Generalized Riccati equations for 1-D magnetotelluric impedances over anisotropic conductors Part I: Plane wave field model

Abstract

In the 1-D magnetotelluric theory, a Riccati equation governs the depth variation of the impedance, or admittance, for a given distribution of the electrical conductivity. This equation can be used to compute the surface magnetotelluric functions for generally piecewise continuous conductivity profiles. In case of a simple layered medium, it provides the classical formulae for recalculating recursively the impedances between the individual layer boundaries. We present an extended version of the Riccati differential equations for generally anisotropic 1-D structures for the case of a plane wave incident field. Relation between the standard matrix propagation procedure for a layered medium and the Riccati equation approach, as a limiting case of the former, is demonstrated. In the anisotropic case, all elements of the 2 × 2 impedance tensor are present and, consequently, a system of four coupled Riccati equations has to be considered. Standard methods for the numerical solution of systems of ordinary differential equations are applied to the Riccati system, which gives an efficient alternative to the current matrix propagation procedures for the numerical evaluation of 1-D magnetotelluric impedances in anisotropic media. As an application, a synthetic study on the influence of a depth-variable regional strike on magnetotelluric decomposition results is presented, with the variable strike simulated by a variable anisotropy within the 1-D section.