Fast finite-element calculation of gravity anomaly in complex geological regions

Forward computation of the gravity anomaly of a density model is often a necessary step in modelling the subsurface density of a region. For geologically complex regions, this step may be computationally demanding and become the bottleneck in gravity inversion. We present a fast finite-element method (FFEM) for solving boundary value problems of the gravitational field in forward computation of gravity anomaly in complex geological regions. Testing against analytical solutions show that the method is more accurate than the classical integration method in cases where density in the material body is highly heterogeneous. At the same time, FFEM is more efficient than the integration method by a factor between s/100 and s/10, where s is the number of stations at which gravity anomalies are computed. Since s is usually much greater than 10-100 in 3-D gravity inversion in geologically complex regions, FFEM may be significantly more efficient in gravity modelling of such regions. We illustrate the utility of this method by calculating the gravity anomalies in central Taiwan.