# COMPUTATION OF GRAVITY AND MAGNETIC ANOMALIES OF
NON-HOMOGENEOUS AND ARBITRARILY SHAPED BODIES
USING FINITE ELEMENT TECHNIQUES

*Ulisses T. Mello*

IBM Thomas J. Watson Research Center

## Abstract

In this paper, 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 the advance of
discretization techniques, such as finite elements, it is convenient to
develop algorithms that can take advantage of these advances. These
algorithms can be especially useful in cases that gravity and magnetic
anomalies need to be computed associated with other calculations using
Finite Element Methods such as monitoring of reservoir production,
integrated basin modeling, tectonic modeling, and mantle flow. 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 is extensively tested
and widely available in practically any finite element implementation to
compute “stiffness” matrices. This method can also be used as first step to
define the necessary boundary conditions in the boundary value approach
instead of large-distance approximations or infinite finite element currently
used on the calculation domain boundary. The finite element Gaussian
quadrature approach is accurate, fast, and 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 functions are utilized.
Key Words: Gravity anomalies, magnetic anomalies, integrated basin
modeling, finite element Gaussian quadrature, finite element method,
variable density contrast, arbitrarily-shaped bodies, parallel computing.