The impact of anisotropic electrical resistivity on surface magnetotelluric responses and the development of two new anisotropic inversions

Abstract

To study the anisotropic effects on the magnetotelluric method, we developed software for the forward modeling process to observe the behaviors of the responses on an anisotropic body and an inversion software to study what we can expect from the real field data. We found that each element of the resistivity tensor has a different level of influence on each component of the impedance tensor and the tipper vector, while some elements may be considered to have negligible influences on responses. To quantify the influence level, we have proposed the impedance influence indices and the tipper edge indices for the influence on the impedance tensor and the tipper vector, respectively. We then used these indices on isotropic models to justify that our indices behave correspondingly to the widely known behaviors of the magnetotelluric and to quantify the negligible level of influence. The indices shown that, while ρ(xy) is zero, ρ(xx) highly affects Z(xy), Z(yy), and T(y); ρ(yy) highly affects Z(yx), Z(xx), and T(x); but ρ(zz), ρ(xz), ρ(yz) has no significant influence. However, if ρ(xy) is not zero, the values of ρ(xx), ρ(yy), and ρ(xy) highly affect all the responses, while ρ(zz), ρ(xz), and ρ(yz) still have no effect. Moreover, with the present ρ(xy); Z(xx), Z(yy), T(x), and T(y) have high amplitude and cover the surface above an anisotropic structure, while only at edges in the absent case. Hence, we proposed two anisotropic inversion methods. First, the decoupled ρ(x)-mode and ρ(y)-mode inversions to recover ρ(xx) (ρ(x)) and ρ(yy) (ρ(y)) independently, respectively, which can also be performed in parallel or as a joint inversion. Second, the reduced coupled azimuthal anisotropic inversion, which is used to recover ρ(xx), ρ(yy), and ρ(xy) at the same time. The two designs do not cover the recovery of ρ(xz), ρ(yz), and ρ(zz) and have low influences. The criterion for choosing the method to be used is related to the high amplitude coverage of Z(xx), Z(yy), T(x), and T(y). These two inversion methods greatly limit the number of searching variables, and the computational resources. We then developed our inversion program based on the idea proposed to recover the axial part of the resistivity tensor. The inversion program for general anisotropy is left for the future work. We compared the result and performance of the ρ(x)-mode, ρ(y)-mode, the joint between them, and the conventional axial inversion and found that there is no significant difference between the recovered ρ(xx) and ρ(yy) models. This confirms the success of the separation. The runtime for decoupled is also faster but uses less memory compared to the conventional method.