3D forward modeling and analysis of the loop-source transient electromagnetic method based on the finite-volume method for an arbitrarily anisotropic medium

Electrical anisotropy of strata has been long recognized by field and laboratory observations. However, nearly all of interpretations of transient electromagnetic (TEM) data is based on the assumption of electric isotropy of media, which can cause misleading data interpretation in regions with strong electrical anisotropy. To clarify the influence of electrical anisotropy on loop-source TEM responses, we present a three dimensional (3D) robust finite-volume (FV) algorithm for simulating TEM responses in an arbitrarily anisotropic medium through solving Helmholtz equations in the time domain. The time domain Maxwell equations are discretized using the mimetic finite-volume method (MFV) on a conventional staggered grid in the space domain and discretized in the time domain using the backward Euler method. To reduce time steps required by computation, the modeling time is first divided into several intervals, each of which has a constant time step size. Then, the resulting system matrix in each interval is factored and solved by a direct solver, which allows the factored matrix to be used to calculate the TEM responses for subsequent time steps in the same time interval. The accuracy of our algorithm is validated against quasi-analytic solutions of a 1-D layered anisotropic model. Finally, by numerical experiments for 3D models with different types of electrical anisotropy, we analyze the influences of electrical anisotropy on TEM responses. The results demonstrate that TEM responses are mainly affected by the horizontal conductivity. The effect of dipping anisotropy on TEM responses is much greater than horizontal anisotropy. Besides, the horizontal principle axis direction of electrical anisotropy could be inferred from the TEM signal.