Triangulated finite difference methods for global‐scale electromagnetic induction simulations of whole mantle electrical heterogeneity

Long‐period, global‐scale electromagnetic induction data have long been recognized as containing potentially useful information for constraining our understanding of the dynamics and physiochemical state of Earth's deep interior. A key component to realizing the potential of this data set is the ability to compute the induction response of a fully 3‐D Earth mantle in global spherical geometries. In this contribution a novel finite difference method is described which preserves many algorithmic advantages of staggered grid discretizations in Cartesian computational electromagnetics but is generalized for the sphere by introducing a hybrid, tensor product mesh consisting of concentrically nested, triangulated, spherical shells topologically connected node‐for‐node in the radial direction. Such a discretization allows for a flexible distribution of mesh nodes in the lateral sense and avoids the problems associated with excessive node density near the poles which results from conformally mapping the standard Cartesian mesh. Modified finite difference templates for spherical geometries are derived and presented, as is a comparison with integral equation solutions for a simple double‐hemisphere test model. As a first step toward applying the algorithm for mantle induction studies, results of a conservative, thermally activated mantle heterogeneity model confirm that mantle structure remains observable in the presence of the strongly conductive ocean and may manifest important, diagnostic signatures in the orientation of the horizontal component of induced magnetic field.