Three-dimensional Fréchet sensitivity kernels for electromagnetic wave propagation

Abstract

Electromagnetic (EM) imaging methods are useful tools for monitoring subsurface changes in pore-fluid content and the associated changes in electrical permittivity and conductivity. The most common method for georadar tomography uses a high frequency ray-theoretic approximation that is valid when material variations are sufficiently small relative to the wavelength of the propagating wave. Georadar methods, however, often utilize EM waves that propagate within heterogeneous media at frequencies where ray theory may not be applicable. In this paper we describe EM wave propagation 3-D Fréchet sensitivity kernels that capture the data sensitivity to material perturbations for a given source–receiver combination. Various data functional types are formulated that consider all three components of the electric wavefield and incorporate near-, intermediate- and far-field contributions. We show that EM waves exhibit substantial variations for different relative source–receiver component orientations. The 3-D sensitivities also illustrate out of plane effects that are not captured in 2-D sensitivity kernels and can influence results obtained using 2-D inversion methods to image structures that are in reality 3-D.