Forward modeling the gravitational field using a direct solution of Poisson's equation

Abstract

Forward modeling of gravity data typically computes the vertical gravitational acceleration using either closed-form formulae, or numerical solution of Poisson's equation governing the gravity potential followed by numerical differentiation. We present a method for computing the vertical gravity anomaly directly from Poisson's equation governing the gravitational acceleration, formally relating the gravity anomaly to spatial derivatives of the density function. We first use a finite-difference approximation to obtain the numerical solution, which we later compare to a finite-volume solution approximation. The accuracy of this method is demonstrated through applications to synthetic models and comparisons with integral solutions. This method can also be easily adapted to compute the horizontal components of gravity anomaly with the same order of accuracy, thereby paving the way for studying the prospect of instrument development that may allow acquisition of the horizontal gravity components in the future.