Theory of the Magnetotelluric Method for a Spherical Conductor

Abstract

Impedance relations for various conductivity distributions are derived considering the Earth as a non‐uniform spherical conductor. The impedance relations are so presented that they can be used for any number of layers inside the Earth, each representing a different conductivity distribution. It is shown theoretically that for small periods the impedance relations derived for a non‐uniform spherical conductor are the same as those for a semi‐infinite conductor with plane boundaries. Calculations of impedance and phase values made for plane and spherical conductors for periods from 1 to 108 s show that the Earth's curvature is important only for periods longer than a day. However, for such long periods at the conductivities of 0.01 and 0.001 ohm‐1 metre‐1, there are effectively no induced currents, and the difference obtained between curves for plane and spherical conductors is attributed to the difference in the coordinate systems used. It is concluded that for these conductivities and periods less than one day, the effect of the Earth's curvature can be neglected when determining conductivity distribution by the magnetotelluric method. Copyright © 1966, Wiley Blackwell. All rights reserved