CHAPTER THIRTY-TWO: STRUCTURAL ANALYSIS 2
Unconventional Dipmeter Methods

Table of Contents
32.00 Introduction To This Chapter
32.01 Statistical Curvature Analysis Techniques - SCAT Diagrams
32.02 Analyzing Dipmeters with Tangent Diagrams
32.03 Dipmeter Calculations With Stereonets
32.04 In Conclusion
32.05 Exercises for Chapter Thirty-Two
32.06 Bibliography for Chapter Thirty-Two

Continue to Chapter Thirty-Three

Publication History: This material formed part of Chapter Six of Volume Two of The Log Analysis Handbook, part of a series of seminars offered by the author beginning in 1979. Updated 1985, 1993. All of the material in this Chapter was condensed from sources stated in the text. Revised and re-organized for this electronic edition Oct 2002.

CHAPTER THIRTY-TWO: STRUCTURAL ANALYSIS 2
Unconventional Dipmeter Methods

32.00 Introduction To This Chapter
Traditional dipmeter analysis techniques used for structural analysis involve pattern recognition on the dip arrow, or tadpole, plot as described in Chapter Thirty-One. While this approach can be learned with study and practice, there are other approaches that can be applied.

Stratigraphic traps, created by the juxtaposition of porous and nonporous rocks, are described in Chapter Thirty-Three. Dipmeter tools and calculation methods are covered beginning in Chapter Twenty-Six, which is a prerequisite to this Chapter. If you plan to use existing dipmeter data for serious exploration, you must be aware of the differences and limitations of each tool.

32.01 Statistical Curvature Analysis Techniques - SCAT Diagrams
Alternatives to the conventional arrow plots have been proposed, mainly because of the effects of statistical variations and ambiguous patterns which sometimes make arrow plots hard to use. The most successful technique is called statistical curvature analysis, better known as SCAT. The method lends itself to interactive computer programming, and was described by C.A. Bengtson in "Statistical Curvature Analysis Techniques for Structural Interpretation of Dipmeter Data", published in AAPG Bulletin in 1981. The paper was also printed in Oil and Gas Journal, June 1980 and in Geobyte, May 1988.

Microcomputer programs for analyzing dipmeter data in this way were presented by Robert Elphick in the May 1988 and March 1989 issues of Geobyte. These programs do not seem to be available from the major service companies.

SCAT is based on four unfamiliar, but empirically well verified, geometric concepts:
1. structural curvature
2. transverse and longitudinal structural directions
3. special points on dip profiles
4. dip isogons or trend lines

Flat or dipping planes have zero or planar curvature. Horizontal or plunging folds have one degree of curvature. Doubly plunging folds have two. Drag and rollover on faults have structural curvature and can be analyzed in the same way as folds. Illustrations of typical surfaces and their dip angle vs dip azimuth plots are shown in Figure 32.01.

FIGURE 32.01: Dip angle vs azimuth plots - basic shapes

The obvious difference between SCAT and the conventional approach is that SCAT uses the dip angle vs dip azimuth plot plus four other machine plotted dip vs depth displays, whereas the conventional method relies on an all purpose display, the arrow plot, augmented by azimuth frequency plots over selected intervals.

The five plots used in SCAT are:
1. dip angle vs dip azimuth
2. dip azimuth vs depth
3. dip angle vs depth
4. transverse section dip angle vs depth
5. longitudinal section dip angle vs depth

Another plot could be generated, based on the analyst's interpretation of the transverse section vs depth. Examples are shown in Figures 32.02 through 32.06.

The patterns on dip angle vs dip azimuth plots may be simple or complex. However, they are usually simpler and never more complex than patterns on arrow plots.

Arrow plots show complex patterns when a well crosses a crestal plane, but transverse dip component plots show smooth trend lines that cross the zero dip axis. Because angle of dip on an arrow plot is neither positive nor negative, there is no chance for a negative scatter to cancel positive scatter in a flat dip situation. Therefore, a zone of zero dip is falsely perceived as a zone of a few degrees average dip with varying dip azimuth. On a dip component vs depth plot, however, half of the points will fall to the right of the zero dip axis and half to the left, correctly indicating zero average dip (Figure 32.02).

SCAT resolves the data into mutually perpendicular transverse and longitudinal (or T- and L-direction) components, using the dip rotation arithmetic described in Chapter Twenty-Seven. The T-direction is defined as the direction of cross section through the well that shows the greatest structural change, and the L-direction as the direction that shows the least structural change. These directions are chosen from the locations of the maximum and minimum dip angle scatter on the dip angle vs azimuth plot, marked T and L on Figure 32.02. They are usually orthogonal directions and can be picked by eye or by statistical analysis.

Average L-direction component of dip is zero for planar and nonplunging fold settings and equal to the angle of plunge for plunging fold settings. On plunge reversal settings the average L-direction component of dip shows a reversal of dip (and hence plunge) with depth. The only exceptions occur in wells cut by cross faults. However, longitudinal dip component plots may show considerable scatter in zones of steep dip.

The shape of the statistical trend line on a transverse dip vs depth plot defines the bedding curvature on a transverse cross section. A trend line conforming to constant dip indicates planar curvature. A smoothly curved trend line with no bends or reversals indicates uniform or smoothly varying curvature, whereas a trend line with bends or reversals will show one or more of eight mathematically definable patterns or special points.

Six of these points serve to locate and identify structural surfaces (axial planes, kink planes, inflection planes, secondary inflection planes, minimum curvature planes, and zero strain boundaries) that intersect the well, and two serve to locate dip-slip faults, distinguishing faults that dip to the right from faults that dip to the left.

Finally, it should be stressed that SCAT has the capacity to find the bearing and plunge of crestal and trough lines of folds, the strike and dip of crestal, axial, and inflection planes of folds, and the strike and direction of dip of dip-slip faults. Dip arrow plots do not handle this function very well.

The concept that there are only a few types of structural curvature greatly simplifies interpretation. Beds are either planar or curved; if planar, the beds are either horizontal or dipping. A zero dip homocline shows no structural change in any direction and hence has no T- or L-directions, as in Figure 32.02 (top). In the low and higher homoclinal dip settings (Figures 32.02 bottom, 32.03 top) the T-direction parallels the dip and the L-direction parallels the strike. Patterns on T, L, and azimuth vs depth plots are vertical and a maximum density of points will occur at the average regional dip on the dip vs azimuth plot.

FIGURE 32.02: SCAT plots for zero dip setting

FIGURE 32.03: SCAT plots for homocline and fold settings

If the beds are curved, they are either singly or doubly curved. If single curved, their crestal or trough lines are either horizontal (Figure 32.03 bottom) or plunging at a constant angle (Figure 32.04 top). In either situation, the T-direction is perpendicular to the crestal or trough lines and the L-direction is parallel. The L component graph will be vertical. The others will be curved. The depth of crestal, axial, and inflection planes are found by observation of the bends in the trends.

FIGURE 32.04: SCAT plots for plunging fold settings

If the beds are doubly curved, their structure contours are either elliptical or circular in plan. If elliptical (Figure 32.04 bottom), their geometry can be approximated by two singly curved plunges joined by a non-plunging central sector, in which case the T-direction is perpendicular to the crestal or trough lines and the L-direction parallels the long dimension. If the structure contours are circular, the transverse directions will converge radially toward the center, and the longitudinal directions will be disposed circumferentially around the center. L-component patterns also have bends.

SCAT plots through faults show the pattern of the structural setting around the fault and the drag is superimposed on it. The fault usually creates a cusp on the transverse dip section, pointing in the direction of the dip of the fault for normal faults and opposite to the dip for reverse faults. (Figures 32.05 and 32.06). The drag patterns are quite distinctive on SCAT plots and help to differentiate faults from folds. Rollover creates a half cusp pattern. These patterns are similar to red and blue patterns seen on dip arrow plots of faults.

FIGURE 32.05: SCAT plots for fault settings

FIGURE 32.06: More SCAT plots for fault settings

32.02 Analyzing Dipmeters with Tangent Diagrams
Some structural analysis problems are easier to visualize when transformed into a single two dimensional domain instead of several, as arrow and SCAT plots do. The two methods available are tangent diagrams and stereonets. Tangent diagrams were described very well by C.A. Bengtson in Geology Vol 8 No 12 (1980) in "Structural Uses of Tangent Diagrams", reprinted in Geobyte, Mar 1989, along with an interactive computer program written by Robert Elphick.

Tangent diagrams, such as the example shown in Figure 32.07A, are special polar coordinate graphs that provide convenient graphic solutions for many problems of structural geology. Direction of dip is read at the circumference, and angle of dip is read from the concentric circles. The radius of each circle is proportional to the tangent of the angle of dip. High dips, therefore, plot farther from the center than low dips. The distinctive feature of this method of display is that planes can be represented by vectors, in a manner similar to stereonets, although tangent diagrams are more easily applied than stereonets.

FIGURE 32.07A: Polar plot for tangent diagram

Figure 32.07B, a block diagram of a sloping plane, illustrates the basic principle of the tangent diagram. Line B1 is a horizontal line in the direction of true dip, and B2 is another horizontal line making an angle with B1. The trigonometric relations on this drawing demonstrate that the tangent of apparent dip in any direction is equal to the tangent of the true dip times the cosine of the angle between the directions of true dip and apparent dip.

FIGURE 32.07B: Tangent diagram for homocline

The problem of finding apparent dip from true dip can be resolved vectorially on a tangent diagram, as shown in Figure 32.07B (right):
1. plot V1, the true dip, as a vector from the origin with length proportional to the tangent of the angle of dip.
2. draw a line V2 in the direction of the apparent dip.
3. from the end of V1, draw a line perpendicular to V2.
4. read the apparent dip from the intersection of the two lines.

Figure 32.08 (top left) shows how the tangent diagram is used to find true dip from two apparent dips:
1. plot V1 and V2, the two apparent dips.
2. draw perpendicular lines through their end points.
3. read the true dip, V3, from the intersection of the perpendicular lines.

If two planes intersect, they have equal apparent dips in the vertical plane containing their line of intersection. Figure 32.08 (top right) shows how this principle is used to find the line of intersection of two planes.
1. plot V1 and V2, the true dip vectors of the two planes.
2. connect the end points of the two vectors with a straight line.
3. draw V3, the perpendicular from the origin to the straight line. This vector gives the bearing and plunge of the line of intersection of the two planes.

The lines of intersection of planes tangent to the bedding on the same or opposite flanks of an ideal cylindrical fold are parallel to the crestal line. Dip measurements obtained at random locations on such a structure will fall on a straight line when plotted on tangent diagrams, as exemplified by the dashed line in Figure 32.08 (middle). The line for non-plunging folds passes through the center of the plot, plunging folds to one side (Figure 32.08 bottom). Cylindrical folds plot as straight lines and conical folds as curved lines (Figure 32.09).

FIGURE 32.08: Tangent diagrams for finding true dip and strike of folds

FIGURE 32.09: More tangent diagrams for folds

32.03 Dipmeter Calculations With Stereonets
The stereonet is an old, traditional tool for dipmeter analysis that has become unconventional by the passage of time. Developed before the days of calculators and computers, it allowed computation of many complex tasks that were tedious to perform by hand. Numerous software packages are available now to plot this data more neatly than can be achieved with pencil and paper.

These tasks include finding the projection of a plane, direction of a line normal to a plane, the line of intersection of two planes, angles between two planes, true dip from two apparent dips and vice versa, and regional dip removal. Some of these functions have been described earlier, using the calculator, SCAT, or tangent diagrams. Some people still prefer the stereonet, but the calculator is easier.

These instructions are paraphrased from "Schlumberger Dipmeter Fundamentals 1981", and the stereonets are copied from the previous edition dated 1970. For working through stereographic problems you should have a stereonet such as the one in Figure 32.10, plus pieces of tracing paper large enough to cover it, or a plastic overlay, made from a xerographic reproduction of Figure 32.11. These two illustrations are used for high angle dips. Figures 32.12 and 32.13 are enlarged versions of the central portions of the previous illustrations, and are used for low angle dips.

FIGURE 32.10: Stereonet for high angle dip

FIGURE 32.11: Stereonet overlay for high angle dip (reproduce on clear film)

FIGURE 32.12: Stereonet for low angle dip

FIGURE 32.13: Stereonet overlay for low angle dip (reproduce on clear film)

The data for each problem are plotted on the tracing paper or overlay, and the stereonet is rotated to suit the differing orientations met with in each case. Although it is usually more convenient to lay the stereonet down and keep it fixed, while rotating the tracing paper over it, keep in mind that it is the tracing paper overlay, and not the net, that represents the fixed Earth.

If you use tracing paper, trace the outer circle of the stereonet on it and mark a "north" point with an N on the circle at some arbitrary point. Tracing the outer circle is necessary so that the two diagrams - overlay and stereonet - can be kept concentric in all orientations. You could achieve the same result by pinning the two layers together so that the tracing paper rotates about the center point of the stereonet. No matter how the overlay is rotated, the N point should be regarded as always pointing north.

If you use a transparent copy of Figure 32.11 or 32.13 as your overlay, the circle and north point (0/360 degrees) are already marked. Use a grease pencil to mark points and lines, so it can be wiped off before the next example.

To understand how a stereogram is constructed, imagine standing on level ground and looking down into a hemisphere contoured at our feet and extending down into the ground, as if the ground were transparent. Any plane that passes through the center of a sphere cuts the spherical surface in an arc called a great circle. If we stand on an outcrop of a bed dipping down into the ground, we can imagine that the bed cuts the underground hemisphere with an arc of a great circle, as in Figure 32.14, top right.

FIGURE 32.14: Stereonet - basic concepts

To project that circle up to the horizontal surface at ground level, we connect every point on the great circle to the zenith point of the sphere, above our head. The intersection of the lines with the horizontal plane form a new circle; many such circles form the north south grid lines of the stereonet, Figure 32.14, middle left.

The intersections of vertical planes that do not pass through the center of the sphere intersect the hemisphere surface as small circles and can be projected up to the stereogram surface, via the zenith point, exactly as before, Figure 32.14, lower right. These form the circles that are centered on the north and south poles, forming the east west grid on the stereonet. Superposition of the two sets of circles creates the final stereonet presentation, Figure 32.14, lower left.

A straight line passing downward at a slant through the point at which we are standing cuts the hemisphere at a point that can be projected onto the stereogram by the same technique. Again, the zenith point provides the reference for the projection, Figure 32.15, top right. Both lines and planes can be plotted on the same diagram, Figure 32.15, middle right. Horizontal and vertical planes are special cases; the projection of a horizontal plane is the outer edge of the stereonet, a vertical plane passing through the center is a straight line, Figure 32.15, lower right.

FIGURE 32.15: Lines and planes on the stereonet

Figure 32.16, upper left, shows how to plot the projection of a plane dipping 20 degrees in a N 40 degrees E direction:
1. trace the outer circle of the stereonet onto the overlay and mark a "north" point on it. It helps to add the other cardinal points and the center.
2. find N 40 degrees E on the edge of the stereonet and mark this point on the overlay. A line drawn between this point and the center represents the direction of dip of the plane.
3. find a great circle appropriate to a dip in this direction by rotating the overlay until the N 40 degree E dip line lies along the east-west diameter. It doesn't matter whether you choose to point the dip line toward the east or the west, because we are going to return it to its rightful orientation later.
4. now trace in the great circle arc corresponding to 20 degrees of dip. The outer circle of the stereonet represents zero dip, so count the 20 degrees inwards from the edge. Do not use the dip angles marked on the overlay - they count degrees in the opposite direction.
5. finally, rotate the overlay back to bring north to the top. The curve on the overlay now represents the great circle which describes a dip of North 40 degrees East.

FIGURE 32.16: Projection of a plane

Figure 32.16, lower right, shows how to plot the direction of the line normal to the surface of the plane in example 1.
1. rotate the overlay on the stereonet to place the dip line onto the east-west axis.
2. the normal to a plane makes a 90 degree angle to the plane in all directions; therefore count 90 degrees from the great circle projection along the east-west diameter and mark point P.

Note that it doesn't matter in which direction you count along the diameter; if you should choose the direction that brings you to the edge of the net before reaching 90 degrees, jump to the other end of the diameter and finish counting from there. Check that both directions bring you to point P.
3. rotate the overlay back to the position with north at the top, and check that point P lies in the southwest quadrant, as you would expect.
4. this point, which represents the direction of the line normal to the given plane, is called the "pole" of the plane.

Figure 32.17, upper left, shows how to find the line of intersection of two planes: Given: plane A dips 20 degrees toward N 40 degrees E (the plane in example 1). plane B dips 30 degrees towards N 20 degrees W.
1. plot the projections of these planes on the stereonet as in example 1.
2. point P is the point of intersection of these two curves, and it therefore represents the projection of the line of intersection.
3. rotate the overlay to bring point P to the north-south diameter of the stereonet, and read off its bearings. Count inward from the edge to find the dip angle and observe the direction along the edge of the stereonet. The line of intersection dips about 19 3/4 degrees in a direction 31 degrees east of north.

FIGURE 32.17: Line of intersection of two planes

Figure 32.17, middle right, shows how to find the angle between the two planes in the previous example. Given: plane A dips 20 degrees toward N 40 degrees E (the plane in example 1). plane B dips 30 degrees towards N 20 degrees W.
1. find the poles of the two intersecting planes (PA and PB), and also the great circle for which the point of intersection, P, is the pole. Notice that PA and PB both lie on this great circle, which follows from the fact that the plane normal to the line of intersection must also be perpendicular to both the given planes. Hence their poles lie on its great circle when plotted on the stereonet.
2. find the dihedral angle between the planes, by either:
a. measure the angle between PA and PB, or
b. measure the angle between the original planes directly, using the third great circle as the measurement path.

Both methods should give the same answers, of course. Notice, however, that with the first method the angle measured directly between PA and PB is 26 degrees, while the angle between the great-circle arcs is 154 degrees. Because 26 degrees + 154 degrees = 180 degrees, we know that 26 degrees is the acute dihedral angle and 154 degrees is the obtuse dihedral angle between the given planes.

Figure 32.17, bottom left, shows how to find true dip from dip measured in two different vertical planes: Given: dip A is 25 degrees, in a plane N 30 degrees E and dip B is 20 degrees, in a plane N 40 degrees W
1. plot these measured dips on the stereonet.
2. rotate the overlay until you find, by trial, the position for which these two points lie on the same great circle, and trace in that great circle arc.
3. true dip angle and azimuth, 28 degrees at N 3 degrees E, can then be read directly from the stereonet.

Notice that this procedure can be worked backwards, to find the slope of a bed on any azimuthal direction if the true dip is known. First trace in the great circle for the bedding plane, knowing its dip; then find where this arc cuts a radial line drawn with the desired azimuth. You would need to do this twice to find transverse and longitudinal dip components.

If an inclined formation contains smaller bedded units within it, the computed dips of the subunits need to be corrected, by subtraction of the dip of the major system, to find their dips at the time of deposition. For the stereonet, the problem is that of rotating one plane by an amount, and in a direction, given by the dip of the other.

Figure 32.18 at the right shows how to eliminate structural dip from computed dip. Given: formation dip of 30 degrees, azimuth N 20 degrees E structural dip of 15 degrees, S 40 degrees W
1. plot the plane of the regional dip and add P, the pole of the formation dip.
2. rotate the structural plane to the horizontal by moving its projection until it lies entirely on the outer circle of the stereonet.
3. rotate the other plane through the same angle, which means moving its pole, point P, across the stereonet by the same distance and in the same direction as we move the projection of the structural plane. Be careful to measure "distance" in degrees and use the small circle arcs as guides to direction. So when the major plane rotates 15 degrees back to the horizontal, point P must move 15 degrees along a small circle arc to position P1.
4. the dip of the sedimentary unit at the time of deposition was 46 degrees, azimuth N 25 degrees E.

32.04 In Conclusion
In this Chapter, use of the dipmeter to delineate structural events has been explained using non-traditional methods. You may find these approaches more satisfying than the traditional arrow plot.

Although dipmeter analysis can be ambiguous, sufficient geological constraints, local knowledge, and experience serve to improve skills and speed analysis. Modern computer processing, in particular regional dip removal, are essential ingredients.

32.05: Exercises for Chapter Thirty-Two
Exercise 32.01: Structural Concepts - SCAT
1. What are the five diagrams that make up a complete SCAT diagram. (10 marks)

2. Draw the cross section and contour map represented by this SCAT diagram. What kind of structure does it represent? (25 marks)

3. Draw schematic SCAT diagrams for this fault. (25 marks)

4. Describe the uses and advantages of tangent diagrams. (10 marks)

5. Describe the uses and advantages of stereonet diagrams. (10 marks)

6. What alternative methods could replace the SCAT, tangent, and stereonet methods? Give at least three examples. (20 marks)

32.06: Bibliography for Chapter Thirty-Two
1. Fundamentals of Dipmeter Interpretation - Schlumberger Training Aid, 145 p., 1970

2. Dipmeter Fundamentals, Schlumberger, 1981

3. Dipmeter interpretation, Schlumberger, 1986

4. Statistical Curvature Analysis Techniques for Structural Interpretation of Dipmeter Data, C.A. Bengtson, AAPG Bulletin, 1981. Also Oil and Gas Journal, June 1980 and Geobyte, May 1988.

5. Structural Uses of Tangent Diagrams, C.A. Bengtson, Geology Vol 8 No 12, 1980,reprinted Geobyte, Mar 1989

ABOUT THE AUTHOR

E. R. (Ross) Crain, P.Eng. is a Consulting Petrophysicist and a Professional Engineer with over 35 years of experience in reservoir description, petrophysical analysis, and management. He has been a specialist in the integration of well log analysis and petrophysics with geophysical, geological, engineering, and simulation phases of oil and gas exploration and exploitation, with widespread Canadian and Overseas experience.

His textbook, "Crain's Petrophysical Handbook on CD-ROM" is widely used as a reference to practical log analysis. Mr. Crain is an Honourary Member and Past President of the Canadian Well Logging Society (CWLS), a Member of Society of Petrophysicists and Well Log Analysts (SPWLA), and a Registered Professional Engineer with Alberta Professional Engineers, Geologists and Geophysicists (APEGGA)