Method</i></b>. This technique involves measuring the angles which the structure makes with lines of known orientation in the core. These lines are the Core Axis (known from a down-hole survey) and the Bottom of Hole line (provided by the driller using a core orientation tool). These angles are:</p>
<p><b><i>Alpha</i></b> (<i>α</i>) &#8211; the acute angle (0°-90°) between the core axis (<i>CA</i>) and the long axis of the intersection ellipse (<i>E-E<sup>I</sup></i>) defined by the trace of the planar structure on the cylindrical core surface. See figure 3.</p>
<p><b><i>Beta</i></b> (<i>β</i>) &#8211; the radial angle (0°– 360°) measured in a <b><i>clockwise</i></b> direction about the core circumference from the Bottom of Hole Line (<i>BOH</i>) to the down-hole end of the intersection ellipse.  Clockwise is determined looking down the axis of the core. See figure 3. Note that in holes drilled below the horizontal (all holes drilled from the surface) the down direction points away from the hole collar. In holes drilled above the horizontal (some underground holes) the down direction will point towards the collar.</p>
<p>Alpha and beta measurements numbers are then subsequently crunched by computer, along with surveyed hole orientation data, to produce a standard strike and dip (or dip and dip direction) measurement, which can then be displayed as a stereonet plot, a histogram or as short lines of intersection on a drill section. It is also relatively easy to do this manually by using a stereonet (for details, see my blog post <a title="A stereonet solution for alpha beta angles in oriented drill core" href="http://rogermarjoribanks.info/stereonet-solution-alpha-beta-angles-oriented-drill-core/">HERE</a>)</p>
<p align="center"><a href="http://rogermarjoribanks.info/wp-content/uploads/2023/07/Stereonet-plots-alpha-beta-caculated-poles_Fig-1.jpeg" rel="wp-prettyPhoto[2105]"><img class="aligncenter size-medium wp-image-2057" alt="Stereonet plots alpha beta ca;culated poles_Fig 1" src="http://rogermarjoribanks.info/wp-content/uploads/2023/07/Stereonet-plots-alpha-beta-caculated-poles_Fig-1-300x230.jpeg" width="300" height="230" /></a></p>
<p><b><i> </i></b><b><i>Figure 3</i></b><i>: The angles which define the orientation of a planar structure in oriented drill core. Click for sharper image.</i></p>
<p><strong><span style="text-decoration: underline;">Potential Errors in Measuring Alpha and Beta</span></strong></p>
<p><span style="text-decoration: underline;"> </span>Measuring alpha is quick and easy using any standard protractor. The core does not need to be oriented. You do not need to know which end of the piece of core points up the hole and which points down. All values of alpha from 0 to 90 degrees can be measured with the same level of accuracy. Where the planar structure is well defined and reasonable care is taken by the geologist, measured alpha angles can usually be taken as accurate to at least +/- 2°. Alphas numbers are seldom a source of error in computer input.</p>
<p><b>Errors in measuring beta angles cause most of the errors when using the internal core angles method.</b></p>
<p>These errors occur in two areas:</p>
<p><i><span style="text-decoration: underline;">a. In identifying point E</span></i></p>
<p>The trace of any planar structure on cylindrical core is an ellipse. The long axis of the ellipse defines points <i>E</i> and <i>E <sup>I </sup></i>on the core surface, where <i>E</i> points down hole and <i>E <sup>I</sup></i> points up hole (see figure 3, above). <i>E</i> and <i>E <sup>I</sup></i> are recognised as inflection points (points of maximum curvature) on the trace of the plane. Where the alpha angle (the acute angle that <i>E-E <sup>I</sup></i> makes with the core axis) is low, the resulting intersection ellipse is elongate, with sharp inflection points easily defined by eye. However, with increasing alpha angle, the ellipse becomes fatter and tends towards circularity until, at alpha = <i>90°</i>, the &#8220;ellipse&#8221; is a circle with no definable axes.  As alpha increases, inflection points become broader and harder to accurately define and e<b><i>rrors in correctly locating point E increase.</i></b> Since measurement of the beta angle is dependent on being able to define point <i>E</i>, high alpha angles can lead to significant beta measurement error. For all alpha angles over 65°, I recommend that a core frame be used to measure structure in core rather than the alpha/beta method. But in my experience, very few geologists taking structural measurements in oriented core do this.</p>
<p><i><span style="text-decoration: underline;">b. In the BOH mark placed on the core by the driller.</span></i></p>
<p>There are a variety of tools currently available to drillers for orienting core. I describe these tools and how they work, as well as the strengths and weaknesses of the various systems in another post <a title="Drill Core Orientation Tools" href="http://rogermarjoribanks.info/drill-core-orientation-tools/">HERE</a>. The tools, although mostly reliable, are capable of producing grossly inaccurate results under some circumstances and it is not always easy for the driller or the geologist to know when this has occurred.</p>
<p>For the two reasons given above, mismeasurement of <b><i>beta is overwhelmingly the major source of error</i></b> when using the internal core angles method of measuring structure in oriented core.</p>
<p><span style="text-decoration-line: underline;"><strong>Stereonet Validation</strong></span></p>
<p>Once a set of measurements have been made on oriented drill core, there is a simple test to determine if inaccurate beta numbers are a significantly affecting your results (see Figure 6). Plot your dip and dip direction results from measured planes as poles on a stereonet. For a set of measurements through a volume of rock, the distribution of poles (see definition in section below) can enable deductions to be made about the accuracy of your measurements or whether or not they are made from approximately parallel surfaces. As a bonus, stereonet plotting of structural measurements can also enables useful geological interpretation of your results.</p>
<p>But first…</p>
<p><span style="text-decoration: underline;">1. A quick Primer on the Stereonet…</span></p>
<p><b> </b>A Stereonet is a pre-printed net of intersecting lines which allows the three-dimensional attitude of measured linear or planar rock structure to be shown as points on a two-dimensional graph. Linear structures (1D) such as fold axes, lineations or drill holes all plot as points on the net. Planar structures (2D) plot as great circles on the net, but their attitude can also be shown as a single point by plotting the line at right angles to that plane. This is called the <em><strong>Pole </strong></em>to the plane. A number of measurements of a planar structure that are plotted on the net as Poles is known as a <em><strong>Pole Figure</strong></em>.<br />
The scales of the net then offer a quick and easy way to provide approximate solutions to problems in 3D geometry, in much the same way as the scales on a slide ruler allow numerical solutions to math problems. Cheap pocket calculators, which first appeared in the 1970’s, have now replaced slide rulers. Computer software can solve math problems in 3D geometry too, but as a cheap, quick, low-tech and always available tool, the stereonet still has a useful role to play in this area. In structural studies, approximate solutions (i.e., to the nearest few degrees) are usually all that can be expected and all that is required.</p>
<p>But an equally important role of a stereonet plot is to provide a graphical way of showing the spatial <em><strong>distribution patterns</strong></em> of a series of orientation measurements taken through a volume of rock. Our brains are analog computers, fine-tuned for recognizing visual patterns (sometimes too fine-tuned). Patterns of plotted points on a stereonet can thus be a great aid in the interpretation of underlying geological processes. But these patterns need to be distinguished from merely coincidental aggregations of random numbers or from the effects of systemic problems with data collection and input. I will show examples of all these effects. Thus, stereonet plots of structural measurements can be a powerful tool in validation of data.</p>
<p><span style="text-decoration: underline;">2. Examples of stereonet Pole Figures for measured planes in outcrop or oriented drill core</span></p>
<p><span style="text-decoration: underline;"> </span><span style="text-decoration: underline;">Example 1</span></p>
<p>If your measurements of planar structure across an area or a through a volume of rocks are completely random, their stereonet pole figure might look something like that of <i>figure 4</i>, below, a plot constructed using a random number generator. You may see partial patterns of lines or circles or ellipses or clumping of points, but these are coincidental and have no meaning.</p>
<p>If you get a random distribution of points such as this from a real set of measurement, it most probably means that your measurements were collected across several distinct structural domains.</p>
<p><b><i>Solution</i></b>: Identify the different structural domains. Group your measurements by domain and plot each group separately.</p>
<p align="center"><a href="http://rogermarjoribanks.info/wp-content/uploads/2023/07/STEREONET-RANDOM-PLOTS-Fig-2.jpg" rel="wp-prettyPhoto[2105]"><img class="aligncenter size-medium wp-image-2058" alt="STEREONET RANDOM PLOTS Fig 2" src="http://rogermarjoribanks.info/wp-content/uploads/2023/07/STEREONET-RANDOM-PLOTS-Fig-2-290x300.jpg" width="290" height="300" /></a></p>
<p style="text-align: center;"><b><i>Figure 4</i></b><i>: A stereonet plot of poles to bedding created using a random number generator. Any patterns or concentrations of points that a visual inspection might suggest are purely coincidental and have no real world meaning. If this was a real set of measurements across an area, then the most probable interpretation would be that the measurements were taken across several distinct structural domains.</i></p>
<p><i></i><span style="text-decoration-line: underline;">Example 2</span></p>
<p>If your measurements are accurately made from a set of parallel, or approximately parallel, planar structures, then the majority of points on a pole figure will form a tight cluster, as shown in figure 5. If the measurements were from oriented drill core, then the centre of the pole cluster will lie at an angle of <i>90-α°</i> to the plot of the core axis.</p>
<p><b><i>Q:</i></b> What is the logic behind this number <i>90-α°?</i></p>
<p><b><i>A:</i></b> This is a plot of <b><i>poles</i></b> to planes measured in oriented drill core. If you refer to <i>figure 3,</i> you will see the poles to these planes lie at <i>90-α°</i> to the core axis (CA).</p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2023/07/Stereonet-plots-alpha-beta-caculated-poles-Fig-3.jpeg" rel="wp-prettyPhoto[2105]"><img class="aligncenter size-medium wp-image-2059" alt="Stereonet plots alpha beta ca;culated poles Fig 3" src="http://rogermarjoribanks.info/wp-content/uploads/2023/07/Stereonet-plots-alpha-beta-caculated-poles-Fig-3-283x300.jpeg" width="283" height="300" /></a></p>
<p align="center"><b><i> </i></b><b><i>Figure 5</i></b><i>: Poles to planes measured in oriented drill core by the internal core angles method. The orientation of the core axis is shown as a red circle. The results indicate the planes are approximately parallel with only minor, acceptable, error in both alpha and beta measurements. The centre of the pole cluster lies at 90-α° to the core axis. Click for a sharper image.</i></p>
<p><i> </i><span style="text-decoration: underline;">Example 3</span></p>
<p>If you are plotting measurements from oriented drill core using the internal core angles method (alpha/beta), your measurements can be assumed accurate as regards to the alpha number but may be subject to random error in beta measurement (a not uncommon occurrence, especially when using electronic core-barrel orientation tools, see <a title="Drill Core Orientation Tools" href="http://rogermarjoribanks.info/drill-core-orientation-tools/">HERE</a>). If this is the case. the pole figure plot will show a partial or complete distribution about a <b><i>small circle</i></b> at <i>90-α°</i> to the core axis. There is no known geological process which will produce such a pattern. This pattern is shown in <i>figure 6, below.</i></p>
<p><b><i>Solution</i></b>: Try using a core-stub orientation system.</p>
<p align="center"><a href="http://rogermarjoribanks.info/wp-content/uploads/2023/07/Stereonet-plots-alpha-beta-caculated-poles-Fig-4.jpeg" rel="wp-prettyPhoto[2105]"><img class="aligncenter size-medium wp-image-2060" alt="Stereonet plots alpha beta ca;culated poles Fig 4" src="http://rogermarjoribanks.info/wp-content/uploads/2023/07/Stereonet-plots-alpha-beta-caculated-poles-Fig-4-282x300.jpeg" width="282" height="300" /></a></p>
<p style="text-align: center;"><b><i>Figure 6:</i></b> <i>Poles to a set of planes measured in oriented drill core by the internal core angles method. The consistency of alpha indicates accurate measurement on planes that are approximately parallel. However, the scatter of points around a small circle at 90-alpha degrees to the core axis indicates that large random errors have been made in the measurement of beta.  Click for a sharper image.</i></p>
<p><span style="text-decoration: underline;">Example 4</span></p>
<p>If the Pole Figure for of large number of orientation measurements taken from scattered surface outcrop or oriented drill core shows distribution about a <b><i>great circle</i></b> on the net (<i>figure 7)</i>, we can draw several conclusions.</p>
<p><span style="font-style: italic;">The results indicate accurate measurement of a set of approximately parallel surfaces.</span></p>
<p><span style="font-style: italic;">Although the measurements show a wide range of orientation, these are distributed in a systematic way that shows they were taken from a geologically coherent structural domain &#8211; namely&#8230;</span></p>
<p><span style="font-style: italic;">The measured planes have been affected by a cylindrical fold, or a set of parallel cylindrical folds (as illustrated by the insert on figure 7).</span></p>
<p><span style="font-style: italic;">A line at 90° to the great circle distribution (which plots as a point in the opposite segment of the net) represents </span><i>the trend and plunge of the fold axis or axes that are affecting the surfaces</i><span style="font-style: italic;">. This point is conventionally labelled </span><b style="font-style: italic;"><i>pi (π).</i></b></p>
<p><span style="font-style: italic;">The two weak bedding-plane maxima which can be seen on the great circle of figure 7 can be interpreted as the relatively planar limbs of the fold or folds. This is because random measurement across a volume of folded rocks will sample more examples of extensive fold limbs than restricted fold hinges.</span><i> </i><b style="font-style: italic;"> </b><span style="font-style: italic;">The two maxima</span><b style="font-style: italic;"> </b><span style="font-style: italic;">further indicates that the fold or folds tend towards </span><b style="font-style: italic;"><i>similar</i></b><i> </i><span style="font-style: italic;">rather than </span><b style="font-style: italic;"><i>concentric</i></b><span style="font-style: italic;"> in style.</span></p>
<p align="center"><a href="http://rogermarjoribanks.info/wp-content/uploads/2023/07/Stereonet-plots-alpha-beta-caculated-poles-Fig-5.jpeg" rel="wp-prettyPhoto[2105]"><img class="aligncenter size-medium wp-image-2061" alt="Stereonet plots alpha beta ca;culated poles Fig 5" src="http://rogermarjoribanks.info/wp-content/uploads/2023/07/Stereonet-plots-alpha-beta-caculated-poles-Fig-5-287x300.jpeg" width="287" height="300" /></a></p>
<p style="text-align: center;"><b><i>Figure 7</i></b><i>: Poles (n=50) to a set of bedding planes measured across scattered surface outcrop or oriented drill core. The great circle distribution indicates folding about a cylindrical fold, or a set of parallel such folds. Click for a sharper image.</i></p>
<div>This essay was first posted October 2023 and modified January 2024.</div>
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<p><a title="" href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/STEREONET%20TESTS%20FOR%20STRUCTURE%20MEASUREMENTS%20IN%20DRILL%20CORE/Stereonet%20Validation%20ver%202%20NO%20FIGURES.docx#_ftnref1"> </a></p>
<p><i> </i></p>
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<p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/stereonet-validation-structural-measurement-oriented-drill-core/">Stereonet validation of structural measurement in oriented drill core</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></content:encoded>
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		<title>Marjex Core Frame Instructions pdf</title>
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		<pubDate>Mon, 02 Jan 2023 03:40:33 +0000</pubDate>
		<dc:creator><![CDATA[Roger Marjoribanks]]></dc:creator>
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		<description><![CDATA[<p>Please click on link below. Core Frame Instruction Booklet  </p><p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/marjex-core-frame-instructions-pdf/">Marjex Core Frame Instructions pdf</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></description>
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		<title>Geologists Wobble and the fractal nature of rocks</title>
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		<dc:creator><![CDATA[Roger Marjoribanks]]></dc:creator>
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		<description><![CDATA[<p>  Here’s the thing You know what Australia looks like. You would recognise it on a map: its general shape, the peninsulas, the great gulfs. You could draw it from memory, probably, and if you did, it might look something like this: Figure 1 That’s a pretty [&#8230;]</p><p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/geologists-wobble/">Geologists Wobble and the fractal nature of rocks</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></description>
				<content:encoded><![CDATA[<p align="center"><b> </b></p>
<p><b>Here’s the thing</b></p>
<p>You know what Australia looks like. You would recognise it on a map: its general shape, the peninsulas, the great gulfs. You could draw it from memory, probably, and if you did, it might look something like this:</p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/11/Australia-map-Euclidean.jpg" rel="wp-prettyPhoto[1609]"><img class="aligncenter size-medium wp-image-1602" alt="Australia map Euclidean" src="http://rogermarjoribanks.info/wp-content/uploads/2021/11/Australia-map-Euclidean-300x239.jpg" width="300" height="239" /></a><span style="color: #0000ff;"><em>Figure 1</em></span></p>
<p>That’s a pretty good effort and would certainly serve to identify the island continent, but it does not look a bit like a real map. No one, for example, would ever think that you had painstakingly traced this outline from an atlas. What you have drawn is a cartoon. Actual coastlines are seldom, if ever, composed of straight lines. Actual continental shapes are not irregular polygons. With some notable exceptions (crystals for example, some biological structures) few things in nature are defined by the straight lines, planes and regular shapes of classical Euclidean geometry.</p>
<p>Now try drawing the same map again, but this time employing an irregular wriggly line to outline the coast and to create a multitude of completely imaginary small-scale bays and headlands. Here it is:</p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/11/Australia-map-Fractal.jpg" rel="wp-prettyPhoto[1609]"><img class="aligncenter size-medium wp-image-1603" alt="Australia map Fractal" src="http://rogermarjoribanks.info/wp-content/uploads/2021/11/Australia-map-Fractal-300x240.jpg" width="300" height="240" /></a><span style="color: #0000ff;"><em>Figure 2</em></span></p>
<p>This looks much more realistic. Why is that? Because that’s what coastlines look like (especially rocky ones).</p>
<p><b>Geographers Wobble</b></p>
<p>What you have done in figure 2 is often referred to as <b><i>“geographers’ wobble”</i></b>, and not usually as a compliment. However, Geographers’ wobble is not artistic license, it is not decoration to make a map look pretty or interesting in the style of old-time cartographers (<em>here be dragons)</em>. In the absence of a finely-detailed data base, the geographer has chosen the correct type of irregular line to use in outlining a coast – and that is not a straight line. It is a <b><i>fractal </i></b>line. The geographer chose to use a line with the correct  <b><i>fractal dimension</i></b> for his purpose.</p>
<p>More on fractals and fractal dimensions later.</p>
<p><b>Geologists Wobble too</b></p>
<p>When making a detailed outcrop map, geologists often use the same technique &#8211; one could call it <b><i>“geologists’ wobble” <span style="color: #0000ff;">(1)</span></i></b></p>
<p style="text-align: center;"><i><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/11/Geologist-wobble-2.jpg" rel="wp-prettyPhoto[1609]"><img class="aligncenter size-medium wp-image-1645" alt="Geologist wobble 2" src="http://rogermarjoribanks.info/wp-content/uploads/2021/11/Geologist-wobble-2-300x293.jpg" width="300" height="293" /></a></i></p>
<p style="text-align: center;"><em><span style="color: #0000ff;">Figure 3</span></em></p>
<p>Consider the map below, originally compiled at 1:1000 scale (the survey pegs are 40m apart). It is a portion (one of 12 field sheets) of a geological map that aims to show all outcrop of more than 1-2 m across within a mineralised prospect area.</p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/11/Geology-outcrop-map.jpg" rel="wp-prettyPhoto[1609]"><img class="aligncenter size-medium wp-image-1604" alt="Geology outcrop map" src="http://rogermarjoribanks.info/wp-content/uploads/2021/11/Geology-outcrop-map-300x294.jpg" width="300" height="294" /></a><span style="color: #0000ff;"><em>Figure 4 An outcrop geology map a 1:1000 scale</em></span></p>
<p>It would be impractical to do an exact point by point survey of each of the outcrops in the area. Rather the geologist compiling the map surveyed a few points on each outcrop by triangulating on survey markers, then took compass bearings and counted paces as he walked around it, sketching in the details. Note that the style of line used to outline each outcrop is dependent upon the rock type. In this area, shale units (sh) are exposed as short, interconnected runs poking through the surface rubble: the map outline of shale outcrop thus has a very complex shape with many large-scale and small-scale re-entrants. The quartzite (qtzite) unit occurs in long, parallel-sided, strike ridges broken by weathering along an orthogonal jointing: by comparison with the shale, its map outline is simpler and more geometric in shape. The simplest outcrop shapes of all are those of the granite (gr) which has rounded outlines resulting from its massive nature and the effects of spheroidal (onion skin) weathering.</p>
<p>Examples – extracted from the map &#8211; of these different line styles are shown below. The outline of each unit has a different  <em><strong>fractal dimension</strong></em> which the geologist attempted to capture with an appropriate type of line.</p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/11/Three-outcrop-shapes.jpg" rel="wp-prettyPhoto[1609]"><img class="aligncenter size-medium wp-image-1605" alt="Three outcrop shapes" src="http://rogermarjoribanks.info/wp-content/uploads/2021/11/Three-outcrop-shapes-300x147.jpg" width="300" height="147" /></a></p>
<p style="text-align: center;"> <span style="color: #0000ff;">Figure 5 Fractal shapes of rock outcrops in figure 4</span></p>
<p><b>Fractals and Fractal Dimensions</b></p>
<p>The idea of a fractal dimension was developed by French-American mathematician Benoit B Mandelbrot in the 1960s and 70s as a way of quantifying the degree of complexity of folded lines and sheets. The idea became widely disseminated beyond his specialist field with the publication of his beautifully illustrated best-selling book <em>The fractal geometry of Nature </em>(1983: W H Freeman, San Francisco, 468pp).</p>
<p>In classical Euclidean geometry, a line is a one-dimensional entity (1-D) with a length but neither width nor thickness. It retains its 1-D identity no matter how complexly it is folded. Mandelbrot reasoned that if a line were sufficiently folded within the plane of a 2-D surface then it would begin to fill that surface and so approach the dimensions of the sheet within which it is embedded. In other words, depending on the degree of complexity of the folding, it will have a dimension somewhere between 1 and 2. He called this the <b><i>fractal dimension</i></b> and the line itself a <b><i>fractal</i></b> object.</p>
<p>Similarly, a 1-D or a 2-D object (think of a length of thread or sheet of paper, ignoring their thickness), folded within 3-D space, will have a fractal dimension somewhere between 2 and 3<a title="" href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/GEOLOGICAL%20WOBBLE/Geologist%20Wobbles.docx#_ftn1">[2]</a>.</p>
<p>Fractal lines and shapes are the characteristic of natural objects. Trees, topography, turbulence, coastlines and cauliflowers, snowflakes and stock markets, protein molecules, distribution of galaxies, folded sediments, the outlines of rock outcrop.</p>
<p>Mandelbrot realised that fractal shapes can be quantified by comparing the detail of the object that is apparent when viewed at different scales.</p>
<p>Take the outline of a coast &#8211; a typical fractal line. How long is this line? Obviously, it will be much longer if we measure it with a 1-meter-long ruler than if we measure it with a 100-meter-long ruler. How much longer? That will depend upon how wriggly and convoluted the coastline at whatever level of detail we view it, and that depends on its fractal dimension. If coastlines had regular Euclidean shapes &#8211; segments of polygons, circles or ellipses, for example &#8211; we could step off its length with dividers of shorter and shorter openings and our succession of results would progressively converge on a finite answer. But for a fractal line there is no convergence: the coastline has an infinite length! The reason for this <a title="The coastline paradox" href="http://en.wikipedia.org/wiki/coastline-paradox" target="_blank">paradoxical result</a> is that the fractal dimension you can measure will be approximately the same no matter how far you zoom down into the detail of the line.</p>
<p>Mandelbrot defined Fractal Dimension (FD) as <b><i>the statistical ratio of the change in detail with the change in scale</i></b>.  It matters little whether the FD ratio of a rocky coast is measured on a 1,000,000 scale map, on the bays and headlands of a 100,000 scale map or on a map of a rock pool on the shore at 1:1 scale. At levels of detail that range through several orders of magnitude, the Fractal Dimension of a rocky coast will be approximately the same.  That is not to say that, if you overlaid a tracing of 100 km of coastline over a tracing of 1 km of coastline, there would be a neat match, but the lines would <em>look</em> the same: they would have the same <em>style</em>.  Without further information, it would be impossible, from the lines alone, to say at what level of detail it was being viewed.  That is what is meant by saying that the <em><strong>Fractal Dimension is scale invariant. </strong><strong>Fractal shapes have scale-invariant self-similarity.</strong></em></p>
<p>The map of the rock pool is a fractal for the map of the bay in which it occurs, and the map of the bay is itself a fractal for the map of the whole rocky coastline. Similarly, small folds on the limbs of large folds can be fractals for the large fold, which may of course be a fractal for an even larger fold. This useful relationship has been known to geologists for almost 130 years, the first example of the practical use of what we now know as fractal geometry. When I was a geology student in the 1960s we were taught to call this <em><strong>&#8220;Pumpelly&#8217;s Rule&#8221;</strong></em> after USGS geologist Raphael Pumpelly (he of the eponymous mineral) who first described these relationships in 1894<span style="color: #0000ff;">(4)</span>.</p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2014/01/Raphael-Pumpelly.jpg" rel="wp-prettyPhoto[1609]"><img class="aligncenter size-medium wp-image-519" alt="Raphael Pumpelly" src="http://rogermarjoribanks.info/wp-content/uploads/2014/01/Raphael-Pumpelly-207x300.jpg" width="207" height="300" /></a><span style="color: #0000ff;"><em>Figure 6: Raphael Pumpelly, 1837-1923. Geology &amp; Mining Professor Harvard University (1866-75). Founding Member of the United States Geological Survey (1879), Director of the USGS (1884). President of the Geological Society of America (1905)</em></span></p>
<p>In Nature, fractal shapes are only ever self-similar through a limited range of scales. There are practical limits. Patterns are never repeated endlessly to infinity. One cannot strictly say (parodying Jonathon Swift) that:</p>
<p style="text-align: center;"><em>So, Geologists observe, a fold,</em></p>
<p style="text-align: center;"><em>Hath smaller folds that on limbs prey, </em></p>
<p style="text-align: center;"><em>And these have smaller yet to parasite &#8216;em,</em></p>
<p style="text-align: center;">And so proceed ad infinitum.</p>
<p style="text-align: left;">However, fractal shapes and patterns created by computer through the iteration of simple non-linear algorithms can have perfect self-similarity through an infinity of scales.  The best-known example of a computer- generated set of fractals is the famous <a title="Mandelbrot Set" href="http://en.wikipedia.org/mandelbrot-set" target="_blank">Mandelbrot Set</a>.</p>
<p>The idea of the scale invariance of fractal shapes has great relevance in structural geology, where the structure of large regions (which cannot be directly observed) has to be deduced from observation of small outcrops in the field. This topic is explored in an earlier post (<span style="color: #ff0000;"><a title="Vergences and Fractals" href="http://rogermarjoribanks.info/vergences-fractals/"><span style="color: #ff0000;">LINK</span></a></span>).</p>
<p><b>The box counting method for calculating Fractal Dimension</b></p>
<p>I understand that some GIS software packages, such as <strong>ArcGIS</strong>, provide sub-programs for calculating fractal dimensions. However, it can be done manually. Mandelbrot&#8217;s insight that the Fractal dimension is the<em> statistical</em> <i>ratio of change in detail with the change in scale</i> enabled him to provide the following formula for calculating the FD of a folded line embedded in 2-D space:</p>
<p align="center"><b><i>C<sup>D</sup> = N/M</i></b></p>
<p style="text-align: left;" align="center"><b><i></i></b>Where the scale is a unit grid in 2-D space, and:</p>
<p><b><i> C</i></b>  is the scale reduction multiple              <b><i>D </i></b> is the fractal dimension</p>
<p><b><i>N  </i></b>is<b><i> </i></b>the number of squares occupied by the fractal in the high-resolution 2-D grid.</p>
<p><b><i>M</i></b>  is the number of squares occupied by the fractal in the low-resolution 2-D grid</p>
<p><em><strong>Figure 7</strong></em> below illustrates the application of the formula to calculate the fractal dimension of a line. To demonstrate the technique and for simplicity of illustration, in the examples below I have chosen a low reduction multiple (C) of 2.  However, it should be noted that the larger the value of <b><i>C</i></b>, the more accurate and precise will be the calculated value of the Fractal Dimension (<b><i>D)</i></b>.</p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/11/Calc-FD-of-Sheet-and-straight-line.jpg" rel="wp-prettyPhoto[1609]"> </a></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/11/Calculating-fractal-dimension-by-box-counting.jpg" rel="wp-prettyPhoto[1609]"><img class="aligncenter size-medium wp-image-1635" alt="Calculating fractal dimension by box counting" src="http://rogermarjoribanks.info/wp-content/uploads/2021/11/Calculating-fractal-dimension-by-box-counting-189x300.jpg" width="189" height="300" /></a></p>
<p style="text-align: center;"><span style="color: #0000ff;"><em>Figure 7 Calculating the fractal dimension of a line (click for a larger, sharper image)</em></span></p>
<p><b>S</b><b>ome numbers</b></p>
<p>A typical rocky coastline has a fractal dimension (FD) of 1.2 &#8211; 1.3. Low-lying coasts of sediment accumulation (the 80-mile beach, for example) have lower fractal dimensions. An FD of around 1.2 was instinctively used in drawing the map of Australia shown in figure 2. That is an exaggeration as the actual coastline, averaged over the whole continent, has been recently measured at 1.114 (<span style="color: #ff0000;"><a href="http://doi.org/10.1038/s41598-021-85405-0"><span style="color: #ff0000;">LINK</span></a></span>)</p>
<p>The FD of the west coast of Britain has been calculated as 1.25 (<a title="How long is the coast of Britain?" href="http://doi.org/10.1126/science.156.3775.636" target="_blank"><span style="color: #ff0000;">LINK</span></a>) <em><span style="color: #0000ff;">(3)</span></em></p>
<p>The FD of the coast of Norway -  a particularly rugged and fiord-indented coastline -  has been calculated (by <span style="color: #ff0000;"><a title="Slartibartfast" href="https://en.wikipedia.org/wiki/slartibartfast" target="_blank"><span style="color: #ff0000;">Slartybartfast</span></a></span>, among others (<a href="http://doi.org/10.1590/s0103-97331998000200007" target="_blank">LINK</a> from p 139)) at 1.52.</p>
<p>The outline of the granite outcrop in figure 5 has an approximate FD of 1.1</p>
<p>The outline of the quartzite outcrop in figure 5 has an approximate FD of 1.2</p>
<p>The outline of the shale outcrop in figure 5 has an approximate FD of 1.3</p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/11/The-coast-of-Norway.jpg" rel="wp-prettyPhoto[1609]"><img class="aligncenter size-medium wp-image-1642" alt="The coast of Norway" src="http://rogermarjoribanks.info/wp-content/uploads/2021/11/The-coast-of-Norway-207x300.jpg" width="207" height="300" /></a></p>
<p style="text-align: center;"><em><span style="color: #0000ff;">Figure 8 The coastline of southwest Norway. Fractal Dimension 1.52</span></em></p>
<p><b>Conclusion</b></p>
<p>The terms Geographers’ Wobble and Geologists’ Wobble may sound unscientific and uncomplimentary, but they describe procedures based on an instinctive understanding that natural objects are fractal and cannot be described graphically using the lines and shapes of classical Euclidean geometry. Fractal lines provide a more accurate representation of reality.</p>
<p>Following Mandelbrot, that reality has come to be known as <em><strong>Chaos</strong> &#8211; t</em>he expression of non-linear natural processes. The descriptors of Chaos are fractals, fractal dimensions and scale-invariant self-similarity.</p>
<div></div>
<hr align="left" size="1" width="33%" />
<div>
<p><span style="color: #0000ff;">(1)</span> See footnote 22, p46 in Marjoribanks R W: <em>Geological methods in mineral exploration and mining</em>. Springer 238pp.</p>
<p><a title="" href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/GEOLOGICAL%20WOBBLE/Geologist%20Wobbles.docx#_ftnref1">[2]</a> The fractal object also assumes the physical properties of the higher dimension. As every schoolboy knows, a pellet of scrunched up paper (<i>FD of, say, 2.8</i>), flicked with a ruler onto the neck of a classmate in front, will always produce a satisfying reaction.</p>
<p><span style="color: #0000ff;">(3)</span> Mandelbrot, BB 1967: <em>How long is the coast of Britain?</em> <em>Statistical self-similarity and fractal dimension</em>. <strong>Science 156, Issue 3775, pp 636-638</strong>  DOI.10.1126/Science.156.3775.636</p>
<p><span style="color: #0000ff;">(4)</span> Pumpelly R, Wolff JE &amp; Dale TN: 1894. <em>The Geology of the Green Mountains.</em> USGS Memoir 23, 157p.</p>
<p><span style="color: #0000ff;"> </span></p>
<p>All comments are welcome</p>
</div>
<p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/geologists-wobble/">Geologists Wobble and the fractal nature of rocks</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></content:encoded>
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		<title>The definition of a geological fault and why most dictionaries get it wrong.</title>
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		<pubDate>Fri, 09 Apr 2021 02:36:13 +0000</pubDate>
		<dc:creator><![CDATA[Roger Marjoribanks]]></dc:creator>
				<category><![CDATA[Geological Mapping]]></category>
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		<description><![CDATA[<p>The definition of a geological fault, and why most dictionaries get it wrong One of the most important structures for any mineral explorer to understand are faults. What, exactly, is a fault? To geologists the answer seems so obvious that few of them (even the writers of many [&#8230;]</p><p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/geological-fault/">The definition of a geological fault and why most dictionaries get it wrong.</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></description>
				<content:encoded><![CDATA[<p align="center"><b>The definition of a geological fault, and why most dictionaries get it wrong</b></p>
<p align="center"><span style="color: #0000ff;"><i>One of the most important structures for any mineral explorer to understand are faults.</i></span></p>
<p>What, exactly, is a fault? To geologists the answer seems so obvious that few of them (even the writers of many geology textbooks or dictionaries) ever bother with a definition. And when they do, they very often get it wrong. When thinking of a fault, geologists usually have in mind a planar dislocation or fracture where the rocks on either side have slid past each other with the displacement across the fault lying in the plane of the fault itself.  Geological dictionaries and structural geology textbooks (or at least the random selection I have read) often reflect this same misunderstanding and offer a definition specifying a direction of movement along the plane of the fault.  They also frequently describe faults are &#8220;brittle fractures&#8221;, and add that the observed fault movement must always be &#8220;observable&#8221;.</p>
<p>The authoritative <em>Glossary of Geology</em><a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftn1">[1]</a> with 36,000 defined terms defines a fault as:</p>
<p style="text-align: center;"><span style="color: #0000ff;">A <em>fracture</em>, or zone of <em>fractures,</em> <em>along</em> which there has been displacement of the sides relative to one another </span><span style="color: #0000ff;"><em>parallel</em> to the <em>fracture</em>. </span><i>(my italics)</i></p>
<p><em>The Oxford Dictionary of Geology and Earth Sciences</em><a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftn2">[2]</a> offers this:</p>
<p style="text-align: center;"><span style="color: #0000ff;">Approximately plane surface of <em>fracture</em> caused by <em>brittle</em> failure and <em>along</em> which <em>observable</em> relative displacement has occurred between adjacent roc</span><span style="color: #0000ff;">k</span><em><span style="color: #0000ff;">s.</span></em> (my italics)</p>
<p><em>Hobbs, Means &amp; Williams</em> in their well-known (and otherwise impeccable) structural geology textbook<a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftn3">[3]</a> provide this definition:</p>
<p style="text-align: center;"><span style="color: #0000ff;">A <span style="color: #000000;">(<em>fault </em></span></span><span style="color: #0000ff;"><span style="color: #000000;"><em>is a</em>)</span> planar discontinuity between blocks of rock that have been displaced past one another in a </span><span style="color: #0000ff;">direction <em>parallel</em> to the discontinuity.</span><em><span style="color: #0000ff;"> </span></em>(my italics)</p>
<p style="text-align: left;">Neville J Price, in his 1964 textbook on rock mechanics <em><span style="color: #0000ff;">(4)</span></em>, describes a fault as:</p>
<p style="text-align: center;"><span style="color: #0000ff;">A fault is a <em>fracture</em> which exhibits <em>obvious</em> signs of differential movement on either side of the plane.&#8221; <span style="color: #000000;">(my italics)</span></span></p>
<p style="text-align: center;">and adds&#8230;</p>
<p style="text-align: center;"><span style="color: #0000ff;"> Joints are cracks and fractures in rock along which there has been extremely little <em>or no movement</em>. <span style="color: #000000;">(my italics)</span></span></p>
<p>From that universal source <em>Wikipedia </em><a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftn4">[5]</a>:</p>
<p style="text-align: center;"><span style="color: #0000ff;">A fault is a planar <em>fracture</em> or discontinuity in a volume of rock across which there has been <em>significant</em> displacement<em> </em><span style="color: #000000;">(my italics)</span></span></p>
<p style="text-align: left;">Or this one, perhaps the worst of all, which I found on the internet <span style="color: #ff0000;"><a href="http://www.files.ethz.ch/structuralgeology/JPB/files/English/3faults.pdf" target="_blank"><span style="color: #ff0000;">here</span></a></span>:</p>
<p style="text-align: center;"><span style="color: #0000ff;"> if rocks on both sides of the <span style="color: #000000;">(fault)</span> plane have moved relative to each other, <em>parallel</em> to the plane of the fault (faults are <em>shear</em> <em>fractures</em>)&#8230;Joints, if there is <em>no component of displacement parallel</em> to the <span style="color: #000000;">(fault)</span> plane (joints are extension fractures). <span style="color: #000000;">(my italics)</span></span></p>
<p style="text-align: left;">Finally, my last example, and probably the best (although still flawed) from <span style="color: #ff0000;"><a href="http://WWW.BRITANICA.COM" target="_blank"><span style="color: #ff0000;">www.brittanica.com</span></a></span> :</p>
<p align="center"><span style="color: #0000ff;">Fault in geology, a planar or gently curved <em>fracture</em> in rocks of the Earth&#8217;s crust, where compressional or tensional stresses cause relative displacement of the rocks on either side of the <em>fracture</em>.</span></p>
<p style="text-align: left;"><strong>Why these definitions are wrong</strong></p>
<p style="text-align: left;"><span style="text-align: left;">In the quotes above I have placed the words I find problematic in italics. They are the words that define fault movement as taking place parallel to (or along) the fault plane. They are the words that require the fault mechanism to be brittle (or a &#8220;fracture&#8221;, which implies the same thing). They are the words that require fault movement to be greater than some vaguely-defined (&#8220;obvious&#8221;, &#8220;significant&#8221;, &#8220;observable&#8221;) and arbitrary minimum value</span>.</p>
<p style="text-align: left;"><span style="text-align: left;">If all the criteria of these definitions were strictly applied, they </span>would exclude almost all structures that geologists normally understand by the term fault. They would make it impossible to understand and interpret the multitude of second order structures that occur <em>within</em> a fault<i style="text-align: left;">, </i>and provide a means of interpreting its history and movement direction. But more importantly, from the point of view of the exploration geologist, these definitions make it impossible to fully understand and predict the emplacement of epigenetic mineral veins.</p>
<p>A fault is a planar zone of rock failure across which relative movement has taken place. The mechanism of that failure may be brittle or ductile. Most faults formed through a combination of both mechanisms.</p>
<p>Any section across a fault, such as an outcrop face, a geological map, or section, is only capable of showing the <i>resolved component of movement on that section</i>. This means that if a pre-fault structure such as a bedding plane is displaced across the fault trace, then, in the general case, the displacement you see is apparent and relates only to marker beds of that orientation. Other beds, with a different orientation, may show different amounts, or even different senses, of apparent displacement. Some displaced beds may show no apparent movement at all on the section on which they are viewed.</p>
<p>The above discussion on apparent displacement applies where the relative movement of the rock masses on either side of the fault have moved <i>laterally past each other along the fault plane</i>. As I have shown, many definitions of geological faults either explicitly or implicitly assume this. But rock masses may also move towards each other or away from each other across the fault plane. This creates a whole new set of geometries.</p>
<p>An accurate definition of a fault must avoid any assumptions about direction of fault movement or the mechanism of fault formation.</p>
<p><b>Discussion on Fault Movement</b></p>
<p><b><i>Fault Movement Vectors (FMVs) </i></b>define the relative movement that has taken place between the rock masses on either side of a fault at the end of any given fault movement.  <i>FMVs are the direction of movement of any <b>point</b> on one side of the  fault with respect to any <b>point</b> on the other side</i>. FMVs can be shown as two parallel arrows pointing in the direction of relative movement – one arrow for the rocks on either side of the fault. These arrows may point towards each other. They may point away from each other. They may lie <em>at any angle</em> to the plane of the fault.  Any plane that includes the these arrows is the plane of the FMVs.</p>
<p>If the plane of the FMVs is parallel to the fault plane, then the rock masses on either side of the fault must have moved laterally past each other and the deformation mechanism is that of simple shear If the arrows are normal (i.e. at right angles) to the fault, then the type of displacement across the fault is known as pure shear.  Pure shear may be compressional or extensional. In compression (where the FMVs point towards each other) the rocks on either side of the fault have moved towards each other and there has been a necessary <em>reduction</em> in the volume of the affected rocks. In extension (where the FMVs point away from each other) the rock masses on either side of the fault have moved away from each other, and there has been an<em> increase</em> in the volume of the affected rocks.</p>
<p>Extensional faults are of vital interest to the exploration geologist because the extension provides the space, and the creation of the space the  driving force, for emplacement of epigenetic mineral veins &#8211; an important source of ore.</p>
<p>A more detailed discussion on the dynamics of fault formation can be found in my earlier blog post <a title="The movement of faults" href="http://rogermarjoribanks.info/movement-faults-2/" target="_blank">here</a>, entitled: <em>The movement of faults.</em></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2020/09/Movement-of-faults-fig-1-2.jpg" rel="wp-prettyPhoto[1340]"><img class="aligncenter size-medium wp-image-1123" alt="Movement of faults fig 1 (2)" src="http://rogermarjoribanks.info/wp-content/uploads/2020/09/Movement-of-faults-fig-1-2-259x300.jpg" width="259" height="300" /></a></p>
<p style="text-align: center;"><span style="color: #0000ff;"><i>The diagram shows a series of two-dimensional slices through rocks affected by different dynamic styles of faulting. The red opposed arrows are the Fault Movement Vectors and indicate the direction of net movement of any point on either side of the fault trace. The sections are all in the plane of the FMVs. Click for a larger, sharper image.</i></span></p>
<p>Simple shear and pure shear faults are end members of a continuum of styles of displacement across a fault. Even where simple shear is the predominant deformation mechanism, some parts of the fault will locally exhibit the effects of pure shear. Conversely, in dominantly pure shear structures, there will be zones where the structures observed formed through the mechanism of simple shear. If the FMV arrows lie some angle between 0⁰ and 90⁰ to the fault plane, then fault deformation took place by some combination of simple shear and pure shear mechanisms.</p>
<p><b><i>Marker Bed Movement Vectors</i></b> (hereafter, MMVs) are the paired arrows with which geologists use to decorate their maps and sections in order to indicate relative displacement of pre-fault planar structure across a fault.  These structures are typically sedimentary marker beds, but may be veins or even pre-existing faults. In the general case where the fault is viewed on a random section, and without further data, MMV arrows indicate apparent displacement only. The MMV plane is any plane which contains the arrows and, by definition, is <em>always parallel to the fault plane</em>.  However, <em>the displacement of a single <strong>plane</strong> across a fault is incapable of fully defining the relative movement of the rock bodies on either side of the fault &#8211; only the relative displacement of <strong>points</strong> on either side of the fault can do that.</em> When a fault is viewed on a random section &#8211; such as an outcrop, a mine opening, a geological section or a piece of diamond drill core &#8211; marker beds with different orientation may give opposed MMVs across the same fault. The angle which the line of intersection of marker bed and fault makes with the Fault Movement Vectors will determine the amount of apparent displacement on that section. An angle of 90 degrees produces maximum displacement; an angle of 0 degrees will produce no apparent displacement. MMV arrows <em>are only equivalent to FMV arrows in the special case where the section on which the displacement is observed is parallel to the FMV plane </em>(as in the left hand map view of the diagram below).</p>
<p>When viewing a fault on the FMV plane, <em>all</em> marker beds will show the same amount and sense of displacement irrespective of their orientation (see figure below). Conversely, if differently-oriented beds show the same amount and sense of displacement, then the plane on which that displacement is being viewed must be the plane of the FMVs.</p>
<p>Many geologists, including the writers of some geological textbooks and dictionaries, confuse FMVs and MMVs, but FMVs are the more fundamental measure of fault movement.</p>
<p><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/06/Plan-and-Section-FMVs-and-MDVs.jpg" rel="wp-prettyPhoto[1340]"><img class="aligncenter size-medium wp-image-1461" alt="Plan and Section FMVs and MDVs" src="http://rogermarjoribanks.info/wp-content/uploads/2021/06/Plan-and-Section-FMVs-and-MDVs-300x147.jpg" width="300" height="147" /></a></p>
<p style="text-align: center;"><span style="color: #0000ff;"><em><span style="color: #0000ff;">A plan view and vertical sections across a strike-slip, simple shear fault affecting differently-oriented marker beds. Red arrows are the Fault Movement Vectors. White arrows are the Marker Bed Movement Vectors. The map view (left) is in the plane of the Fault Movement Vectors: marker beds therefore show the true displacement. Sections AB and BC are planes at right angles to the FMVs: marker beds displacements are apparent only. </span><em style="color: #0000ff;">Vectors. Click for a larger, sharper image. </em></em></span></p>
<p style="text-align: left;"><b>Discussion on Joints</b></p>
<p>The amount of movement that has taken place across a fault can vary through several orders of magnitude – from a fraction of a millimeter to hundreds of kilometers. However, locally developed, brittle fracture surfaces of limited extent across which insignificant displacement has taken place are usually called <b><i>joints</i></b>. The suggestion by Neville Price (see his definition above) that there may have been no movement across a joint is of course nonsense: if there had been no movement, there would have been no fracture. By “insignificant” I mean difficult or impossible to see with the naked eye.  However, in practice, a displacement can only be quantified where the fracture affects a marker surface &#8211; and sometimes not even then.</p>
<p>Joints are presumably the category of fracture which the lexicographers sought to exclude from their definition of faults by their requirement that displacement be “significant”, “observable” or &#8220;obvious&#8221;.</p>
<p>Joints form in the same way as faults and should be regarded as a &#8211; somewhat vaguely-defined -sub-category of brittle faulting. There is no logic for imposing an artificial division between faults and joints based on some arbitrarily defined amount of movement &#8211; what has the resolution of the human eye got to do with rock mechanics?</p>
<p>All faults are caused by stress. In faults with a significant strike extent, the causative force is usually the deviatoric stresses associated with tectonism. Joints can also be caused by tectonic stress but may also be the result of changes of non-deviatoric stresses. Examples are the change in lithostatic stress caused by weathering or rock excavation, and thermal gradients associated with igneous activity. Stress is an abstract force which can only be deduced (if you are lucky). It cannot therefore be used as the basis for a definition of a physical structure such as a fault. That would be putting the cart before the horse.</p>
<p>Joints, as you will have gathered, are notoriously difficult to define. However, even with the  fuzzy definitions that are out there (including mine), the term &#8220;joint&#8221; remains a useful <em>field</em> term for describing arrays of small-scale brittle fractures.</p>
<p>But joints are micro-faults, nonetheless.</p>
<p><b>Discussion on Brittle and Ductile Deformation</b></p>
<p>The method of deformation that enables faults to form, and movement to take place across them, can be either brittle or ductile, or, more typically, some combination of brittle and ductile. Ductile deformation is promoted by high temperature and confining pressure, but if rocks are sufficiently incompetent they can deform in a ductile manner at almost any temperature or pressure. Most faults show evidence for both styles of deformation either at different places within the same fault zone, and/or at different times during its formation. This is particularly true for large-displacement faults which typically affect a range of rocks with different physical and chemical properties, and are a composite of episodic movements that took place over a long period of time.</p>
<p>Where the dominant deformation mechanism is brittle, faults typically consist of tabular arrays of close-spaced, sub-parallel anastomosing fractures separating slices of lesser deformed, or unreformed, rock. This pattern is fractal in that it can occur at all scales from that of a regional map to that of a microscope slide.</p>
<p>Where the dominant fault deformation mechanism is ductile, the strain is more uniformly and smoothly distributed across across the width of the fault.  Ductile faults are often described as ductile shear zones, but they are faults, nonetheless.</p>
<p><b>So here is my definition of a fault:</b></p>
<p align="center"><span style="color: #0000ff;"><b><i>A fault is a restricted tabular zone of high strain with relative displacement of the rocks on either side.</i></b></span></p>
<p style="text-align: left;" align="center"><strong><span style="color: #000000;"> </span></strong></p>
<p align="center"><strong>**********</strong></p>
<p><a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftnref1">[1]</a> J A Jackson &amp; R L Bates (eds), 1980: <i>Glossary of Geology</i>. Published by the American Geophysical Institute, 2<sup>nd</sup> Edition, 1980.</p>
<p><a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftnref2">[2]</a> Michael Allaby 4<sup>th</sup> Ed. 2013 online version. DOI: 10.1093/acref/9780198839033.001.001</p>
<p><a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftnref3">[3]</a> Hobbs B E, Means W D &amp; Williams P F, 1976: <i>An outline of structural geology</i>. John F Wiley and Sons, 571p.</p>
<p><span style="color: #0000ff;">(4)</span> Price, Neville J: 1964. <em>Fault and joint development in brittle and semi-brittle rocks.</em> Pergamon Press, 176p.</p>
<p><a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftnref4">[5]</a> <i>Accessed July 2020</i></p>
<p><a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftnref5"> </a></p>
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		<title>The movement of faults</title>
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		<pubDate>Sun, 27 Sep 2020 01:41:28 +0000</pubDate>
		<dc:creator><![CDATA[Roger Marjoribanks]]></dc:creator>
				<category><![CDATA[Geological Mapping]]></category>
		<category><![CDATA[Structural Geology]]></category>

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		<description><![CDATA[<p>The movement of faults Faults are not mathematical planes (2D surfaces with length and depth but no thickness) but 3D tabular zones of deformed rock. The length and depth of a fault is always much greater than its thickness, but fault width can vary through many orders [&#8230;]</p><p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/movement-faults-2/">The movement of faults</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></description>
				<content:encoded><![CDATA[<p style="text-align: center;"><strong>The movement of faults</strong></p>
<p style="text-align: left;">Faults are not mathematical planes (2D surfaces with length and depth but no thickness) but 3D tabular zones of deformed rock. The length and depth of a fault is always much greater than its thickness, but fault width can vary through many orders of magnitude from a fraction of a millimeter to to tens of kilometers.</p>
<p style="text-align: left;">There is widespread confusion in the geological literature as to the exact definition of a fault. I discuss this in another blog post <span style="color: #ff0000;">here</span>.</p>
<p style="text-align: left;">Small, locally developed, fracture surfaces across which insignificant displacement has taken place are called <b style="font-style: italic;">joints</b>. By “insignificant” I mean difficult or impossible to see with the naked eye. Joints form in the same way as faults and should be regarded as a sub-category of brittle faulting.</p>
<p style="text-align: left;">No fault is ever strictly planar. Normal and Thrust faults (more on these later) are typically curved: steep dipping near the surface and progressively flattening with depth – a shape known as listric. In addition, at all scales, faults show irregularities – bends and bumps and jogs. During fault movement the variations from strict planarity lead to complex patterns of stress along the fault surfaces. These stress variations are the key to understanding the location and shape of ore that might form within the fault zones.</p>
<p style="text-align: left;">The method of deformation in a fault can be either brittle or ductile, or, more typically, some combination of brittle and ductile.</p>
<p style="text-align: left;">Fault Movement Vectors (hereafter FMVs) indicate the direction that  any point on one side of the fault trace has been displaced relative to any point on the other side during fault movement. On any plane passing through the FMVs, the FMVs can be shown as a pair of opposed arrows, one for the rocks on either side of the fault.</p>
<p style="text-align: center;"><em><span style="color: #0000ff;">FMVs can lie at any angle to the fault surface</span></em></p>
<p style="text-align: left;">FMVs can lie at any angle to the fault surface. Where the FMVs are <em>parallel</em> to the fault plane, the fault has formed by a deformation mechanism known as <i>Simple Shear</i>. Where the FMVs are at <i>90°</i> to the fault surface, the fault was formed through the process of <i>Pure Shear</i>. Where FMVs lie between <i>0˚</i> and <i>90˚</i> to the fault plane, deformation was accomplished by a mixture of both simple shear and pure shear mechanisms.</p>
<p style="text-align: left;">In <strong>Simple Shear</strong> <strong>Faults</strong>, the rocks on either side of the fault zone have moved laterally with respect to each other. FMVs are parallel to the fault plane.</p>
<p style="text-align: left;">In <strong>Pure Shear Faults</strong>, the rocks on either side of the zone have either moved towards each other in compression or moved apart in extension<a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftn5">[1]</a>. For this to happen, there must be a reduction or increase in the volume of the rocks affected by the external stress field.</p>
<p style="text-align: center;"><em><span style="color: #0000ff;">Most fault zones are the result of both simple shear and pure shear deformation styles. The relative proportion of these two processes can vary both across and along the fault zone.</span></em></p>
<p style="text-align: left;">Because changing rock volume is difficult, they deform much more easily by the mechanism of simple shear than by pure shear. Thus, displacements of more than a few meters indicates that the dominant mechanism was probably that of simple shear. Note the deliberate use here of the vague terms: “dominantly”, “more than”, “few” and “probably”.  In dealing with real rocks in the field, as opposed to simplified textbook examples, that is the best that can be done.</p>
<p style="text-align: left;">Because of the above, the most commonly occurring map-scale faults are those where the amount of displacement attributable to simple shear is greatest. For most purposes, and to a first order approximation, map scale faults can be regarded as dominantly simple shear faults.</p>
<p>As rock is incompressible, faulting can only reduce its volume by the physical removal of material from the faces of the fault zone. This happens predominantly by means of selective solution (or in extreme cases, melting) of rock material into fluids within the fault zone. The process is promoted by high temperature and high confining pressure and controlled by the chemical/mineralogical nature of the affected rocks. The dissolved material in solution moves along (laterally and upwards) the fault zone. Movement is driven by pressure and temperature gradients as well as by the “pumping” effects of periodic seismicity<a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftn6">[6]</a>.  It will ultimately be deposited as vein material (typically quartz or calcite) elsewhere in the fault in regions that are under relative tension. Left behind in the fault zone are the relatively insoluble rock components such as clay or graphite.  Any puggy, clay-rich material in a fault is the insoluble residuum of material lost through pressure solution during pure shear compression. This type of fault fill is usually described as fault gouge.</p>
<p>In the upper few kilometers of the earth&#8217;s crust, where confining pressure and temperature are relatively low, rocks have little strength under tension. Pure shear extension stress creates fractures – planar zones of extension – that (unless at or near the surface) will suck in fluids from along the fault zone or from adjacent rocks. The presence of such pressurized fluids can aid the propagation of a tensional fracture.  The fluids deposit vein material in the fracture.  Igneous fluids (magma) may crystallize as dykes or sills.   Vein filled zones in former tensional sites of a fault are the so-called “<i>dilational jogs</i>” that host many epithermal ore deposits.</p>
<p>The important point to remember is that pure shear deformation, as opposed to simple shear deformation, always results in a change in volume – either an increase or a decrease – of the affected rocks.<i> </i></p>
<p align="center"><a href="http://rogermarjoribanks.info/wp-content/uploads/2020/09/Movement-of-faults-fig-1-2.jpg" rel="wp-prettyPhoto[1124]"><img class="aligncenter size-medium wp-image-1123" alt="Movement of faults fig 1 (2)" src="http://rogermarjoribanks.info/wp-content/uploads/2020/09/Movement-of-faults-fig-1-2-259x300.jpg" width="259" height="300" /></a></p>
<p><i></i><em><span style="color: #0000ff;">Figure 1: The diagram shows a series of two-dimensional slices through rocks affected by different dynamic styles of faulting. The red opposed paired arrows are the Fault Movement Vectors and indicate the relative net movement of any point on either side of the fault trace. The sections are all in the plane of the FMVs. Where the vectors are parallel to the fault plane (as in a), the opposed blocks have moved laterally past each other: sinistral if to the left (as shown) or dextral if to the right. However, FMVs can lie at any angle to the fault plane. Where FMVs point towards each other, and are not parallel to the fault plane, the stress state is known as <span style="text-decoration: underline;">trans-pression</span>; if the arrows point away from each other, and not parallel to the fault plane (b), the stress state is known as <span style="text-decoration: underline;">trans-tension</span>. Two end member states, either of pure compression or pure extension, occur where the vectors are normal to the fault (b &amp; c). There is a continuum between these different styles of fault movement, not just between different faults, but within any one fault at different places and at different times during its formation. Click for a larger, sharper image.</span></em></p>
<p>Simple shear and pure shear faults are end members of a continuum of styles of displacement across a fault. Even where simple shear might be the predominant mechanism, different parts of the fault will locally exhibit the effects of pure shear. Conversely, in dominantly pure shear structures, there will be zones where the structures observed formed through the mechanism of simple shear.</p>
<p>Faults develop incrementally over geological time through the accumulation of large numbers of relatively small movements. During this process, each part of a final fault structure may have been sequentially subjected to, and show the effects of, both displacement mechanisms. Therefore, in addition to evidence for different structural structural styles that operated in different parts of a fault at any one time, at any one point in a fault different styles of faulting may have operated over time. Typically, early formed structures are destroyed by later movement, but this is not always the case.</p>
<p><b> </b><b>The displacement of marker beds</b></p>
<p>Any marker bed intersected by a fault will be displaced by an amount which depends on the angle which the bed makes with the plane which contains the FMVs. If the angle is <i>0˚</i> there will be <i>no apparent lateral displacement</i> of the bed across the fault on any section.  The amount of lateral displacement will increase with increasing angle. Maximum displacement is reached when the angle is <i>90˚</i>.<i> </i>On figure 2 below, the FMVs are parallel to the fault plane. The blue marker beds intersect the fault plane at an angle of around 45⁰ to the FMVs, both to the east and to the west. The vertical anticlinal axial plane (green dash line) makes an angle of 0⁰ with the FMVs.<i> </i> Fault movement thus displaces the marker beds to the east and to the west, but has no apparent effect on the axial plane.</p>
<p>This is a simple geometrical consequence and applies whether the fault mechanism is simple shear or pure shear.</p>
<p style="text-align: center;"><b> <a href="http://rogermarjoribanks.info/wp-content/uploads/2020/09/FDVs-MDVs-Block-Diagram.jpg" rel="wp-prettyPhoto[1124]"><img class="aligncenter size-medium wp-image-1119" alt="FDVs &amp; MDVs Block Diagram" src="http://rogermarjoribanks.info/wp-content/uploads/2020/09/FDVs-MDVs-Block-Diagram-300x229.jpg" width="300" height="229" /></a></b></p>
<p align="center"><span style="color: #0000ff;"><em>Figure 2: Block diagram of a vertical simple shear fault (red) with S block down displacement. The fault displaces a marker bed (blue) that dips to E and W on opposite limbs of an upright anticline. On all sections parallel to the Fault Movement Vectors (i.e. any vertical section) the displacement of all marker beds or structural planes is the same, irrespective of orientation, and is parallel to the FMVs. When the structures are viewed on any section that is not in the vertical plane (in this example, the plan or map view) differently-oriented structures will show differing amounts, or even sense, of displacement. Click for a larger, sharper image.</em></span></p>
<p>The displacement of a single plane across a fault is incapable of providing the FMVs for the fault.</p>
<p>However, the displacement of a unique linear structure across a fault plane will provide a measure of the FMVs. A frequently occurring linear structure is the line of intersection of two differently oriented marker beds. Even although not directly observed, the line of intersection of the marker beds can be easily calculated and its intersection with the fault plane plotted. In the map and section shown in figure 3 below, the intersection of a NE-dipping bed (blue) and a vertical dyke (green) on either side of a fault defines two displaced points across the fault. The line joining the points is the Fault Movement Vector. In this example it has a sinistral strike slip movement (70%) plus a small component (30%) of dip-slip S-block down movement. The analysis only works, of course, if the FMVs lie within the plane of the fault (i.e., a simple shear fault).</p>
<p><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/04/Displacement-of-a-point-across-a-simple-shear-fault.jpg" rel="wp-prettyPhoto[1124]"><img class="aligncenter size-medium wp-image-1362" alt="Displacement of a point across a simple shear fault" src="http://rogermarjoribanks.info/wp-content/uploads/2021/04/Displacement-of-a-point-across-a-simple-shear-fault-300x268.jpg" width="300" height="268" /></a></p>
<p style="text-align: center;"> <em><span style="color: #0000ff;">Figure 3: The displacement of a point across a simple shear fault defines the Fault Movement Vector.</span></em></p>
<p><strong>Simple rules for interpreting simple shear faults</strong></p>
<p>For a first pass interpretation of any geological section across a simple shear fault:</p>
<ol>
<li>On any section or plan, if marker units of differing orientation are displaced in the same sense and by the same amount, then that section or plan must lie in the plane of the FMVs for that fault.</li>
<li>On any section or plan, if marker units of differing orientation are displaced by different amounts and/or in different senses, then that section or plan must lie at an angle other than zero to the FMV plane for that fault. From which it follows that:</li>
<li>In a horizontal section (usually called a map) the fault movement is STRIKE-SLIP (i.e. a transcurrent fault) if marker beds of different orientation show the same displacement across it.</li>
<li>In a vertical section, the fault movement is DIP-SLIP (a thrust or normal fault) if marker beds of different orientation show the same displacement across it.</li>
</ol>
<p><b> </b><b>The descriptive nomenclature of Simple Shear Faults</b></p>
<p>In faults where the dominant displacement style is that of simple shear, the fault can be described in purely geometrical terms as either strike-slip (where the movement parallel to the strike of the fault), dip-slip (movement parallel to the dip of the fault), or oblique-slip (a direction between dip-slip and strike-slip).<i> </i></p>
<p><i></i><span style="text-align: left;">A more fundamental classification of simple shear faults is based on the orientation of the stress axes which cause them.  There are three classes: Transcurrent Faults, Normal Faults and Thrust Faults.</span></p>
<p style="text-align: center;" align="center"><span style="color: #0000ff;"><em>Scottish geologist Ernest Anderson who first proposed it in 1905</em></span></p>
<p style="text-align: left;" align="center">Transcurrent faults are strike-slip.  Normal and Thrust faults are dip-slip. Reverse faults are usually included in this scheme as steep-dipping Thrust faults. This 3-fold  classification of faults (four, if you count Reverse faults separately) is sometimes called “Andersonian” after the Scottish geologist Ernest Anderson who first proposed it in 1905<a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftn7">[2]</a> The classification reflects the orientation the three orthogonally-resolved principal external stress axes (greatest, least and intermediate) in the upper part of the earth’s crust. Here, these axes are dominantly either parallel to the earth&#8217;s surface, or at right angles to it<a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftn8">[4]</a>. If the direction of greatest stress is vertical, Normal faults may form; if the intermediate stress direction is vertical, Transcurrent faults may form; if the least stress direction is vertical, Thrust or Reverse faults may form. This is certainly a simplification, but Anderson’s classification of simple shear faults stands up remarkably well.</p>
<p> Consider an orthogonal section across a simple shear fault with a dip-slip displacement that affects a layered sequence whose dip is less than the fault (Figure 3).  The fault (if dipping less than <i>90˚</i>) will separate a hanging wall block from a footwall block. Where the hanging wall has moved up relative to the footwall, such faults are called reverse or, if the dip is less than around <i>45˚</i>, they are called thrust faults. In all thrust or reverse faults, movement has shortened the affected rock sequence in the horizontal direction but increased it in the vertical direction. There is no volume loss. If reverse or thrust faults affect strata whose dip is shallower than the fault, there will be vertical repetitions of marker beds on any section across it.</p>
<p style="text-align: center;"><span style="color: #0000ff;"><em>In steep drill holes, where there is repetition of stratigraphy, and older units overlying younger, the presence of thrust faulting is indicated.</em></span></p>
<p>Where the hanging wall block has moved down relative to the footwall, dip-slip faults are called Normal. With Normal faults, the affected rocks have been extended horizontally and compressed vertically. Where Normal faults affect shallow-dip strata, elements of the sequence might be missing on vertical sections.<i> </i></p>
<p style="text-align: center;"><span style="color: #0000ff;"><i>In steep drill holes, missing stratigraphy is a good indicator of the presence of normal faulting.</i></span></p>
<p align="center"><i><a href="http://rogermarjoribanks.info/wp-content/uploads/2020/08/The-movement-of-faults-fig-3-jpg.jpg" rel="wp-prettyPhoto[1124]"><img class="aligncenter size-medium wp-image-1080" alt="The movement of faults fig 3 jpg" src="http://rogermarjoribanks.info/wp-content/uploads/2020/08/The-movement-of-faults-fig-3-jpg-300x93.jpg" width="300" height="93" /></a> </i></p>
<p align="center"><span style="color: #0000ff;"><i>Figure 4:  Vertical sections through dip-slip Simple Shear Faults drawn in the plane of the Fault Movement Vectors (red arrows). On the left, Thrust Faults leading to horizontal compression and vertical thickening of a sequence. On the right, Normal Faults leading to horizontal extension and vertical thinning. Click for a larger, sharper image.</i></span></p>
<p><b> </b><b>Recognizing Dominantly Pure Shear Faults</b></p>
<p style="text-align: center;"><em><span style="color: #0000ff;">left-stepping bends in sinistral faults and right-stepping bends in dextral faults are regions of transtension</span></em></p>
<p>Transpression and transtension stresses occur where FMVs are at an angle to the fault plane so as to cause either compressive or tensile stress across it. This situation arises at bends in simple shear faults such as the steep portions, or ramps, of thrust faults (transpression) or the steeper dipping portions of normal faults (transtension). In transcurrent or strike slip faults, bends that tend to oppose fault movement (i.e. left-stepping bends in dextral faults or right stepping bends in sinistral faults) are areas of transpression: bends that are congruent with the sense of fault movement (i.e. left-stepping bends in sinistral faults or right-stepping bends in dextral faults) are regions of transtension. Structures typical of regions of transpression are fault gouge, folds, cleavages, thrusts, back-thrusts and flower structures. Structures typical of regions of transtension are vein-filled dilational jogs, normal faults and graben.</p>
<p style="text-align: center;"><span style="color: #0000ff;"><em>left-stepping bends in dextral faults or right stepping bends in sinistral faults are areas of transpression</em></span></p>
<p>During their formation, extensional faults move rocks apart and create a new volume which (except at the surface) sucks in fluids from further along the fault zone or from wall rocks. The fluids may be meteoric water or derived from metamorphic processes or an igneous source.  The fluids deposit vein material (typically quartz or calcite) or will crystallize as an igneous dyke. The presence of this epigenetic material in the fault plane is the main way of identifying such faults.<i> </i></p>
<p align="center"><a href="http://rogermarjoribanks.info/wp-content/uploads/2020/08/The-movement-of-faults-FIG-4-JPG.jpg" rel="wp-prettyPhoto[1124]"><img class="aligncenter size-medium wp-image-1081" alt="The movement of faults FIG 4 JPG" src="http://rogermarjoribanks.info/wp-content/uploads/2020/08/The-movement-of-faults-FIG-4-JPG-300x210.jpg" width="300" height="210" /></a></p>
<p style="text-align: center;"><i> </i><span style="color: #0000ff;"><i>Figure 5: Before and after block diagrams along with a plan view of an Extensional Pure Shear Fault (FMVs  &#8211; red arrows &#8211; point away from each other and are at right angles to the fault plane).  On the plan view, the displacement of the marker bed (MMVs &#8211; black arrows) is not he result of simple shear. Click for a larger image.</i></span></p>
<p>A pure shear compressional fault has lost material from the fault face. The presence of clay gouge in the fault zone indicates that material has been lost through pressure solution. Other structures that may be present in the fault zone such as fine penetrative cleavage parallel to the zone margins, are also indicative of compression.</p>
<p align="center"><a href="http://rogermarjoribanks.info/wp-content/uploads/2020/08/The-movement-of-faults-fig-5-jpg.jpg" rel="wp-prettyPhoto[1124]"><img class="aligncenter size-medium wp-image-1082" alt="The movement of faults fig 5 jpg" src="http://rogermarjoribanks.info/wp-content/uploads/2020/08/The-movement-of-faults-fig-5-jpg-300x244.jpg" width="300" height="244" /></a></p>
<p style="text-align: center;"><i> </i><span style="color: #0000ff;"><i><span style="color: #0000ff;">Figure 6: Before and after block diagrams of a pure shear compressional fault (i.e. the FMVs point towards each other and are at right angles to the fault plane). Note that the dextral strike-slip displacement of the marker bed across the fault (MMVs) is not caused by simple shear. Click for a larger image.</span></i></span></p>
<p><b> </b><i>First posted November 2013.  Modified July 2020, April 2021</i></p>
<p>&nbsp;</p>
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<p><a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftnref5">[1]</a> I have always found the terms “simple shear” and “pure shear” unfortunate and non-intuitive. For a start, the word “shear” or “shearing” in all non-technical dictionaries refers only to the lateral movement of two bodies past each other. And what is the logic in calling one type of deformation “simple” and one type “pure”?  However, the terms are long established and well defined in rock mechanics. We must live with them.</p>
<p><a href="https://d.docs.live.net/2f5da36964e08837/Documents/BLOG%20POSTS/The%20Nature%20and%20Movement%20of%20Faults%20Txt%20only.docx#_ftnref6">[2]</a> Sibson R H, Moore J McM &amp; Rankin A H 1975: <i>Seismic pumping</i><i> and hydrothermal fluid flow mechanisms. </i>J  Geol Soc London Vol 131, pp 653-659</p>
<p><span style="color: #0000ff;">(3)</span> E M Anderson, 1905: <em>The dynamics of faulting</em>. Trans Geol Soc Edinburgh, vol 8, pt 3</p>
<p><span style="color: #0000ff;">(4)</span> There are good theoretical reasons why this is so, but that explanation lies beyond the scope of this essay.</p>
<p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/movement-faults-2/">The movement of faults</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></content:encoded>
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		<title>Stereonet solution for non-oriented core</title>
		<link>https://rogermarjoribanks.info/stereonet-solution-non-oriented-core/</link>
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		<pubDate>Wed, 11 May 2016 10:54:27 +0000</pubDate>
		<dc:creator><![CDATA[Roger Marjoribanks]]></dc:creator>
				<category><![CDATA[Diamond Drilling]]></category>
		<category><![CDATA[Sterenet Solutions in structural geology]]></category>
		<category><![CDATA[Structural Geology]]></category>

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		<description><![CDATA[<p>Stereonet solutions for non oriented drill core Shawn Harvey of Saskatchewan sent me this email earlier this year: Hello again Roger,  You previously helped me out with some alpha-beta stereonet solutions which worked great (thanks again!!). I am now looking into a slightly more complex stereonet issue. [&#8230;]</p><p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/stereonet-solution-non-oriented-core/">Stereonet solution for non-oriented core</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></description>
				<content:encoded><![CDATA[<p style="text-align: center;"><strong>Stereonet solutions for non oriented drill core</strong></p>
<p><span style="color: #000000; font-family: Calibri;">Shawn Harvey of Saskatchewan sent me this email earlier this year:</span></p>
<p><span style="color: #0000ff;"><i><span style="font-family: Calibri; font-size: medium;">Hello again Roger,</span></i><i><span style="font-family: Calibri; font-size: medium;"> </span></i></span></p>
<p><span style="color: #0000ff;"><i><span style="font-family: Calibri; font-size: medium;">You previously helped me out with some alpha-beta stereonet solutions which worked great (thanks again!!). I am now looking into a slightly more complex stereonet issue. I have some semi-oriented core in which I have a “known” orientation of a foliation and want to use this plane to help calculate the orientation of a fault relative to this foliation. I have made the alpha measurement for the fault and the beta measurement relative to the bottom of ellipse mark for the foliation (i.e. Beta angle between the foliation reference line and the bottom of ellipse for the fault plane). Ideally I would use a core frame but the facility is metal rich and compass accuracy is an issue and it is -30 degrees Celsius outside; as such, I was hoping to use the stereonet to convert the internal angle relationships to geographic coordinates. I could also use Geocalculator but I would really like to understand the derivation of the results.</span></i></span></p>
<p><span style="color: #0000ff;"><i><span style="font-family: Calibri; font-size: medium;"> </span></i><i><span style="font-family: Calibri; font-size: medium;">For the alpha-beta solution of planes I have used your 6 step process from your 2010 publication but I was hoping you could pass on how to modify the steps for the semi-oriented core calculations. Your assistance would be greatly appreciated.</span></i></span></p>
<p><span style="color: #0000ff;"><i><span style="font-family: Calibri; font-size: medium;"> </span></i><i><span style="font-family: Calibri; font-size: medium;">thanks, shawn</span></i></span></p>
<p><i><span style="font-family: Calibri; font-size: medium;"> </span></i><span style="color: #0000ff;"><i>Good morning Shawn,</i><i> </i></span></p>
<p><span style="color: #0000ff;"><i>I appreciate your problems. –30 degrees sounds pretty tough. After a lifetime of working in Australia I find UK winter temps of –1 or –2 a trial. Where are you?  Northern Canada?  </i></span></p>
<p><span style="color: #0000ff;"><i> </i><i>Your other problem with the semi-oriented magnetic core is obviously susceptible to a stereonet solution, but I will have to think about it a bit.   Maybe this weekend ?  I will get back to you.</i></span></p>
<p><span style="color: #0000ff;"><i>Best wishes, Roger</i></span></p>
<p><i><span style="font-family: Calibri; font-size: medium;"> </span></i><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri; text-decoration: underline;">Statement of the problem</span></span></b></p>
<p><span style="color: #000000; font-family: Calibri;">Non oriented core (i.e. no bottom of hole line on core).  However, the drill hole has been surveyed and the azimuth and inclination of the core axis (</span><b><i><span style="color: #000000; font-family: Calibri;">CA</span></i></b><span style="color: #000000; font-family: Calibri;">) are known.  </span></p>
<p><span style="color: #000000; font-family: Calibri;">The core contains two structures: a foliation (labelled </span><b><i><span style="color: #000000; font-family: Calibri;">s</span></i></b><span style="color: #000000; font-family: Calibri;">) and a fault (labelled </span><b><i><span style="color: #000000; font-family: Calibri;">f</span></i></b><span style="color: #000000; font-family: Calibri;">). </span></p>
<p><span style="color: #000000; font-family: Calibri;">The dip and dip direction of the foliation are known from other data.</span></p>
<p><span style="color: #000000; font-family: Calibri;">The orientation of the fault is unknown. </span></p>
<p><span style="color: #000000; font-family: Calibri;">We have the following measurements on the fault:  (1) its alpha angle (</span><b><i><span style="color: #000000; font-family: Calibri;">α</span><sub><span style="color: #000000; font-family: Calibri;">f</span></sub></i></b><b><i></i></b><span style="color: #000000; font-family: Calibri;">) and, (2) the angle measured around the core circumference in a clockwise direction between point </span><b><span style="color: #000000; font-family: Calibri;">E</span></b><span style="color: #000000; font-family: Calibri;"> for the foliation (</span><b><span style="color: #000000; font-family: Calibri;">Es</span></b><span style="color: #000000; font-family: Calibri;">) and point </span><b><span style="color: #000000; font-family: Calibri;">E</span></b><span style="color: #000000; font-family: Calibri;"> for the fault (</span><b><span style="color: #000000; font-family: Calibri;">Ef</span></b><span style="color: #000000; font-family: Calibri;"> ).  We will call this radial angle theta</span><i><span style="color: #000000; font-family: Calibri;"> (</span><b><span style="color: #000000; font-family: Calibri;">ϴ</span></b><span style="color: #000000; font-family: Calibri;">).  </span></i><span style="color: #000000; font-family: Calibri;">Note that the radial angle between </span><b><i><span style="color: #000000; font-family: Calibri;">E</span><sup><span style="color: #000000; font-family: Calibri;">l</span></sup></i></b><b><i><sub><span style="color: #000000; font-family: Calibri;">s</span></sub></i></b><b><i></i></b><span style="color: #000000; font-family: Calibri;">and </span><b><i><span style="color: #000000; font-family: Calibri;">E</span><sup><span style="color: #000000; font-family: Calibri;">l</span></sup></i></b><b><i><sub><span style="color: #000000; font-family: Calibri;">f</span></sub></i></b><span style="color: #000000; font-family: Calibri;"> is also ϴ.</span></p>
<p><b><span style="color: #000000; font-family: Calibri;">Using a stereonet, calculate the strike and dip of the fault.</span></b></p>
<p style="text-align: left;" align="center"><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri; text-decoration: underline;">A  Worked example:</span></span></b></p>
<p><b><i><span style="color: #000000; font-family: Calibri; font-size: medium;">CA(Core Axis): 56° to 240°;    s (foliation): 078/60 South;  α (for fault): 45°;    ϴ (as defined above): 25°</span></i></b></p>
<p><b><i><span style="color: #000000; font-family: Calibri;">E</span><sub><span style="color: #000000; font-family: Calibri;">s</span></sub></i></b><span style="color: #000000; font-family: Calibri;"> and </span><b><i><span style="color: #000000; font-family: Calibri;">E</span><sup><span style="color: #000000; font-family: Calibri;">l</span></sup><sub><span style="color: #000000; font-family: Calibri;">s </span></sub></i></b><span style="color: #000000; font-family: Calibri;">: mark the ends of the long axis of the intersection ellipse of the foliation (s)</span></p>
<p><em><span style="color: #000000; font-family: Calibri;">E</span></em><sub><span style="color: #000000; font-family: Calibri;">f</span></sub><span style="color: #000000; font-family: Calibri;"> and </span><i><span style="color: #000000; font-family: Calibri;">E</span><sup><span style="color: #000000; font-family: Calibri;">l</span></sup><sub><span style="color: #000000; font-family: Calibri;">f</span></sub></i><span style="color: #000000; font-family: Calibri;">: mark the ends of the long axis of the intersection ellipse of the fault (f)</span></p>
<p><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri; text-decoration: underline;">Procedure</span></span></b></p>
<p><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/05/Stereonet-solution-part-orient-core.jpg" rel="wp-prettyPhoto[986]"><img class="aligncenter size-large wp-image-984" alt="Stereonet solution part orient core" src="http://rogermarjoribanks.info/wp-content/uploads/2016/05/Stereonet-solution-part-orient-core-958x1024.jpg" width="958" height="1024" /></a></p>
<p style="text-align: center;"><em>Stereonet solution to problem. The fault strikes 010 and dips 69 east</em></p>
<p><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri; text-decoration: underline;">Step 1: </span></span></b><span style="color: #000000; font-family: Calibri;"> On the stereonet plot the information that is known; i.e the Core Axis, the core circumference plane (the plane at right angles to the CA) and the trace of the foliation (s).</span></p>
<p><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri; text-decoration: underline;">Step 2:</span></span></b><span style="color: #000000; font-family: Calibri;">  The intersection of the foliation plane and the circumference plane is the plot of the long axis the intersection ellipse of the foliation. If this plots in the lower quadrant of the circumference plane (as in our example) then the point represents </span><b><i><span style="color: #000000; font-family: Calibri;">E</span></i></b><b><i><sub><span style="color: #000000; font-family: Calibri;">s</span></sub></i></b><span style="color: #000000; font-family: Calibri;">.  If it plots in the upper quadrant then it represents </span><b><i><span style="color: #000000; font-family: Calibri;">E</span></i></b><b><i><sup><span style="color: #000000; font-family: Calibri;">l</span></sup></i></b><b><i><sub><span style="color: #000000; font-family: Calibri;">s </span></sub></i></b><span style="color: #000000; font-family: Calibri;">(E primed).</span></p>
<p><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri; text-decoration: underline;">Step 3</span></span></b><span style="color: #000000; font-family: Calibri;">:  Along the circumference plane, in a clockwise direction from E</span><sub><span style="color: #000000; font-family: Calibri;">s</span></sub><span style="color: #000000; font-family: Calibri;"> (or E</span><b><i><sup><span style="color: #000000; font-family: Calibri;">l</span></sup></i></b><sub><span style="color: #000000; font-family: Calibri;">s</span></sub><span style="color: #000000; font-family: Calibri;">) , measure the angle theta (ϴ).  This will plot either point E</span><sub><span style="color: #000000; font-family: Calibri;">f  or </span></sub><span style="color: #000000; font-family: Calibri;">E</span><b><i><sup><span style="color: #000000; font-family: Calibri;">l</span></sup></i></b><sub><span style="color: #000000; font-family: Calibri;">f.</span></sub></p>
<p><b><i><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri; text-decoration: underline;">Step 4</span></span></i></b><b><i><span style="color: #000000; font-family: Calibri;">:</span></i></b><span style="color: #000000; font-family: Calibri;">  By rotating the stereonet overlay, locate and plot the Great Circle that connects points CA and E</span><sub><span style="color: #000000; font-family: Calibri;">f  </span></sub><span style="color: #000000; font-family: Calibri;">(or E</span><i><sup><span style="color: #000000; font-family: Calibri;">l</span></sup></i><sub><span style="color: #000000; font-family: Calibri;">f</span></sub><span style="color: #000000; font-family: Calibri;">).</span></p>
<p><b><i><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri; text-decoration: underline;">Step 5</span></span></i></b><b><i><span style="color: #000000; font-family: Calibri;">:</span></i></b><span style="color: #000000; font-family: Calibri;">  Along this Great Circle, starting at point CA, measure the angle (90-</span><span style="color: #000000; font-family: Calibri;">α</span><span style="color: #000000; font-family: Calibri;">)</span><sub><span style="color: #000000; font-family: Calibri;">f</span></sub><span style="color: #000000; font-family: Calibri;"> .  If E</span><sub><span style="color: #000000; font-family: Calibri;">f</span></sub><span style="color: #000000; font-family: Calibri;"> has been plotted, measure the angle in the direction </span><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri; text-decoration: underline;">away</span></span><span style="color: #000000; font-family: Calibri;"> from E</span><sub><span style="color: #000000; font-family: Calibri;">f </span></sub><span style="color: #000000; font-family: Calibri;">(as in the worked example).  If E</span><i><sup><span style="color: #000000; font-family: Calibri;">l</span></sup></i><span style="color: #000000; font-family: Calibri;">f has been plotted, measure 90-α in a direction </span><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri; text-decoration: underline;">towards</span></span><span style="color: #000000; font-family: Calibri;"> E</span><i><sup><span style="color: #000000; font-family: Calibri;">l</span></sup></i><span style="color: #000000; font-family: Calibri;">f.  This plots the pole to the fault plane (P</span><sub><span style="color: #000000; font-family: Calibri;">f</span></sub><span style="color: #000000; font-family: Calibri;">)</span></p>
<p><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri; text-decoration: underline;">Step 6:</span></span></b><span style="color: #000000; font-family: Calibri;">  From the pole to the fault read off its strike and dip :  in this example strike 010° dip 69° E</span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/05/Core-long-sect-in-plane-E-E-CA.jpg" rel="wp-prettyPhoto[986]"><img class="aligncenter size-medium wp-image-985" alt="Core long sect in plane E-E &amp; CA" src="http://rogermarjoribanks.info/wp-content/uploads/2016/05/Core-long-sect-in-plane-E-E-CA-226x300.jpg" width="226" height="300" /></a></p>
<p style="text-align: center;"><em>Longitudinal section of core in the plane of the Core Axis, and the long axis of the intersection ellipse of a cross-cutting plane.</em></p>
<p>&nbsp;</p>
<p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/stereonet-solution-non-oriented-core/">Stereonet solution for non-oriented core</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></content:encoded>
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		<title>A stereonet solution for alpha beta angles in oriented drill core</title>
		<link>https://rogermarjoribanks.info/stereonet-solution-alpha-beta-angles-oriented-drill-core/</link>
		<comments>https://rogermarjoribanks.info/stereonet-solution-alpha-beta-angles-oriented-drill-core/#comments</comments>
		<pubDate>Thu, 31 Mar 2016 13:49:14 +0000</pubDate>
		<dc:creator><![CDATA[Roger Marjoribanks]]></dc:creator>
				<category><![CDATA[Diamond Drilling]]></category>
		<category><![CDATA[Sterenet Solutions in structural geology]]></category>
		<category><![CDATA[Structural Geology]]></category>

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		<description><![CDATA[<p>Using a stereonet to calculate strike and dip from alpha-beta angles in oriented drill core The attitude of a surface in oriented drill core can be determined by the measuring two internal core angles known as alpha (α) and beta (β). These numbers are then normally entered [&#8230;]</p><p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/stereonet-solution-alpha-beta-angles-oriented-drill-core/">A stereonet solution for alpha beta angles in oriented drill core</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></description>
				<content:encoded><![CDATA[<p align="center"><b><span style="color: #000000; font-family: Calibri;">Using a stereonet to calculate strike and dip from alpha-beta angles in oriented drill core</span></b></p>
<p><span style="color: #000000; font-family: Calibri;">The attitude of a surface in oriented drill core can be determined by the measuring two internal core angles known as alpha (α) and beta (β). These numbers are then normally entered into a software program which calculates the strike and dip of the surface</span><a title="" href="file:///C:/Users/Roger/Desktop/Stereonet%20reduction%20of%20alpha%20and%20%20beta.docx#_ftn1">[1]</a><span style="font-family: Calibri;"><span style="color: #000000;">.</span><span style="color: #000000;">  </span><span style="color: #000000;">There is a simple and quick stereonet procedure which produces the same results.</span></span></p>
<p><span style="color: #000000;"><span style="font-family: Calibri;">How to use a stereonet to convert alpha and beta angles in to strike and dip is the subject of this post.  </span></span></p>
<p><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri;">Oriented drill core is core which meets three criteria:</span></span></b></p>
<ol>
<li><i>A down-hole survey has established the azimuth and inclination of the core axis  along its length.</i></li>
<li><i>A core orientation survey has established the intersection of the original gravity vector  with the core surface. This is usually shown as a line, called the Bottom of Hole Line, marked along the original bottom surface of the core. </i></li>
<li><i>The down direction of the core is marked by an arrow placed on each piece of core. For holes angled below the horizontal (that is, all surface holes) these arrows will point away from the hole collar towards the hole termination.  For holes angled above the horizontal (some underground holes) the arrows on the core will point towards the hole collar and way from the hole termination.</i></li>
</ol>
<p><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/03/Geometry-or-oriented-drill-core.jpg" rel="wp-prettyPhoto[973]"><img class="aligncenter size-large wp-image-967" alt="Geometry or oriented drill core" src="http://rogermarjoribanks.info/wp-content/uploads/2016/03/Geometry-or-oriented-drill-core-1024x484.jpg" width="1024" height="484" /></a></span></span></b></p>
<p align="center"><span style="color: #0000ff;"><i><span style="font-family: Calibri;">Figure 1: The geometry of a planar structure in drill core. (a) is a perspective view of a piece of drill core containing a penetrative planar structure (bedding or cleavage) along which the top of the core has broken. (b) is a view looking down the core axis. (c) is a longitudinal section through the core containing the core axis, the long axis of the intersection ellipse of the planar structure and the pole to that structure.</span></i></span></p>
<p><span style="text-decoration: underline;"><strong>The internal reference lines and planes in oriented core</strong></span></p>
<p>These are:</p>
<p><span style="color: #000000; font-family: Calibri;"> 1. </span><i>The Core Axis (i.e. the imaginary line along the centre of the core), labelled </i><em><strong>CA</strong></em><i>. </i></p>
<p><i>2.  The plane at right angles to the core axis, known as the circumference plane (by some, the propeller plane). </i></p>
<p><i>3. The bottom of the hole line – labelled </i><em><strong>BOH</strong></em><i>.</i></p>
<p><i>4. The long axis of the intersection ellipse of the planar structure. This line requires some further explanation:</i></p>
<p><span style="font-family: Calibri;"><span style="color: #000000;">The trace of any planar rock structure on the surface of cylindrical drill core defines an ellipse, known as the intersection ellipse. <i> </i></span><span style="color: #000000;">The long axis of the ellipse is marked on the core surface by points of maximum curvature on the trace of the plane. These are called inflection points.</span><span style="color: #000000;">There are two inflection points marking the opposite ends of the long ellipse axis. </span></span></p>
<p><span style="font-family: Calibri;"><span style="color: #000000;">The inflection point that makes an acute angle with the <em>down</em> direction core axis is known as point <em><strong>E</strong></em>. The inflection point that makes an obtuse angle with the down direction core axis is known as point <em><strong>E<sup>l</sup></strong></em></span><span style="color: #000000;"> ( pronounced E primed). </span></span></p>
<p><span style="color: #000000; font-family: Calibri;">Note the two special cases:</span></p>
<ol>
<li><i>Where a hole is drilled at </i><em><strong>right angles</strong> </em><i>to the planar structure, then the trace on the core surface is a circle and no ellipse long axis is definable. </i></li>
<li><i>Where a hole is drilled </i><em><strong>parallel</strong></em> <i>to a structure, the trace of the structure trends along the along the length of the core and no inflection points can be defined &#8211; at any rate, for as long as this particular geometry holds good (which in real rocks is seldom more than a meter or so).</i><i> </i></li>
</ol>
<p><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri;">The orientation of a planar structure in core is defined by two angles (figure 1)</span></span></b></p>
<ol>
<li><i>The acute angle between the core axis and the long axis (E-E<sup>l</sup>) of the intersection ellipse. This angle is known by the Greek letter alpha – whose symbol is: </i><b><i>α</i></b><i>   The alpha angle can be measured in any core, irrespective of whether the core is oriented or even whether the hole is surveyed.  </i></li>
<li><i>The radial angle between the BOH line and the point E.  This angle is measured from BOH around the core circumference <strong>in a clockwise direction</strong>.  Note that &#8221;clockwise&#8221; refers to a view looking down the core (i.e. in the direction of the arrow marked on the core).  The angle is known by the Greek letter beta – whose symbol is: </i><b><i>β</i></b></li>
</ol>
<p>Now for the stereonet procedure&#8230;</p>
<p><b><span style="text-decoration: underline;"><span style="font-family: Calibri;"><span style="color: #000000;">Step 1:  </span><span style="color: #000000;">Plotting the core reference lines and planes<a href="http://rogermarjoribanks.info/wp-content/uploads/2016/03/Stereonet-plot-of-core-reference-planes.jpg" rel="wp-prettyPhoto[973]"><img class="aligncenter size-medium wp-image-968" alt="Stereonet plot of core reference planes" src="http://rogermarjoribanks.info/wp-content/uploads/2016/03/Stereonet-plot-of-core-reference-planes-300x242.jpg" width="300" height="242" /></a></span></span></span></b></p>
<p style="text-align: center;"><span style="color: #0000ff;"><i><span style="font-family: Calibri; font-size: medium;">Figure 2: Stereonet plot of reference lines and planes for a hole drilled at &#8211; 45° to 225° azimuth or + 45 to 045 (click for larger image).</span></i></span></p>
<p><span style="color: #000000; font-family: Calibri;">On a stereonet lines plot as points and planes plot as great circles (i.e. planes which pass through the centre of the sphere). The azimuth and inclination of the core axis (at the depth of the measured structure) enables it to be plotted as a point on the net. The core circumference plane is a great circle at 90° to the plot of the core axis. A vertical plane is a straight line passing through the centre of the net. The circumference of the stereonet is the horizontal plane. The BOH line is the point where the vertical plane passing through the core axis intersects the lower half of core circumference plane. </span></p>
<p><span style="color: #000000;"><span style="font-family: Calibri;">A plane can also be shown by plotting the line that is normal to the plane (this point is known as the pole to the plane). The core axis is the pole to its circumference plane.  </span></span></p>
<p><span style="font-family: Calibri;"><span style="color: #000000;">Remember that a stereo net is a projection of the lower half of a sphere and the centre of the net represents the down direction of the vertical (the line pointing to the centre of the earth: the gravity vector).   To a stereonet, a drill hole is a line oriented in space.  The direction in which the hole was drilled is immaterial. </span><span style="color: #000000;"> This means that an underground hole that is inclined at +45 degrees above the horizontal towards azimuth 045 ° will be plotted on the net as a line at -°45 (below the horizontal) to 225° (the reciprocal of the azimuth). </span></span></p>
<p><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri;"> </span></span></b><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri;">Step 2: Plotting the beta (β ) angle.</span></span></b></p>
<p><span style="color: #000000; font-family: Calibri;">This is the step where most care needs to be exercised. </span></p>
<p><span style="font-family: Calibri;"><span style="color: #000000;">The beta angle defines the position of the long axis of the intersection ellipse on the net. This <sup> </sup></span><span style="color: #000000;">line ( E –E</span><sup><span style="color: #000000;">l</span></sup><span style="color: #000000;"> ) is represented by a point on the net.</span><span style="color: #000000;">  </span><span style="color: #000000;">The angle is measured in a clockwise direction along the trace of the circumference plane, starting at point BOH.</span><span style="color: #000000;">  </span><span style="color: #000000;">For all beta values between 0° and 90°, point E lies on the net (see left diagram of figure 3).  When beta is 90 ° (figure 3, right) point E lies on the circumference of the net, indicating a horizontal line. The opposite end of that line is point E</span><sup><span style="color: #000000;">l</span></sup><span style="color: #000000;"> , which now lies on the net circumference at the diametrically opposite side of the net from point E.</span></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/03/Plotting-beta-range-0-to-90.jpg" rel="wp-prettyPhoto[973]"><img class="aligncenter size-large wp-image-969" alt="Plotting beta range 0 to 90" src="http://rogermarjoribanks.info/wp-content/uploads/2016/03/Plotting-beta-range-0-to-90-1024x527.jpg" width="1024" height="527" /></a></p>
<p align="center"><span style="color: #0000ff;"><i><span style="font-family: Calibri; font-size: medium;">Figure 3: Plotting the beta angle for the range β=0° to β=90°</span></i></span></p>
<p><span style="font-family: Calibri;"><span style="color: #000000;"><span style="font-size: medium;">For all beta angles between 90° and 270° , the E end of the long axis of the intersection ellipse is rotated out of the net projection and cannot be shown (it may help to think of E as now pointing “up in the air” out of the plane of the page). However, for this range of beta angles, the opposite end of the axis, E</span><sup><span style="font-size: small;">l</span></sup></span><span style="color: #000000; font-size: medium;"> , is now rotated on to the net and its position can be plotted by continuing to measure beta around the circumference plane.</span><span style="color: #000000; font-size: medium;">  </span><span style="color: #000000; font-size: medium;">The measurement is now made from the point where the left edge (&#8220;left&#8221; when looking in the direction of dip) of the core circumference plane meets the net circumference. This point is β = 90° </span><span style="color: #000000; font-size: medium;">(figure 4).</span></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/03/Plotting-beta-range-90-to-270.jpg" rel="wp-prettyPhoto[973]"><img class="aligncenter size-large wp-image-970" alt="Plotting beta range 90 to 270" src="http://rogermarjoribanks.info/wp-content/uploads/2016/03/Plotting-beta-range-90-to-270-1024x524.jpg" width="1024" height="524" /></a></p>
<p align="center"><span style="color: #0000ff;"><i><span style="font-family: Calibri; font-size: medium;">Figure 4: Plotting the beta angle for the range 90° to 270°</span></i></span></p>
<p><span style="font-family: Calibri;"><span style="color: #000000;"><span style="font-size: medium;">When the beta angle is exactly 270°, the line E – E</span><sup><span style="font-size: small;">l</span></sup></span><span style="color: #000000; font-size: medium;"> is again horizontal and its two end points lie at diametrically opposite locations on the circumference of the net as shown in figure 5, left. In this case, point E is on the left, and E</span><sup><span style="color: #000000; font-size: small;">l</span></sup><span style="color: #000000; font-size: medium;"> is on the right (compare to the plot of β=90° on figure 3, right diagram).</span></span></p>
<p><span style="color: #000000; font-family: Calibri; font-size: medium;">For all beta angles in the range 270° to 360°, point E will plot once again on the net (right diagram of figure 5). The left intersection of the circumference plane with the net circumference represents 270°.</span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/03/Plotting-beta-range-270-to-360.jpg" rel="wp-prettyPhoto[973]"><img class="aligncenter size-large wp-image-971" alt="Plotting beta range 270 to 360" src="http://rogermarjoribanks.info/wp-content/uploads/2016/03/Plotting-beta-range-270-to-360-1024x511.jpg" width="1024" height="511" /></a></p>
<p align="center"><span style="color: #0000ff;"><i><span style="font-family: Calibri; font-size: medium;">Figure 5: Plotting the beta angle for the range 270° to 360°.</span></i></span></p>
<p><span style="color: #000000; font-family: Calibri; font-size: medium;"> </span><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri; font-size: medium;">Step 3: Plotting the Alpha angle</span></span></b></p>
<p><span style="font-family: Calibri;"><span style="color: #000000;"><span style="font-size: medium;">By rotating the overlay, locate the great circle which contains the points CA and E (or E</span><sup><span style="font-size: small;">l</span></sup></span><span style="color: #000000; font-size: medium;">).  There is only ones such great circle. This is the trace of the longitudinal core section shown at (c) on figure 1. </span></span></p>
<p><span style="font-family: Calibri;"><span style="font-size: medium;"><span style="color: #000000;">On figure 6, the great circle has been drawn as a purple dashed line. Along this line, starting at the point CA, measure the angle 90-α °.  </span></span><span style="color: #000000; font-size: medium;">If point E has been plotted on the net, the angle 90-α° is measured in a direction </span><i><span style="text-decoration: underline;"><span style="color: #000000; font-size: medium;">away</span></span></i><span style="color: #000000; font-size: medium;"> from point E (as in figure 6, left).</span><span style="color: #000000; font-size: medium;">  </span><span style="color: #000000; font-size: medium;">If point E</span><sup><span style="color: #000000; font-size: small;">l</span></sup><span style="color: #000000; font-size: medium;"> is plotted on the net, the 90-α° angle is measured in a direction </span><span style="text-decoration: underline;"><span style="color: #000000; font-size: medium;">towards</span></span><span style="color: #000000; font-size: medium;"> E</span><sup><span style="color: #000000; font-size: small;">l </span></sup><span style="color: #000000; font-size: medium;">(figure 6, right).</span><span style="color: #000000; font-size: medium;">  The logic of this step should be obvious from figure 1(c). </span><span style="color: #000000; font-size: medium;">The measurement locates point P - the pole, or normal, to the planar rock structure being measured.</span></span></p>
<p><span style="color: #000000; font-family: Calibri; font-size: medium;">Once the pole to the plane has been plotted, the net scales can be used to read off the its dip and dip direction, strike and dip, or apparent dip on drill section, as required. </span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/03/Plotting-alpha-to-locate-P.jpg" rel="wp-prettyPhoto[973]"><img class="aligncenter size-large wp-image-972" alt="Plotting alpha to locate P" src="http://rogermarjoribanks.info/wp-content/uploads/2016/03/Plotting-alpha-to-locate-P-1024x519.jpg" width="1024" height="519" /></a></p>
<p align="center"><span style="color: #0000ff;"><i><span style="font-family: Calibri; font-size: medium;">Figure 6: Plotting the alpha angle and locating the Pole</span></i></span></p>
<p><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Calibri; font-size: medium;">Speed and Accuracy</span></span></b></p>
<p><span style="font-family: Calibri;"><span style="font-size: medium;"><span style="color: #000000;">On a standard 15 cm stereonet, the thickness of a pencil line or point is 1-5 degrees, depending on where the line is on the net. As a result, most stereonet measurement can be considered, as a rule of thumb, to be within one or two degrees of the correct value. That is to say, a stereonet measurement of 45° could be anywhere between 43° and 47°.  </span></span><span style="color: #000000; font-size: medium;">By contrast, mathematical manipulation of spatial data would give exact numbers, to a fraction of a degree if required, and limited only by the accuracy of the input numbers. But calculating a figure with this sort of accuracy would be both misleading and spurious. Plus or minus 2 degrees is an entirely appropriate and acceptable range of accuracy for geological measurements. In fact, most geologists would consider themselves favoured if their result is within 2° of the notional “correct” answer. This is because “planar” rock structures are seldom perfectly planar or constant in orientation over distances of more than a few tens of centimetres. In addition to this, orientation lines marked on core are generally considered acceptable if the match of the BOH orientation line from run to run, or from core piece to core piece, is less than +/- 5°.  Finally, measurements of alpha and beta angles (and especially of beta angles) taken by geologists on core typically have similar levels of accuracy. Fortunately, these various sources of error are not cumulative &#8211; that is what a +/- designation means.</span></span></p>
<p><span style="color: #000000; font-family: Calibri; font-size: medium;">The long verbal description and many figures that I have had to use in describing the stereonet reduction of internal core angles probably has given the reader the impression that this is a long and complex process. So that the logic of the solution and the plotting techniques can be understood I have shown all the construction lines. However, after a little practise, it will be found that most of these lines can be omitted. Almost everything can be done by eye using the pre-printed net scales, and just two points need to be plotted on the net overlay. Here is how it is done:</span></p>
<p><span style="font-family: Calibri;"><span style="font-size: medium;"><span style="color: #000000;">1. Plot the core axis and BOH points on the net overlay with permanent inked marks.  </span></span><span style="color: #000000; font-size: medium;">A single plot of these points will usually be good for a large number of measurements taken on core with that axial orientation (deviations in the hole azimuth and inclination of less than 2 degrees can be safely ignored). </span></span></p>
<p><span style="font-family: Calibri;"><span style="color: #000000;"><span style="font-size: medium;">2. Rotate the BOH point on to a principal net diameter. Using the degree divisions of the net, use angle beta to locate point E (or E</span><sup><span style="font-size: small;">l</span></sup></span><span style="color: #000000; font-size: medium;">) and mark this onto the overlay with a pencil mark.</span></span></p>
<p><span style="font-family: Calibri;"><span style="color: #000000;"><span style="font-size: medium;">3. Rotate the overlay again so as to bring points CA and E (or E</span><sup><span style="font-size: small;">l </span></sup></span><span style="color: #000000; font-size: medium;">) on to a great circle, then, with the overlay in this position, measure the angle 90 minus alpha to locate the pole to the plane. Mark this point on to the overlay with a pencil.</span></span></p>
<p><span style="font-family: Calibri;"><span style="color: #000000; font-size: medium;">4. Rotate the pole to the plane on to a principal net diameter:  read off the dip and dip direction of the plane from the scales of the net.</span></span></p>
<p><span style="color: #000000; font-family: Calibri; font-size: medium;">Now erase the two pencil marks to be ready ready for the next calculation.</span></p>
<p><span style="color: #000000; font-family: Calibri; font-size: medium;">Total time – 20 seconds. </span></p>
<p><span style="color: #000000; font-family: Calibri; font-size: medium;">Try beating that, from cold, with a computer. </span></p>
<div></div>
<hr align="left" size="1" width="33%" />
<div>
<p><a title="" href="file:///C:/Users/Roger/Desktop/Stereonet%20reduction%20of%20alpha%20and%20%20beta.docx#_ftnref1">[1]</a><span style="font-family: Calibri;"><i><span style="color: #000000;">In previous posts I have argued strongly that, except in special circumstances, structures in core should be measured using a core orientation frame rather than by internal core angles. But, perhaps because it is quicker and easier, the alpha beta method is still the preferred route for many, perhaps the majority of exploration drilling programs. Typically, the computer crunching is done as a separate, later, operation to the logging: the geologist logs her core blind, entering alpha-beta numbers to a data base, oblivious as she logs to the spatial meaning of the structures in front of her. </span></i></span></p>
<p><i><span style="font-family: Calibri;"><span style="color: #000000;">If the geologist converts her own alpha beta measurements to strike and dip manually, using a stereonet, on top of the core rack she will have useable geological data as she logs the core.  </span><span style="color: #000000;">Computers can of course be used on top of the core racks also, but manual stereonet manipulation provides a mental engagement with spatial data which is invaluable in understanding the geometry of the rocks, and, for a small number of measurements, is at least as quick as the use of a computer. </span></span></i></p>
<p>&nbsp;</p>
<p><em><strong><span style="color: #0000ff;">Any comments, questions or criticisms on this post are welcome. Please email me direct at marjex@ozemail.com.au </span></strong></em></p>
<p><span style="color: #000000; font-family: Calibri; font-size: small;"> </span></p>
</div>
<p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/stereonet-solution-alpha-beta-angles-oriented-drill-core/">A stereonet solution for alpha beta angles in oriented drill core</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></content:encoded>
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		<title>Sense of movement structures in fault zones  Part 3: Identification Criteria</title>
		<link>https://rogermarjoribanks.info/sense-movement-structures-fault-zones-part-3-identification-criteria/</link>
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		<pubDate>Wed, 17 Feb 2016 16:31:13 +0000</pubDate>
		<dc:creator><![CDATA[Roger Marjoribanks]]></dc:creator>
				<category><![CDATA[Diamond Drilling]]></category>
		<category><![CDATA[Geological Mapping]]></category>
		<category><![CDATA[Structural Geology]]></category>

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		<description><![CDATA[<p>Sense of Movement Structures in Fault Zones.  Part 3: Identification criteria Within or adjacent to a fault zone, various minor structures can be present that enable the sense of movement across the fault to be determined.  These structures are often called kinematic indicators. In Part 1 of [&#8230;]</p><p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/sense-movement-structures-fault-zones-part-3-identification-criteria/">Sense of movement structures in fault zones  Part 3: Identification Criteria</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></description>
				<content:encoded><![CDATA[<p align="center"><b><span style="font-family: Calibri;"><span style="color: #000000;">Sense of Movement Structures in Fault Zones.  </span><span style="color: #000000;">Part 3: Identification criteria</span></span></b></p>
<p><span style="font-family: Calibri;"><span style="font-size: medium;"><span style="color: #000000;">Within or adjacent to a fault zone, various minor structures can be present that enable the sense of movement across the fault to be determined.  </span></span><span style="color: #000000; font-size: medium;">These structures are often called kinematic indicators.</span></span></p>
<p><span style="font-family: Calibri;"><span style="font-size: medium;"><span style="color: #000000;">In <a title="Sense of movement structures – Part 1, Theory" href="http://rogermarjoribanks.info/sense-movement-structures-part-1-theory/">Part 1</a> of this series of posts, I classified kinematic indicators as T (tension), S (compressive), R (simple shear) and C (laminar flow). The part described how and why these structures formed and explained their use as kinematic indicators.  </span></span><span style="color: #000000; font-size: medium;"><a title="Sense Of Movement Structures in Fault Zones: Part 2: Examples" href="http://rogermarjoribanks.info/sense-movement-structures-kinematic-indicators-part-2-examples/">Part 2</a> consisted largely of photographs of actual structures in outcrop and drill core. In this final post, simple tabulated rules are provided that enable the various classes of structure to be identified in outcrop.</span></span></p>
<p><span style="font-family: Calibri;"><span style="font-size: medium;"><span style="color: #000000;">Most faults, especially large ones, have poor outcrop so when you are lucky enough to find an exposure of a fault it is worthwhile spending time examining it in detail to find out what it can tell you.  </span></span><span style="color: #000000; font-size: medium;">The type of exposure that is most likely to provide useful kinematic indicator structures is a section that cuts at right angles (orthogonally) across the full width of the zone. A stream section offers the best chance of finding such an exposure.</span><span style="color: #000000; font-size: medium;">   </span><span style="color: #000000; font-size: medium;">Although relatively rare in nature, orthogonal or near orthogonal sections across fault zones are frequently exposed in man-made outcrop such as road cuttings, trenches, the walls of open cuts, underground openings or in drill core. Next to an orthogonal section, the next most useful fault exposure for the structural geologist to work with is an exposure of the face of a fault – the plane of movement. </span><span style="color: #000000; font-size: medium;"> </span><span style="color: #000000; font-size: medium;">This is probably the most common type of natural fault exposure.</span></span></p>
<p><span style="font-family: Calibri;"><span style="font-size: medium;"><span style="color: #000000;">Don’t expect every exposure of a fault to contain sense of movement indicators that can be reliably identified and interpreted.  </span></span><span style="color: #000000; font-size: medium;">In fact, most will not. The minor structures within fault zones can be chaotic, apparently contradictory and difficult to assess in three dimensions.</span><span style="color: #000000; font-size: medium;">  </span><span style="color: #000000; font-size: medium;">If you are not certain how to identify the minor fault structures that you see it is better to walk away and try for a better exposure elsewhere.</span><span style="color: #000000; font-size: medium;">  </span></span></p>
<p><span style="font-family: Calibri;"><span style="font-size: medium;"><span style="color: #000000;">Being able to distinguish between different sense of movement structures is vital. Confusing S surfaces with T surfaces, for example, leads to radically-different interpretations of the direction of fault movement. The Table below sets out the criteria that can be used to identify structures.   </span></span><span style="color: #000000; font-size: medium;">Note that no single criteria is definitive and many of the fields overlap. The more criteria that a particular structure meets, the more certain is its identification. </span><span style="color: #000000; font-size: medium;"> </span></span></p>
<p><span style="font-family: Calibri;"><span style="font-size: medium;"><span style="color: #000000;">It is worth bearing in mind that identifying one single structure, or even a number of structures from a single outcrop, does not give 100% certainty as to the overall fault movement.  </span></span><span style="color: #000000; font-size: medium;">You have good evidence, but the important point is that a credible working hypothesis about the nature of the fault can now be constructed.</span><span style="color: #000000; font-size: medium;">  </span><span style="color: #000000; font-size: medium;">From this hypothesis predictions can be made which can tested against the evidence from future exposures of the structure. </span><span style="color: #000000; font-size: medium;"> </span><span style="color: #000000; font-size: medium;">This is the Scientific Method and from this process knowledge is gained.</span></span></p>
<p><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/02/Criteria-for-structure-in-fault-zones.jpg" rel="wp-prettyPhoto[946]"><img class="aligncenter size-large wp-image-935" alt="Criteria for structure in fault zones" src="http://rogermarjoribanks.info/wp-content/uploads/2016/02/Criteria-for-structure-in-fault-zones-1024x629.jpg" width="1024" height="629" /></a></p>
<p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/sense-movement-structures-fault-zones-part-3-identification-criteria/">Sense of movement structures in fault zones  Part 3: Identification Criteria</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></content:encoded>
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		<title>Sense Of Movement Structures in Fault Zones: Part 2: Examples</title>
		<link>https://rogermarjoribanks.info/sense-movement-structures-kinematic-indicators-part-2-examples/</link>
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		<pubDate>Fri, 15 Jan 2016 16:09:41 +0000</pubDate>
		<dc:creator><![CDATA[Roger Marjoribanks]]></dc:creator>
				<category><![CDATA[Diamond Drilling]]></category>
		<category><![CDATA[Geological Mapping]]></category>
		<category><![CDATA[Structural Geology]]></category>

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		<description><![CDATA[<p>Sense of Movement  Structures in Fault Zones :  Part 2 &#8211; Examples Within or adjacent to fault zones, various minor associated structures can be present that enable the sense of movement across the fault to be determined. These structures are often called kinematic indicators. This is the [&#8230;]</p><p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/sense-movement-structures-kinematic-indicators-part-2-examples/">Sense Of Movement Structures in Fault Zones: Part 2: Examples</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></description>
				<content:encoded><![CDATA[<p align="center"><b><span style="text-decoration: underline;"><span style="font-family: Arial;"><span style="color: #000000; text-decoration: underline;">Sense of Movement  </span><span style="color: #000000; text-decoration: underline;">Structures in Fault Zones : </span><span style="color: #000000; text-decoration: underline;"> </span><span style="color: #000000; text-decoration: underline;">Part 2 &#8211; Examples</span></span></span></b></p>
<p>Within or adjacent to fault zones, various minor associated structures can be present that enable the sense of movement across the fault to be determined. These structures are often called kinematic indicators.</p>
<p><span style="font-family: Arial;"><span style="color: #000000;">This is the second of three posts (see <a title="Sense of movement structures – Part 1, Theory" href="http://rogermarjoribanks.info/sense-movement-structures-part-1-theory/">part 1</a> and <a title="Sense of movement structures in fault zones  Part 3: Identification Criteria" href="http://rogermarjoribanks.info/sense-movement-structures-fault-zones-part-3-identification-criteria/">part 3</a> ) about </span><b><i><span style="color: #000000;">sense of movement  indicator </span></i></b><span style="color: #000000;">structures in fault zones. </span><span style="color: #000000;">In the first part, the theory behind sense of movement indicators is explained and it is recommended that this part be read in conjunction with part 2. </span><span style="color: #000000;"> </span><span style="color: #000000;">This post provides illustrations of sense of movement structures as seen in outcrop and drill core. In Part 3, the criteria for identifying the different classes of structure are tabulated.</span></span></p>
<p><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Arial; text-decoration: underline;">Preamble</span></span></b></p>
<p><span style="color: #000000; font-family: Arial;"> </span><span style="color: #000000; font-family: Arial;">Knowing the movement that has taken place across a fault makes it possible to predict the location and orientation of tensional zones &#8211; and hence potential veins of ore &#8211; within or adjacent to the fault. </span></p>
<p><span style="color: #000000; font-family: Arial;"> </span><span style="color: #000000; font-family: Arial;">If the fault is later than the ore body, knowing its movement allows prediction of the location of any mineralisation that may be displaced by it.</span></p>
<p><span style="font-family: Arial;"><span style="color: #000000;">Determining the strike of a fault is usually simple. Determining its dip requires some vertical exposure or drill hole information.  </span><span style="color: #000000;">However, to completely define a fault, it is necessary to know the movement (or displacement) vector and the amount of movement that has taken place</span><span style="color: #000000;">  </span><span style="color: #000000;">between the two sides of the fault.</span></span></p>
<p><span style="color: #000000; font-family: Arial;">For all these reasons, knowing the sense of movement on a fault is of the greatest importance.</span></p>
<p><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Arial; text-decoration: underline;">Some cautionary words</span></span></b></p>
<p>1. Faults develop over time through the accumulation of hundreds of relatively small movements.   Although these will add up to a final overall displacement vector, at any given point in a fault zone it is possible to find the preserved evidence for a short term or localised movement that might contradict the overall displacement.  You would be unlucky if the one indicator you found happened to be one of these outliers, but nevertheless, many separate observations of kinematic indicators are needed before you can be absolutely certain of the overall displacement.</p>
<p>2. Remember also that many faults are re-activated by successive tectonic events, and later movements may be completely different to earlier ones.   As a general rule, movement indicators seen in a rock will reflect only the latest phase of movement that has taken place, but like all rules, there are always exceptions.</p>
<p>3. Rock structure is 3-dimentional, but most structures seen in field exposure or on maps and sections are observed on two-dimensional surfaces that are randomly-oriented with respect to the structure.   When interpreting sense of movement structures it must be borne in mind that <b><i>a 2-D surface is only capable of showing  the resolved component of movement on that surface. </i></b> The true movement direction (the movement vector) may lie at any angle to that surface. To determine the true movement direction it is necessary to have some idea of the 3-D shape of the structure. This is best done by observing the structure on several differently oriented planes.</p>
<p>4. All the examples shown in this post (with the exception of <em>&#8220;M</em>&#8220;) show structures observed in the plane of maximum movement i.e. the plane containing the greatest and least stress axes for that deformation (see Part 1) or else in a view looking directly at the fault face (a very common type of natural exposure).</p>
<p><span style="color: #000000; font-family: Arial;"> </span><b><span style="text-decoration: underline;"><span style="color: #000000; font-family: Arial; text-decoration: underline;">Brittle Structures</span></span></b></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/A.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-904" alt="A" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/A-1024x701.jpg" width="1024" height="701" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>A:  Slickenlines (parallel to pencil) developed on a fault surface. The surface containing these lines is called a slickenside &#8211; old Cornish miners term. An alternative name for slickenlines is <strong>striations, </strong>or, if they are deep enough,<strong> grooves</strong>.  These are mechanical scratch marks on the fault surface. Slickensides are common where the fault surface is coated with clay (as in the example shown) or graphite. They indicate the line of movement but not its direction or vector. In this example the  fault is dip-slip, but it could be either normal or reverse. Slickenlines are easily formed and easily destroyed (you can usually make a few yourself with the point of your hammer): as such they are generally unreliable indicators of overall fault movement.</em></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/B.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-905" alt="B" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/B-1024x628.jpg" width="1024" height="628" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>B.  The movement across a small fault at a high angle to layering is easily determined by the displacement of marker beds. However, in this case, even without the marker beds, fault displacement could have been determined by the presence of small calcite-filled dilational jogs along the fault. Such jogs are a type of mineral filled T (tension) surface characteristic of brittle deformation. Although this is an insignificant fault, through a fractal relationship, it gives insight into the movement of an adjacent, unexposed, larger fault of the same generation. This unusual rock from Jervoise, Northern Territory, Australia is a bedded tourmalinite &#8211; which I interpret as a metamorphosed, boron-rich, exhalative sediment.</em></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/C.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-906" alt="C" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/C-1024x677.jpg" width="1024" height="677" /></a></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/12/Lunate-tectoglyphs-line-diagram.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-medium wp-image-1738" alt="Lunate tectoglyphs line diagram" src="http://rogermarjoribanks.info/wp-content/uploads/2021/12/Lunate-tectoglyphs-line-diagram-300x279.jpg" width="300" height="279" /></a></p>
<p style="text-align: left;"><em style="color: #0000ff;">C.  View of the exposed face of a fault which cuts a large (pre-fault) quartz vein.  On the face, short, lineated, crescentic fractures trend away from the fault surface at an angle of around 20 degrees. The low angle and the presence of lineation on the surfaces indicates that these are <span style="text-decoration: underline;">not</span> tensional (T) fractures but <strong>Reidel Shears</strong> (R). The attitude of the shears and the horns of the crescents point to the direction of movement of the missing block (it has moved to the right indicating a sinistral strike-slip movement).  Kerimenge Fault, Wau District, Papua Nugini.</em></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/D.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-907" alt="D" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/D-921x1024.jpg" width="921" height="1024" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>D.  A zone of sigmoidal quartz-filled tension (T) fractures indicates sinistral strike-slip movement on a fault cutting meta-basalt. Poseidon pit, Higginsville, Western Australia.</em></span></p>
<p style="text-align: left;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/12/PAULSEN-SHEAR.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-medium wp-image-1731" alt="PAULSEN SHEAR" src="http://rogermarjoribanks.info/wp-content/uploads/2021/12/PAULSEN-SHEAR-300x198.jpg" width="300" height="198" /></a></p>
<p style="text-align: center;"><em><span style="color: #0000ff;">Sigmoidal quartz tension veins in Proterozoic sandstone, Ashburton Province, Western Australia</span></em></p>
<p style="text-align: left;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/03/gold-veins-Sigma-Mine-Val-Dor-Robert-F-Poulsen-KH-2001-Reviews-Econ-Geol-v14-111-152.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-959" alt="gold veins Sigma Mine, Val Dor Robert F &amp; Poulsen KH 2001 Reviews Econ Geol v14 111-152" src="http://rogermarjoribanks.info/wp-content/uploads/2016/03/gold-veins-Sigma-Mine-Val-Dor-Robert-F-Poulsen-KH-2001-Reviews-Econ-Geol-v14-111-152-758x1024.jpg" width="758" height="1024" /></a></p>
<p style="text-align: center;"><span style="color: #0000ff;"><em>(above) Gold-bearing Tension veins as splays from a small thrust fault exposed on the wall of the Sigma underground Mine, Val D&#8217;or, Canada.  Note the S surfaces (foliation) at 90 degrees to the tension veins. Illustration taken from Robert F &amp; Poulsen KH 2001: <strong>Vein formation and deformation in greenstone gold deposits</strong>. Reviews in Economic Geology v14 pp 111-152.</em></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2025/11/Quartz-fibres-mathew-swift.jpg" rel="wp-prettyPhoto[921]"><a href="http://rogermarjoribanks.info/wp-content/uploads/2025/11/Quartz-fibres-mathew-swift.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-medium wp-image-2633" alt="KODAK Digital Still Camera" src="http://rogermarjoribanks.info/wp-content/uploads/2025/11/Quartz-fibres-mathew-swift-300x225.jpg" width="300" height="225" /></a></a></p>
<p style="text-align: center;"><em><span style="color: #0000ff;">Sheeted quartz fibres with down-dip facing terminations exposed on a vertical fault surface. The missing plate has moved <strong>down</strong> relative to the exposed face &#8211; 70% normal fault dip-slip + 20% dextral strike-slip, movement. Underground gold mine near Kadoma, Zimbabwe. Photo by Mathew Swift. </span></em></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/E.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-908" alt="E" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/E-1024x704.jpg" width="1024" height="704" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>E.  Calcite fibres showing strong lineation and a pronounced &#8220;shingling&#8221; effect coat an exposed vertical fault surface. <span style="text-decoration: underline;">These structures should not be confused with Slickenlines</span> (see A). The facing of the steps (white crescentic lines) indicates sinistral strike-slip movement on the fault (i.e. the missing plate has moved to the right).  Fibres are an example of an overlapping  stack of mineral filled dilational jogs &#8211; a category of T fracture. Although fibres are a more useful and significant movement indicator than Slickenlines, they are generally <span style="text-decoration: underline;">typical of joints and faults with small movement along them</span>.   Any really significant fault movement will usually grind them off<span style="text-decoration: underline;">.</span>   This example from the Snow Mountains, Sichuan, China.</em></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/12/RAV-8-Pit-asbestos-fibres.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-medium wp-image-1732" alt="RAV 8 Pit asbestos fibres" src="http://rogermarjoribanks.info/wp-content/uploads/2021/12/RAV-8-Pit-asbestos-fibres-300x198.jpg" width="300" height="198" /></a><em><span style="color: #0000ff;">Acicular tremolite crystals (fibres) form sheeted overlapping veins on a fault face in peridotite. Missing block has moved down and to the right. RAV8 open cut nickel sulphide mine, Ravensthorpe, Western Australia</span></em></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/F.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-909" alt="F" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/F-1018x1024.jpg" width="1018" height="1024" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>F.  A fine penetrative compressive foliation (S surfaces) in a small clay-filled fault zone indicates dominant normal fault movement. Host rocks are weathered granite (saprolite). </em></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/G.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-910" alt="G" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/G-868x1024.jpg" width="868" height="1024" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>G.  A fine penetrative foliation at 30degrees to the fault zone (S surfaces) shows rotation into the top and bottom shears of a thrust zone. This is an example of a small thrust duplex. Host rocks are sandstone. </em></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/H.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-911" alt="H" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/H-1024x706.jpg" width="1024" height="706" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>H.  A small thrust duplex cutting dolerite. S-surfaces in the fault zone are sigmoidal shaped and clay coated (brown staining). This example from the Nyankanga gold mine, Tanzania.  At this mine, the thrusts are post ore and have a significant effect on ore distribution.</em></span></p>
<p style="text-align: left;"><span style="color: #000000;"><span style="text-decoration: underline;"><span style="text-decoration: underline;">Ductile Structures</span></span></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/I.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-912" alt="I" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/I-1024x753.jpg" width="1024" height="753" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>I.  A sawn surfaces in HQ drill core (left) shows the effects of ductile reverse faulting on a distinctive big feldspar gabbro.  The appearance of the undeformed gabbro can be seen in the core sample at right. A sense of movement can be determined  from the asymmetric chlorite &#8220;tails&#8221; on the margins of relict anorthosite feldspar crystals. In the Mt Ida gold camp, reverse faults such as this are the controls on high grade ore shoots. Note: sense-of-movement indications can only be obtained from oriented drill core.</em></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/J.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-913" alt="J" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/J-1024x707.jpg" width="1024" height="707" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>J.  More sense-of-movement indicators from oriented drill core.  Note asymmetric &#8220;tails&#8221; on the sedimentary clasts at right. Reverse faulting at this gold deposit controls distribution and orientation of high grade ore shoots.</em></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/K.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-914" alt="K" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/K-1024x757.jpg" width="1024" height="757" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>K.  Large orthoclase phenocrysts (<em>that grew during deformation</em> by potassic metasomatism) have grown within, and then been flattened, in a quartz-feldspar-biotite mylonite zone. A dominant pure flattening strain (pure shear) across the rock is indicated, although one phenocryst has slightly asymmetric &#8220;tails&#8221; suggesting a component of dextral strike-slip movement (can you spot it?). The Redbank Zone is a major E-W trending ductile shear zone with a long and complex history. It is at least 20 km wide and can be traced for over 600 km across Central Australia..</em></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/L.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-915" alt="L" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/L-1024x693.jpg" width="1024" height="693" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>L.  A view of the backs (roof) of the Hemlo underground gold mine (the rock-bolt gives scale). The strong foliation of a major shear zone contains an amphibolite band which has broken and been pulled apart in a brittle fashion (boudinage). White quartz and albite has grown in the strain shadows between the amphibolite fragments. As with the previous example, a  dominant pure flattening strain is indicated.</em></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/M.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-916" alt="M" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/M-1024x790.jpg" width="1024" height="790" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>M.  A Section and Level Plan from an underground gold mine. The mine lies within a regional ductile shear zone.  The zone contains lenses of undeformed felsic porphyry &#8211; probably part of a once continuous sill intruded during deformation.  Quartz vein stockworks in the porphyry contain high-grade gold values. Individual veins occupy T (tension) fractures and their orientation indicates that shear movement on the zone was oblique-slip, with a resolved sinistral strike-slip component on plan view, and reverse fault component on cross section. Individual veins are too small to map, but their distribution and shape is reflected in the contoured gold values. Meekatharra is in the Achaean age Yilgarn Craton of Western Australia.</em></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/N.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-917" alt="N" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/N-1024x681.jpg" width="1024" height="681" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>N. A ductile shear zone affecting an Ordovician age basaltic agglomerate at Gympie, Queensland Australia. Asymmetric &#8220;tails&#8221; on the clasts and a small asymmetric fold pair indicate a dextral strike-slip movement on the fault.</em></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2021/12/Sheared-conglomerate-Gympie.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-medium wp-image-1730" alt="Sheared conglomerate, Gympie" src="http://rogermarjoribanks.info/wp-content/uploads/2021/12/Sheared-conglomerate-Gympie-300x240.jpg" width="300" height="240" /></a><span style="color: #0000ff;"><em>Quartzite cobbles in sheared Ordovician conglomerate. Note asymmetric &#8220;tails&#8221; indicating a sinistral sense of shear. Gympie region. Queensland.</em></span></p>
<p style="text-align: center;"><a href="http://rogermarjoribanks.info/wp-content/uploads/2016/01/O.jpg" rel="wp-prettyPhoto[921]"><img class="aligncenter size-large wp-image-918" alt="O" src="http://rogermarjoribanks.info/wp-content/uploads/2016/01/O-1024x681.jpg" width="1024" height="681" /></a></p>
<p style="text-align: left;"><span style="color: #0000ff;"><em>O.  An amphibolite in a migmatite zone has resisted ductile deformation and partial melting. The amphibolite has broken into separate fragments.  In the low-strain zones between the fragments thick zones of quartz-feldspar have grown. Another example of boudinage. Pure flattening strain only.</em></span></p>
<p style="text-align: left;">All comments, questions even crticisms are welcome. Please email me using the details under the &#8220;contact&#8221; tab.</p>
<p>The post <a rel="nofollow" href="https://rogermarjoribanks.info/sense-movement-structures-kinematic-indicators-part-2-examples/">Sense Of Movement Structures in Fault Zones: Part 2: Examples</a> appeared first on <a rel="nofollow" href="https://rogermarjoribanks.info">Roger Marjoribanks</a>.</p>]]></content:encoded>
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