FORTRAN IV Program for Vector Trend Analyses of Directional Data

Abstract

A FORTRAN IV computer program for the IBM 7090/7094 uses orthogonal polynomial trend-surface mapping techniques in the analysis of regional trends in directional data. Direction cosines are used for each cell in the grid to compute the vector mean azimuth, mean dip angle, length of resultant vector, and spherical radius of the circle of confidence around the resultant vector. Linear, quadratic, cubic, quartic, and quintic orthogonal polynomial response surfaces are computed and plotted as isoazimuth and vector trend maps to aid in interpreting regional flow patterns. Residuals from the trend-surface maps emphasize local topographic anomalies on the depositional surface.

The first example output consists of 20 azimuth and dip measurements of cross-bedding from the Wasatch Formation of Wyoming. A second example is based on a study of the orientation of drumlins south of Lake Ontario in New York State. The third example uses cross-bedding measurements from the Pocono Formation in Pennsylvania. In the last two examples, linear, quadratic, and cubic isoazimuth and vector trend maps are used to interpret the major current pattern, and residual maps to outline topographic highs or lows.