A Fast, Spatial Domain Technique for Terrain Corrections in Gravity Field Modelling

Abstract

A fast computation of terrain corrections requires (1) a quick forward algorithm, and (2) a strategy for organising the data in a computer program. In this paper we present some new ideas on (1). The discussion of (2) is very brief. The proposed method is a space domain method, similar to prism integration, but quicker and more flexible. We show that the method works both in the flat-Earth geometry and in the spherical Earth geometry. The “elementary body” of the mass density model is an infinitely thin, horizontal and homogenous rectangular lamina.

The main speedup comes from replacing the exact formulas for the gravitational attraction of a lamina by an approximation, a polynomial model. We argue that such approximation is sufficient to ensure the high accuracy of the approximation. In fact, we have tried it in numerical simulations (not shown here). We chose a polynomial model, because it is straightforward to use it for derivation of similar models for other types of gravity data.

In practice, terrain corrections are computed from height data given on a regular grid in either spherical or Cartesian geometry. The regular grid structure of the terrain information is a particular advantage. For a given grid spacing, and prior to terrain correction computations, one can construct a polynomial model for all the geometrical aspects of the gravity station-mass point configuration. This is valid for any type of gravity data. We briefly mention how such general polynomial model can be used for optimizing the computations of the terrain corrections.