Electromagnetic induction in a layered earth with arbitrary anisotropy

Abstract

The traditional model for interpreting geoelectromagnetic data is a layered isotropic earth, but in regions with distinct dipping stratification, this model is inadequate. In this case, it is useful to extend the model to a layered earth with general anistropy, assigning each layer a symmetrical (3 × 3) resistivity tensor. The electromagnetic (EM) field is presented by two scalar potentials which describe the poloidal and toroidal part of the magnetic field. After stripping off the horizontal coordinates by a 2-D Fourier transform, we obtain two coupled ordinary differential equations in the vertical coordinate. To stabilize the numerical calculation, the wavenumber domain is divided into two parts. For small wavenumbers, the EM field is calculated through continuation from layer to layer, where the tranverse isotropy requires an extra treatment because the two potentials are in this case uncoupled and the requirement for the field continuation is not satisfied. To calculate the EM field for greater wavenumbers, a Green's function is applied. The apparent resistivities in the controlled source audio-magnetotellurics (CSAMT) method and the EM field in the earth are calculated for this model. From both EM fields and the apparent resistivities, one can clearly recognize the effect of the electrical anisotropy of the earth on the CSAMT measurements.