The importance of anisotropic conductivity in magnetotelluric interpretation

The importance of anisotropic conductivity as a part of a model for magnetotelluric interpretation has been pointed out by Cantwell [1960], Bostick and Smith [1962], and others. In their discussions, lateral changes in conductivity are also treated as anisotropic. Analytical description of the reflection of a plane wave from a half-space whose conductivity is anisotropic has features which illustrate some of the principles of magnetotelluric interpretation. When we consider a half-space as shown in Figure 1 whose conductivity is different in different directions, we write Ohm's law as ((1))In (1) and following, Cartesian tensor notation is used and i, j take the values 1, 2, 3. Since only ad hoc arguments can be given for a symmetric conductivity tensor, we will treat the tensor as nonsymmetric. We now wish to formulate a mathematical problem whose solution will tell us how a plane wave is reflected from an anisotropic half-space. We will restrict our analysis to waves propagating at right angles to the surface of the solid.