Three-dimensional magnetotelluric modeling with nontrivial anisotropy by a regularization approach

The regularization approach has been successfully applied to remove spurious solutions in the magnetotelluric (MT) forward problems of isotropic Earth media. However, spurious modes are more likely to occur in numerical solutions of anisotropic media, as electrical anisotropy introduces many more complications to electromagnetic (EM) induction in such media. This study focuses on developing the regularization approach to 3D MT forward problems of anisotropic media, especially those of nontrivial anisotropy. The governing equation is now derived with a conductivity tensor, and an accordingly adapted form of a scaled grad-div term is augmented to regularize the solutions and constrain the divergence-free condition. A new scaling scheme is proposed to cope with the complicated distribution of current densities in nontrivial anisotropy media, and an effective conductivity is approximated by the diagonal elements of the conductivity tensor to formulate the scaling factor. Numerical tests show that, for various models of electrical anisotropy, the regularization approach can effectively enforce the divergence condition and successfully suppress spurious solutions. Therefore, for nontrivial anisotropy media, this approach can also improve the efficiency of the iterative solvers while retaining the accuracy of the solutions. The derivation of the governing equation is based on the MT method. However, this strategy should be generally applicable to other frequency-domain EM methods.