Inherent nonuniqueness in magnetotelluric inversion for 1D anisotropic models

Abstract

This paper investigates the inherent nonuniqueness in the inversion of magnetotelluric (MT) measurements over an earth with a layered anisotropic resistivity distribution. This kind of nonuniqueness arises from the fact that even accurate and complete data contain insufficient information to uniquely resolve the earth parameters. For a very simple anisotropic case, where all layers in the earth have at least one horizontal principal axis in common coinciding with the x‐ or y‐axis of the Cartesian coordinate system, the resolvable parameters or parameter combinations from MT surface observations are identified by analyzing the structure of the conductivity tensor of the earth and the differential equations the electromagnetic (EM) fields satify. It is found that for a layered anisotropic earth model, several parameters can be uniquely resolved from the MT inversion while others are nonresolvable. However, particular combinations of the nonresolvable parameters can be uniquely resolved. These theoretical findings on the parameter resolvability of MT anisotropic inversion are further verified by a number of numerical experiments using synthetic data and a nonlinear parameter estimation technique. For this purpose, I parameterize the resistivity tensor assigned to each layer of the earth with three principal resistivities and three Euler angles, and then use the three Euler angles, the logarithms of three principal resistivities, and the logarithmic thickness as inverse parameters. This guarantees that the layer thickness is positive and the resistivity tensor is positive‐definite, while at the same time the inverse parameters may span the whole real axis. Numerical inversion results for different anisotropic models also reveal the fact that the resolvable parameters and parameter combinations are invariant with respect to the starting model. This means that for different starting models, the inversion results for some earth parameters might be individually quite different; however, particular combinations of these parameters remain unchanged.