Computation of Gravity and Magnetic Anomalies of Non-homogeneous and Arbitrarily Shaped Bodies Using Finite Element Techniques

Mello, Ulisses T.

IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598

Abstract

In this study, I discuss alternative techniques to calculate gravity and magnetic anomalies of non-homogeneous, arbitrarily shaped geological bodies by using 2D and 3D finite element discretization. To compute magnetic and gravity anomalies it is common to represent geological bodies by irregular polygons or polyhedral shapes. However with advances in discretization techniques, such as finite element, it is convenient to develop algorithms that take advantage of these advances. These algorithms can be especially useful in cases where gravity and magnetic anomalies need to be computed in association with other calculations using Finite Element Methods such as monitoring of reservoir production, integrated basin modeling and tectonic modeling. Although magnetic and gravity anomalies can be calculated by using traditional finite element solutions for boundary value problems (Laplace and Poisson equations), I suggest the use of finite element Gaussian quadrature as an alternative method. This numerical integration method was extensively tested and is widely available in practically any finite element implementation to compute “stiffness” matrices. This method can also be used as a first step to define the necessary boundary conditions in the boundary value approach instead of large- distance approximations or infinite finite elements currently used on the calculation of domain boundaries. The finite element Gaussian quadrature approach is accurate, fast, easily implemented and parallelized. In addition, it allows an arbitrary representation of complex geological bodies and non-homogeneous property distributions, such as density contrast and magnetic susceptibility, with fewer elements when higher order interpolation are utilized.