# Stereo Net Validation and Interpretation of Structural Measurements

THE STEREONET

A Stereonet is a pre-printed net of intersecting lines which allows the attitude of a measured linear or planar rock structure to be shown as points on a two-dimensional graph. 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 [1]. 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.

But an equally important function of stereonet plots is as a graphical way of showing the distribution pattern 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 be a great aid in 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 the input data. I will show examples of all these effects. Thus, stereonet plots of structural measurements can be a powerful tool in validation of data.

MEASURING STRUCTURE IN ORIENTED DRILL CORE

Problems with erroneous input data are particularly common when measuring planar structure (bedding, cleavage, veins etc.) in oriented drill core (the cartoon figures 8 and 9 graphically illustrate the difference between oriented and non-oriented core). The best way to do this – one that produces fewest errors – is by using a geologists’ compass to directly measure structure in oriented core pieces set up in a Core Orientation Frame (see previous posts HERE and HERE). However, because it is quicker and easier, and no doubt because it a routine mindless process that avoids having to engage mentally with the rocks in front of them, it is my experience that most geologists today measure and record the attitude of planes in core by the Internal Core Angles Method (see previous post HERE). 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 through the use of a special core orientation tool). The two angles, known as  alpha (α) and beta (β), are defined on figure 1, below. Alpha and beta 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 be displayed as a stereonet plot, a histogram or as lines on a drill section.

Figure 1: The angles which define the orientation of a planar structure in oriented drill core. Click for sharper image.

POTENTIAL ERRORS IN MEASURING ALPHA AND BETA

Measuring alpha is quick and easy using any standard protractor. Measurement accuracy is the same irrespective of the value of alpha. It is not dependent on the Bottom of Hole (BOM) orientation line provided by the driller and not dependent on the down-hole direction of the core axis. With any reasonable care on the part of the geologist, alpha angles can be taken as accurate to at least +/- 2°. They are seldom a source of error in the final computer output.

Errors in measuring beta angles cause of almost all problems with the internal core angles method. These errors occur in two areas:

1.       In the BOH mark placed on the core by the driller.

Drillers use one of two methods to determine the position of down gravity vector on the surface of the drill core.

The first method is to measure the orientation of the core barrel after a run of core has been drilled, but before the core is broken free from the ground and brought to surface inside the rod string. The position of the down gravity vector across the barrel is determined by an accelerometer, then stored in a memory against a time stamp. After the barrel with its core has been pulled to surface, the barrel orientation data during the time interval between drilling and extraction is recovered by means of an LCD readout and transferred to the bottom piece of core still gripped by the core lifter. The assumption is that this end piece of core was still attached to Mother Earth when the gravity reading across the core barrel was made. In most cases, this assumption is valid, and the orientation of the barrel is the same as the orientation of this piece of core. The whole drilled core run, with the drillers mark at one end, is then extracted from the barrel, placed in a core tray, and delivered to the geologists to make their measurements. However, where the core is broken or contains a fissile surface (such as cleavage or bedding) the end piece of core may have been broken free by the rapidly turning drill teeth and rotated by some unknown amount prior to it being gripped by the core lifter. In which case, the drillers orientation mark is meaningless. There is no way that the driller can know when this has happened. And there is no easy way that the geologist can know when this has happened.

Figure 2: The REFLEX ACT electronic core barrel orientation tool. This 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 Reflex website.

Electronic tools work perfectly every time at orienting core barrels, but the orientation of the barrel is not necessarily the same as the orientation of the core inside the barrel.

The second method, and generally a much more reliable one, is to orient the core stub before it is drilled. The core stub is the broken rock surface at the bottom of a drill hole which then becomes the top surface of the next drilled run. These systems are all mechanical. They orient the core stub by means of a percussion or wax pencil mark, a shape template, or some combination of these techniques.

In the simplest (and oldest) system, a narrow but heavy steel rod with a pointed tip (known as a spear) is dropped down the rod string. 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 lower edge of the stub. More sophisticated systems use a template to record the shape of the core stub and are equipped with internal level bubbles (lockable before the tool is extracted) to record the gravity direction across the tool at time of impact.

Failure rates for mechanical systems are about as frequent as the failure rates for the electronic systems. But the important difference between them is this: when mechanical systems fail, that failure is almost always obvious. Their results, in other words, are auditable at the point of core recovery and no time need be wasted marking up such core or 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 systems fail. The reverse is also true.

For more details on core orientation systems see my previous post HERE.

At present, to the best of my knowledge, there are no mechanical core-stub orientation tools available for purchase or hire[2]. Only electronic core-barrel orienting systems are available. This is because drillers, and drilling companies get to choose, and they choose one of the electronic systems.  Electronic tools are easier to use than the clunky mechanical systems and their “black box” electronics and LCD readouts give them a 21st Century “sciency” feel.  And as far drillers and the companies [3] that make these instruments are concerned, they provide accurate orientation results every time. A claim that is true with regard to core barrels, but for the actual core inside the barrels, not so much.

Companies that design and manufacture drilling tools do not primarily deal with geologists, they deal with drilling companies. They cannot be blamed for meeting the demands of their customers.

Geologists are the end users of oriented core, but they are often ignorant of, or disinterested in, the details of core orientation systems. Most seem happy to accept whatever system the drilling company offers.

Thus, the bad drives out the good, and geologists have only themselves to blame. I fear that errors in core orientation lines can only get worse.

Figure 3: The pointy end of the EzyMark mechanical core-stub orientation tool. It fits inside the bottom end of the core barrel and slides up inside the barrel ahead of the advancing core. The pins and wax pencil record the shape of the core stub. Lockable level bubbles inside the tool record the gravity vector across the tool at moment of contact. Image accessed in 2019 from www.2icAustralia.com.

2.    In identifying point E

The trace of any planar structure on cylindrical core is an ellipse. The long axis of the ellipse defines points E and E I on the core surface, where E points down hole and E I points up hole (see figure 1, above). E and E I can be recognised as inflection points (points of maximum curvature) on the trace of the plane. Where the alpha angle (the acute angle that E-E 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 tends towards circularity until, at alpha = 90°, the ellipse becomes a circle with no definable axes.  Inflection points become broader and harder to accurately define. Errors in correctly locating point E thus increase as the angle alpha increases. Since measurement of the beta angle is dependent on being able to define point E, this factor 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.

For these two reasons (but particularly the first) mismeasurement of beta is overwhelmingly the major source of error when using the internal core angles method.

There is a simple test to determine if this is a significant factor in you results. Once your alpha/beta data has been recalculated as dip and dip direction, plot these results as poles on a stereonet. For a set of measurements through a volume of rock, the distribution of poles (known as a pole figure) can enable deductions to be made about the accuracy and possible geological meaning of the measurements.

Examples follow in figures 4, 5, 6 & 7.

STREONET VALIDATION AND INTERPRETATION

If your measurements of planar structure across an area or a through a volume of rocks are completely random, their pole figure might look something like figure 4, 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.

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.

Solution: Identify the different structural domains. Group your measurements by domain and plot each group separately.

Figure 4: 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.

If your measurements are accurately made from a set of parallel, or approximately parallel, planar structure (bedding, cleavage etc.), 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 90-α° to the plot of the core axis.

Q: What is the logic behind this number 90-α° ?

A: This is a plot of poles to planes measured in oriented drill core using the internal core angles method. If you refer to figure 1 you will see the poles to these planes lie at 90-α° to the core axis (CA).

Figure 5: 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 more or less 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.

If your measurements of alpha angles are accurate (as is usually the case) but are subject to random error in beta measurement (as can happen when using electronic core-barrel orientation tools), the pole figure plot will show a partial or complete distribution about a small circle at 90-α° to the core axis. There is no known geological process which will produce such a pattern. This pattern is shown in figure 6, below.

Solution: Try using a core-stub orientation system.

Figure 6: 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 more or less 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.

If the pole figure for a large number of measurements taken from scattered surface outcrop or oriented drill core shows distribution about a great circle on the net (figure 7), we can draw several conclusions.

1. The results indicate accurate measurement.
2. The measurements are from a coherent structural domain.
3. The surface has been affected by a cylindrical fold, or a set of parallel cylindrical folds (illustrated by the insert on figure 7).
4. A line at 90° to that great circle (which plots as a point in the opposite segment of the net) represents the trend and plunge of the fold axis or axes. This point is conventionally labelled pi (π).
5. The two weak bedding-plane maxima which can be seen on the great circle of figure 7 can be interpreted as the two limbs of the fold. This is because random measurement across a volume of folded rocks is much more likely to have been taken on extensive fold limbs rather than on restricted fold hinges.  The two maxima further indicates that the fold or folds tend towards similar rather than concentric in style.

Figure 7: 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 set of parallel, cylindrical folds. Click for a sharper image.

AND FINALLY:

Figure 8: Although the orientation of the core axis may be known, the core has rotated by an unknown amount around that axis. Cartoon by RM, 2018
Figure 9: The core is now fully oriented in 3D space. Cartoon by RM 2018.

[1] A stereonet is a nomogram. A nomogram is a graphical analog computation device that offers an approximate graphical solution to a mathematical problem – in this case the stereonet, problems in spherical trigonometry. The classic example of a nomogram is the slide ruler.

[2] If any reader knows of a current commercially available core stub orientation tool, please let me know. The last such system that I am aware of was the EzyMarkTM, designed and made by 2icAustralia.com.au, taken over by Reflex a few years ago and sold as their AuditorTM System, but now apparently discontinued by them.

[3] The two electronic systems that I am aware of are the ACTTM System made by the Reflex company and the TruCoreTM system made by Boart-Longyear. There may be others.