A stable finite element solution for two-dimensional magnetotelluric modelling

Abstract

We report herein on a finite element algorithm for 2-D magnetotelluric modelling which solves directly for secondary variations in the field parallel to strike, plus the subsequent vertical and transverse auxiliary fields, for both transverse electric and transverse magnetic modes. The governing Helmholtz equations for the secondary fields along strike are the same as those for total field algorithms with the addition of source terms involving the primary fields and the conductivity difference between the body and the host. Our approach has overcome a difficulty with numerical accuracy at low frequencies observed in total field solutions with 32-bit arithmetic for the transverse magnetic mode especially, but also for the transverse electric mode. Matrix ill-conditioning, which affects total field solutions, increases with the number of element rows with the square of the maximum element aspect ratio and with the inverse of frequency. In the secondary formulation, the field along strike and the auxiliary fields do not need to be extracted in the face of an approximately computed primary field which increasingly dominates the total field solution towards low frequencies. In addition to low-frequency stability, the absolute accuracy of our algorithm is verified by comparison with the TM and the TE mode analytic responses of a segmented overburden model.