Near-station terrain corrections for gravity data by a surface-integral technique

Abstract

A new method of computing gravity terrain corrections by use of a digitizer and digital computer can result in substantial savings in the time and manual labor required to perform such corrections by conventional manual ring-chart techniques. The method is typically applied to estimate terrain effects for topography near the station, for example within 3 km of the station, although it has been used successfully to a radius of 15 km to estimate corrections in areas where topographic mapping is poor. Points (about 20) that define topographic maxima, minima, and changes in the slope gradient are picked on the topographic map, within the desired radius of correction about the station. Particular attention must be paid to the area immediately surrounding the station to ensure a good topographic representation. The horizontal and vertical coordinates of these points are entered into the computer, usually by means of a digitizer. The computer then fits a multiquadric surface to the input points to form an analytic representation of the surface. By means of the divergence theorem, the gravity effect of an interior closed solid can be expressed as a surface integral, and the terrain correction is calculated by numerical evaluation of the integral over the surfaces of a cylinder, The vertical sides of which are at the correction radius about the station, the flat bottom surface at the topographic minimum, and the upper surface given by the multiquadric equation. The method has been tested with favorable results against models for which an exact result is available and against manually computed field-station locations in areas of rugged topography. By increasing the number of points defining the topographic surface, any desired degree of accuracy can be obtained. The method is more objective than manual ring-chart techniques because no average compartment elevations need be estimated ?