Methods and Applications of Analysis

Volume 11 (2004)

Number 4

Magnetotellurics in locally-layered random media

Pages: 493 – 514



Werner E. Kohler

Benjamin S. White


Magnetotellurics (MT) is a method of determining the electrical resistivity of the earth's subsurface as a function of position by analyzing the electromagnetic (EM) field on the earth's surface. It is a passive method, in that ambient EM radiation is used as a source. In this paper we consider model subsurfaces for MT that contain small scale random stratification; that is, we introduce random microlayers and allow the earth's electrical properties to vary rapidly and randomly in space as the layer boundaries are crossed. The layers are not assumed to be plane, but are allowed to vary laterally in space in a direction that changes smoothly on the scale of an EM wavelength. By asymptotic analysis of the resulting stochastic differential equations with a small parameter we generalize previous results of White, Kohler and Srnka for plane layered media; we show that the resulting EM field may be approximated using a non-random effective medium theory, but with random corrections. These corrections are a gaussian random process which represents multiple scattering from the random microlayers. We show how the effective medium theory differs from the plane layered case, and derive a spatially varying correction for the EM field on the surface of the earth, which accounts for stratifications that are not planar.

2010 Mathematics Subject Classification

Primary 78A48. Secondary 60H15, 60H30.

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