A rigorous three-dimensional magnetotelluric inversion

Abstract

The limited-memory quasi-Newton optimization method with simple bounds has been applied to develop a novel fully three-dimensional (3-D) magnetotelluric (MT) inversion technique. This nonlinear inversion is based on iterative minimization of a classical Tikhonov-type regularized penalty functional. But instead of the usual model space of log resistivities, the approach iterates in a model space with simple bounds imposed on the conductivities of the 3-D target. The method requires storage that is proportional to ncp × N, where the N is the number of conductivities to be recovered and ncp is the number of the correction pairs (practically, only a few). This is much less than requirements imposed by other Newton type methods (that usually require storage proportional to N × M, or N × N, where M is the number of data to be inverted). Using an adjoint method to calculate the gradients of the misfit drastically accelerates the inversion. The inversion also involves all four entries of the MT impedance matrix. The integral equation forward modelling code x3d by Avdeev et al. [1, 2] is employed as an engine for this inversion. Convergence, performance and accuracy of the inversion are demonstrated on a 3D MT synthetic, but realistic, example.