HR: 16:45h
AN: H14C-04    [Abstracts]
TI: A fractional calculus approach to interpreting transient electromagnetic field behavior in near--surface hydrogeophysical investigations
AU: Bartel, L C
EM: lcbarte@sandia.gov
AF: Sandia National Laboratories, Geophysical Technology Department PO Box 5800 MS-0750, Albuquerque, NM 87185 United States
AU: * Weiss, C J
EM: cjweiss@sandia.gov
AF: Sandia National Laboratories, Geophysical Technology Department PO Box 5800 MS-0750, Albuquerque, NM 87185 United States
AU: Everett, M E
EM: everett@geo.tamu.edu
AF: Texas A&M University, Department of Geology and Geophysics, College Station, TX 77843 United States
AB: Among the various geophysical technologies that have found a niche in shallow subsurface characterization and monitoring is the electromagnetic induction (EMI) method---a method that maps the spatial variability in ground conductivity arising from lithologic changes and the presence of pore fluids. Interestingly, a growing body of evidence suggests that the electrical structure in some geological settings is inherently hierarchical, and presumed to arise from the dynamical systems that generate and alter the formation and its overlying soil. In these limited cases, the observations challenge the applicability of the standard modeling paradigm which rests squarely on the assumption of a spatially smooth (or at least piecewise smooth) distribution of physical parameters within the subsurface. As an alternative, and drawing upon additional near--surface EMI data recently collected from geologically distinct sites throughout New Mexico and Texas, we investigate the concepts of fractal signals and random walks through spatially-correlated heterogeneous media as a means to describe the observed variations in shallow subsurface EMI response. The fundamental hypothesis examined in this phase of the research is that low-frequency electromagnetic fields penetrate into a multiscale, hierarchical geological medium according to a fractional--order diffusion equation. Such an equation is fully compatible with Maxwell's equations and naturally reduces to the classical limit of integer order derivatives (which seem to be adequate for the vast majority of geological settings) but has the advantage of naturally accommodating generalized constitutive laws and the effects of multi--scale heterogeneity when they arise. Sections of this work were performed at Sandia National Laboratories. Sandia is a multi--program laboratory operated by the Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE--AC04--94AL85000.
DE: 8010 Fractures and faults
DE: 1894 Instruments and techniques
DE: 1832 Groundwater transport
DE: 0694 Instrumentation and techniques
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting