Challenges associated with finite element methods for forward modelling of unbounded gravity fields

Gravity forward modelling is the calculation of gravity field from a specific density distribution, and is essential for reconstructing ground density in an inversion process. Finite element (FE) methods have been effectively used for forward modelling of gravity data. In contrast to the closed-form and analytical methods, FEM can model complicated geometries and density distributions. Since the gravity field is an unbounded domain, numerical modelling of the boundary condition is the main challenge associated with the FE formulation of the gravity data. In the majority of numerical cases, the domain of the gravity is truncated at a relatively far distance from the zone of density contrast in order to reduce the effect of the boundary conditions on the results. Some researchers have applied a zero gravitational potential value to the boundary while others have applied an estimated gravitational potential value to the truncated edges. In both cases, a large zone of zero-density contrast has to be added around the zone of density contrast which considerably increases the computational time. Another type of the boundary condition, which is less developed in the field of gravity modelling, is the use of a single layer of infinite elements around the zone of density contrast to model the boundary. The scope of this paper is the discussion and comparison of the aforementioned types of modelling boundary conditions in FE analyses with respect to gravity field modelling. The advantages and disadvantages of each method, especially the infinite element boundary over the truncation methods, are presented. The results show that a trade-off between the size of the additional zero density zone around the zone of density contrast, and the meshing element sizes is essential for the truncation methods. Furthermore, the infinite element boundary is shown to have great potential to overcome the computational issues related to the truncation methods. A high accuracy in the results with less computational time can be obtained using infinite elements.