Magnetotelluric theory of the sinusoidal interface

Abstract

Most of the theoreticians working on the magnetotelluric method have concentrated on models of the earth which are flat and composed of parallel layers of material having differing conductivities. The purpose of this paper is to demonstrate the effect which nonparallel layers have on the electric and magnetic fields. We simulate the earth by two conducting layers which are joined at an interface which is sinusoidal. The incident waves are plane and of two polarizations chosen to make the electric or the magnetic field parallel to the corrugations of the interface. The electromagnetic field is found for both polarizations by formulating a set of integral equations which are solved by a perturbation technique in conjunction with an established Fourier transform method. The resulting electromagnetic fields are used to form the ratios Ey/Hx and Ex/Hy. When the interface is flat, these ratios are equal, but when it is sinusoidal, they are not, in general. Although usually small, this difference may be diagnostic for some cases of geological significance. The amplitude of the perturbed part of the electromagnetic field also has the interesting property of decaying or increasing above the surface of the earth, depending upon whether the ratio of the wavelength of the incident wave to the wavelength of the interface is greater or less than unity.