Sensitivity of the high-frequency sounding method to variations in electrical properties

Abstract

Instrumentation for high-frequency sounding (HFS) was developed by the U.S. Geological Survey (USGS) in the late 1980s, continuing until 2006. To aid in this development, forward modeling and sensitivity analysis of vertical magnetic fields to electromagnetic (EM) properties between [Formula: see text] and [Formula: see text] were completed. Because these frequencies encompass the transition between the diffusion and propagation regimes, the HFS method ought to be sensitive to all properties contained in the EM wavenumber — namely, electrical conductivity, dielectric permittivity, and magnetic permeability as well as layer thickness. The models consist of three layers that simulate the contam-ination and remediation of dense nonaqueous-phase liquid (DNAPL) contaminants by oxidation. This scenario provides values of [Formula: see text] that would attenuate ground-penetrating radar signals and a range of [Formula: see text] which is a parameter that direct-current resistivity and low-frequency electromagnetic-induction (EMI) techniques are insensitive to. Conductivity and permittivity parameters are calculated with Archie’s law and the Bruggeman-Hanai-Sen (BHS) mixing formula. The importance of thickness and electrical properties to vertical-magnetic-field response of the models initially was addressed using numerical differencing between models containing slight perturbations in electrical properties. Results from this procedure were oscillatory and hence problematic, so analytic partial derivatives of the vertical magnetic field with respect to each parameter were computed for the same scenarios. The derivatives show that the sensitivity to the second-layer permittivity is less than the sensitivity to other properties, and the response is sensitive to slightly magnetic soils. It is also evident that sensitivity and resolution are limited by depth of penetration. The sensitivity curves and plots of the real and imaginary portions of the EM wavenumber demonstrate that propagation begins near [Formula: see text].