Five rules for use of alpha-beta measurements in drill core

Measurement of planar structure such as a bedding plane a vein or a cleavage in oriented diamond drill core can be done in two ways. The simplest way is to set up the core in its original orientation by means of a core frame and then measure structures within it using a geologists’ compass.  The second way is to measure the angles which the plane makes with lines of known orientation in the core and then, knowing the hole orientation, use these angles to calculate the strike, dip and dip direction. This is called the internal core angles method. I described these methods in some detail in an earlier blog post and discussed the advantages and disadvantages of the two methods (Measuring structures in oriented core, Oct 19 2013). This post provides some further discussion on the internal core angles method and offers five simple rules for their interpretation and use. 

First, to recap the internal core angles method: two angles in the core , called alpha (α) and beta (β) are measured. Their definition is given in the diagram below: alpha and beta angles defined_0001

 In themselves alpha and beta angles are generally meaningless: they have to be converted into a geologically-meaningful strike, dip and dip direction by graphical (stereonet) or mathematical means (appropriate software). Before employing elaborate procedures to convert core angles into the familiar strike-dip measurement, it is important to know that some sets of core angles can be converted by simple mental arithmetic. This point may seem rather obvious, but it is not unknown (indeed it is almost standard procedure) for geologists to mindlessly enter alpha/beta measurements into a computer for processing, where a trivial mental effort could have provided the answer. This is akin to using computer software to add together two 2-digit numbers. As a corollary, if such angles have been entered into a reduction software program, they provide a quick way of checking the accuracy of the computer program, or, more particularly (since errors are unlikely in the software), of the data entry process. Besides this error checking function, it is always better to know the orientation of planar structures at the time of logging rather than at some later date when the structure in core that was actually measured is long forgotten and returned to its stack in the core yard.

 There are four special combinations of alpha/beta angles, detailed below, where strike, dip and dip direction can be derived from alpha and beta angles through trivial mental calculation.  In a fifth example I explain where a particular set of alpha angles indicate that the internal core angles method should not be used and only a core frame can provide the correct answers.

 *In this discussion, Az stands for the AZIMUTH of the drill hole (i.e. the horizontal direction of drilling in compass degrees) and In stands for the INCLINATION of the hole in degrees down from the horizontal. These measurements are taken from the hole orientation survey at the depth from which the measured plane was observed.

 ** No alpha or beta measurements made in core can ever be considered accurate to more than +/- 2 degrees.  Therefore, in the discussion below, for 180° you should read 178° – 182°, for 0° read 358°-002° and for 90° read 88°-90°.

 Rule 1                        If β = 180º, then you are drilling at right angles to strike of the plane and in the direction of its dip. In this case… 

                                    Dip direction = Az

                                    Dip =  In – α    

  1 core beta 180

Rule 2                        If β = 180° and angle α = In, then..

 Dip = 0° (i.e. horizontal)

No strike can be defined 

2 core beta 180 alpha=In

Note that if the measured alpha angle is within a few degrees of the Inclination angle then any computer software will calculate an exact strike for the plane – but strike  will be essentially meaningless since even the smallest error in measuring either α or In will lead to an order of magnitude greater error in the calculated strike.

 

 Rule 3                        If   β = 0º, then the hole is drilled at right angles to the strike of the beds. There are 3 possibilities for the dip:

 (a)Where In + α < (is less than) 90º

                                           Dip Direction = Az

                                           Dip = In + α 

3a core beta 0 In+alpha less than 90

  (b)  Where In + α > (is greater than) 90º, then…. 

                                           Dip Direction = Az + 180º

                                           Dip = 90 – α 

3b core beta 0 In+alpha more than 90

   (c)  Where In + α = 90º, then… 

                                          Strike = Az + 90º (Note: no dip direction can be assigned)

                                          Dip =90º             (i.e. Vertical) 

3c core beta 0 In +alpha = 90

 

Rule 4                        If α = 90º, then the hole is drilled at right angles to the strike of the plane in a direction that is opposed to the dip of the beds. There is no useful definable beta angle (if you think you can measure a beta angle then the number you get is meaningless – see Rule 5). The relationships are these: 

                                                Dip direction = Az + 180º

                                               Dip = 90º – In    

4 core beta 0 In = alpha

 

 Rule 5                        As the angle alpha approaches 90°, the intersection ellipse approaches an intersection circle on which no unique long axis can be defined (see Rule 4). For large α angles it is not possible to define the point E (or E’) on the core surface with sufficient accuracy to enable an accurate measurement of the beta angle.  Small errors in measuring beta can produce large errors in the calculated strike and dip for that bed. How large does alpha have to be for this Rule to kick in There is no fixed cut-off point: every increase in alpha above 50° causes potential measurement  error in beta to rise exponentially. Experience suggests any alpha angle greater than 65º is large - but how much error you are prepared to tolerate is a matter for judgement and is to some extent dependent upon how well the plane is defined in core and how many parallel planes of that orientation are present.

5 two views core with high alpha angle

 Where large alpha angles are encountered the alpha/beta method should not be used and core should be set up in a core frame and the surface measured with a geologists’ compass.

 

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