When dipping layers are encountered in a borehole, and we have a core sample to study, we know two facts: the dip of the bed relative to the borehole, and the location of the bed below the surface. What we don't know is the strike and the dip direction, because the core sample rotates as it comes out of the hole. It is difficult and expensive to get oriented samples from drill holes, although downhole cameras have greatly improved matters.
Two boreholes are sufficient to narrow the strike and dip to two alternatives. Of course, three boreholes define the strike and dip uniquely because we have three elevation points in the plane.
In the borehole above, the bedding plane has dip D and intersects the core with angle U. The bed could have all possible strikes, and the range of possible bedding orientations outlines a cone with an apical angle of 2U.
If the angle U is significantly different in the two boreholes, the structure is not planar.
If the sample occurs at depth h, the possible outcrops of the bed at the surface lie somewhere on a circle of radius r. The radius of the circle is given by r = h Cot D = h Tan U. (You can also solve the problem graphically, by drawing a cross-section as above)
Two such boreholes define two circles. In practice it is most convenient to refer depths to a common datum elevation. When we do this, the strike of the plane must be tangent to both circles.
This construction requires that the circles be on the same plane. If they're not, then a line tangent to the circles won't be horizontal, and therefore will not be the true strike. Thus all depths have to be calculated with respect to some convenient datum plane.
If one circle contains the other, there are no solutions. This most often happens if there is a fault or other structural disturbance between the two boreholes. If the circles intersect there are only two lines tangent to both and both are possible strike directions. If the circles touch, there are three tangents and if the circles are separate there are four. However, in every case only two are possible strike directions.
The rule for telling valid strike directions is simple: lines that pass between the circles are not permissible because the bed would have to dip in two directions at once. The dip is always toward the centers of both circles.
In practice, and why this technique is useful, is that we can often rule out one of the two strike directions because it does not agree with other geologic data from the area. If we know the structures are upright folds trending 25 degrees, and our strike directions from borehole data are 27 and 84 degrees, the 27 degree strike is much more likely to be correct.
We may have two boreholes but only one dip measurement. For example, the critical portion of the core may be too highly farctured in one borehole. Two boreholes allow us to confirm that the structure has the same dip in both and is in fact a plane. If we only have one dip determination, we have to assume the structure is a plane (which may or may not be true). Assume the dip is the same in both the known and the unknown borehole and proceed as usual, but be careful in applying the results.
1. Given the borehole data, find the possible strike of the marker bed encountered in each borehole. We also know that regional structural trends are as shown.
2. By construction or calculation, find the radii of the circles where the bedding plane might intersect the surface.
3. Construct the circles.
4. Draw the possible strike orientations (you already know the dip). In this case direction b is most likely to be the strike direction.
It may happen that we have a borehole and an outcrop, but we cannot get an attitude measurement (too massive, too fractured, etc.). We can think of the outcrop as a borehole of zero depth. If we place the datum plane at the elevation of the outcrop, we will have one circle defined by the borehole and a point (or a circle of zero radius) at the outcrop. The strike must pass through the outcrop and be tangent to the circle.
1. We have a single borehole and an outcrop.
2. By construction or calculation, find the radius of the circle where the bedding plane might intersect the datum plane at the elevation of the outcrop.
3. Construct the circle.
4. Draw the possible strike orientations.
Created 17 March 1999, Last Update
31 January 2012
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