Simulation of Electromagnetic Diffusion in Anisotropic Media

I present an algorithm to simulate low-frequency electromagnetic propagation in an anisotropic earth, described by a general (non-diagonal) conductivity tensor. I solve the electric formulation by explicitly imposing an approximate form of the condition ∇ · J = 0, where J is the current density vector, which includes the source and the induced current. The numerical algorithm consists of a fully spectral explicit scheme for solving linear, periodic parabolic equations. It is based on a Chebyshev expansion of the evolution operator and the Fourier and Chebyshev pseudospectral methods to compute the spatial derivatives. The latter is used to implement the air/ocean boundary conditions. The results of the simulations are verified by comparison to analytical solutions obtained from the Green function. Examples of the electromagnetic field generated by a source located at the bottom of the ocean illustrate the practical uses of the algorithm.