A finite volume method for global electromagnetic induction forward modeling on collocated unstructured grids

Abstract

Global electromagnetic induction provides an efficient way to probe the electrical conductivity in the Earth’s deep interior. Owing to the increasing geomagnetic data especially from high-accuracy geomagnetic satellites, inverting the Earth’s three-dimensional conductivity distribution on a global scale becomes attainable. A key requirement in the global conductivity inversion is to have a forward solver with high-accuracy and efficiency. In this study, a finite volume method for global electromagnetic induction forward modeling is developed based on unstructured grids. Arbitrary polyhedral grids are supported in our algorithms to obtain high geometric adaptability. We employ a cell-centered collocated variable arrangement which allows convenient discretization for complex geometries and straightforward implementation of multigrid technique. To validate the method, we test our code with two synthetic models and compare our finite volume results with an analytical solution and a finite element numerical solution. Good agreements are observed between our solution and other results, indicating acceptable accuracy of the proposed method.

Keywords

• global electromagnetic induction
• mantle electrical conductivity
• finite volume method
• unstructured grids