Computers & Geosciences Vol. 18, No. 9, pp. 1107-1119, 1992 0098-3004/92 $5.00+ 0.00 Printed in Great Britain. All rights reserved Copyright© 1992PergamonPress Ltd A NEW TECHNIQUE FOR THE ANALYSIS OF DIRECTIONAL AND ORIENTATIONAL DATA ADEL R. Moustafa* Faculty of Earth Sciences, King Abdulaziz University, P.O. Box 1744, Jeddah 21441, Saudi Arabia (Received 7 May 1991; revised 5 October 1991; accepted 16 March 1992) Abstract--A new technique (termed sorting technique) is proposed in this study for the analysis of geologic directional and orientational data. A sorted part of the data is analyzed by 3-D vector analysis for accurate determination of the mean preferred direction (or orientation) and plunge (or dip). A PC FORTRAN program (VECTOR) is given herein to facilitate the sorting and vector analysis of data sets. Two examples of geologic L- and S-data also are given and processed to show the applicability of the new technique. Key Words: Analysis of geologic L- and S-data, Sorting geologic L- and S-data, 3-D vector analysis. INTRODUCTION The spatial position of geologic features can be represented by directional or orientational data. Directional data are used for linear features (L-data); for example glacial striations, paleocurrent direc- tions, slickenside lineations, fold hinges, etc. Orienta- tional data are used for planar features (S-surfaces); for example bedding surfaces, foliations of metamor- phic rocks, etc. L-data are represented by trend and plunge angle whereas S-data are represented by strike, dip direction, and dip angle. The geologic analysis of L- and S-data involves the construction of lower hemisphere projections such as scatter diagrams which are analyzed statistically in almost all situations by the construction of contour diagrams (Turner and Weiss, 1963). The constructed contour diagram shows the clustered data in the form of girdles or maxima. It is not unusual that such maxima are too wide to allow the accurate identifi- cation of the mean preferred direction or orientation. It therefore is a usual practice to use the centers of such maxima to represent the mean direction of preferred orientation although these centers do not necessarily represent the statistical mean. A new technique is proposed in this study through which some of the data are sorted and analyzed by 3-D vector analysis. Scatter and contour diagrams first are constructed for the whole data. These dia- grams help determine the parameters of the sorting process. These parameters are in the form of mini- mum and maximum values of trend (or strike) and minimum and maximum values of plunge (or dip). The sorted data are analyzed by 3-D vector algebra. A PC FORTRAN program is given herein (Appendix *Present address: Department of Geology, Faculty of Science, University of Kuwait, P.O. Box 5969, Kuwait 13060. 1) to facilitate the sorting of the data and the application of 3-D vector analysis to the sorted subpopulation. Two examples of geologic data also are given, one for L-data and the other for S-data. These two sets of data are processed by the sorting technique in order to evaluate its validity. 3-D VECTOR ANALYSIS Vector analysis has been dealt with in several publications; for example Steinmetz (1962), Green (1964), Mardia (1972), Spiegel (1974), Priest (1985), and Davis (1986) among others. A vector is a line that has both magnitude (or length) and direction. The direction of a vector is represented by its trend (a) and plunge (~). A vector (V) can be defined by three mutually perpendicular components (Vx, Vy, and V z) relative to the Cartesian coordinate axes x, y, and z (Fig. 1). The positive end of the coordinate y axis coincides with the north direction in geology. There- fore, the trend (a) of a certain line is measured clockwise from this position. As we are concerned in geology with lines in the lower hemisphere, all lines (vectors) will have positive Vz components. Each line in a set of geologic data can be con- sidered a unit vector, that is a vector of magnitude (length) equal to one. The three components of each vector can be calculated in terms of a and/~ where Vx = sin ~ cos ~ (1) vy = cos • cos ~ (2) v~ = sin//. (3) The procedure followed in vector analysis depends on calculating the x, y, and z components of each vector. The obtained values are used to calculate the resultant vector which is comparable to the mean of nondirectional data. The resultant vector also has a magnitude (V,) and direction. The direction is rep- 1107