Print this pageComputation of Gravity and Magnetic Anomalies of Non-Homogeneous and Arbitrarily Shaped Bodies Using Finite Element Techniques
MELLO, U. T.
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.