Abstract

The graphical stereonet methods usually employed to obtain original direction of dip and original amount of dip from cross-beds in structurally tilted strata are time-consuming and subject to operator error. A trigonometric solution has been devised and a FORTRAN IV computer program has been written to perform the rotations. The pole positions of (1) the plane of the horizontal, (2) the plane of normal bedding, and (3) the plane of cross-bedding form a spherical triangle in which two sides and the enclosed angle are known. Trigonometric functions are used to solve for the remaining side (amount of original dip) and one of the remaining angles (from which the azimuth of the rotated dip direction can be determined). Inputs to the computer program are strike and dip of normal beds and strike and dip of cross-beds as usually recorded in the field, for example, N. 30° E., 40° SE.; N. 50° E., 55° SE. Special provision is made for rotations on overturned beds. Output is the azimuth of the rotated dip direction and amount of rotated dip, for example, 172, 21. The results can be fed directly to another program to calculate vector means and other statistical parameters. This trigonometric computer method can be used to perform other types of rotations, either to the horizontal or to a specified plane, for structural analyses.

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