Anomalous diffusion of electromagnetic eddy currents in geological formations
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Controlled-source electromagnetic (EM) induction in some geological formations is shown here to be compactly described by an anomalous subdiffusion process. Such a process, which is not universal, is governed by a fractional diffusion equation or alternatively the convolutional form of Ohm's law. A subdiffusing eddy current vortex, or electromagnetic smoke ring, propagates in such a way that its position of median intensity overruns its position of peak intensity. This behavior is not allowed in classical diffusion but is a simple consequence of diffusion within a stationary fractal medium. A similar analysis has been applied to understand heavy-tailed traveltime distributions that appear in certain hydrological time series. The tell-tale signature of anomalous electromagnetic diffusion is a slope β of the magnetic zero-crossing moveout curve that is constant with transmitter-receiver (RX) offset and significantly different from unity. Neither lateral heterogeneity nor unixial anisotropy can generate such a constant-slope moveout curve with an economy of model parameters. Controlled-source EM data from two sites in Texas and one in New Mexico are used in this study to test the eddy current subdiffusion hypothesis. Copyright 2007 by the American Geophysical Union.
author list (cited authors)
Weiss, C. J., & Everett, M. E.