3D forward modeling of controlled-source audio-frequency magnetotellurics in arbitrarily anisotropic media

Controlled-source audio-frequency magnetotellurics (CSAMT) is playing an important role in shallow subsurface exploration. Most current three-dimensional (3D) forward modeling for CSAMT are based on an isotropic earth model which neglects the electrical anisotropy in the earth. Here we implement a 3D vector finite-element modeling algorithm to solve the frequency domain Helmholtz equation for the total electrical field and analyze the effect of earth anisotropy on tensor CSAMT apparent resistivity responses. First we introduce a 3 X 3 positive-definite conductivity tensor to represent the arbitrarily electrical anisotropy. Then we discretize the weak-form of vector Helmholtz equation with an unstructured tetrahedral grid and lowest order of Nedelec vector basis functions. Besides, we approximate the horizontal transmitting sources for CSAMT by a series of electrical dipoles and solve the final system of equations with the direct solver MUMPS that can speed up the forward modeling while guaranteeing the numerical precision. We compare our 3D numerical results with one-dimensional solutions for a layered anisotropic earth to verify the accuracy and reliability of the proposed 3D anisotropic finite element algorithm. To further explore the anisotropic effect of a 3D anomalous body and host rock, we design a conductive brick model embedded in a homogeneous half-space. Then, we rotate the principal conductivity tensor of the anomalous body and host rock around x-axis and z-axis separately, and simulate the apparent resistivity for tensor CSAMT. Numerical results show that both the amplitude and distribution pattern of the CSAMT apparent resistivity vary with the anisotropic conductivity tensors. To recognize the electrical anisotropy of the earth, we show the CSAMT apparent resistivity in polar plots, thus one can clearly identify the principal axis of the anisotropic conductivity.