Terrain modeling in forward gravimetric problems: a case study on local terrain effects

Abstract

The computation of the gravitational effect of a known density distribution at an arbitrary point in space is a common task in forward modeling and enters many routine applications in geophysical prospecting and exploration geophysics. The availability of data banks with gravity, terrain and, lately, density data, covering with a rather high resolution large areas mainly of the continental part of the planet, permits the evaluation of gravity field-related quantities not only at individual, but also at normally distributed target points laid on a regular raster. The role of the different geometric approximations used for the representation of the topographic relief is investigated in the frame of several methodologies for the computation of the same quantity: the vertical component of the gravitational attraction resulting from the given masses of a digital elevation model (DEM) assuming a constant density value. The considered methods include the right rectangular prism, the general polyhedron, the mass line and the mass prism FFT methods. Between these purely numerical, purely analytical and hybrid solutions, discrepancies of up to several milligal were detected, using the data of a fairly dense DEM of a part of the Bavarian Alps. The numerical investigations which were carried out using all the above techniques established the polyhedral modeling as the most accurate, flexible and, under circumstances, efficient method for the computation of local gravimetric terrain effects.