Effective modeling of ground penetrating radar in fractured media using analytic solutions for propagation, thin-bed interaction and dipolar scattering

Abstract

please cite as: Shakas, A., and N. Linde (2015), Effective modeling of ground penetrating radar in fractured media using analytic solutions for propagation, thin-bed interaction and dipolar scattering. ABSTRACTWe propose a new approach to model ground penetrating radar signals that propagate through a homogeneous and isotropic medium, and are scattered at thin planar fractures of arbitrary dip, azimuth, thickness and material filling. We use analytical expressions for the Maxwell equations in a homogeneous space to describe the propagation of the signal in the rock matrix, and account for frequency-dependent dispersion and attenuation through the empirical Jonscher formulation.We discretize fractures into elements that are linearly polarized by the incoming electric field that arrives from the source to each element, locally, as a plane wave. To model the effective source wavelet we use a generalized Gamma distribution to define the antenna dipole moment.We combine microscopic and macroscopic Maxwell's equations to derive an analytic expression for the response of each element, which describe the full electric dipole radiation patterns along with effective reflection coefficients of thin layers. Our results compare favorably with finitedifference time-domain modeling in the case of constant electrical parameters of the rock-matrix and fracture filling. Compared with traditional finite-difference time-domain modeling, the proposed approach is faster and more flexible in terms of fracture orientations. A comparison with published laboratory results suggests that the modeling approach can reproduce the main characteristics of the reflected wavelet.

Hydrogeophysical characterization of transport processes in fractured rock by combining push‐pull and single‐hole ground penetrating radar experiments

“…(b) The simulated GPR section with formation water, (c) the same section with the tracer distribution (shown in Figure 3a), (d) their difference and the migrated difference section, along with the fracture location and injection point (e). The GPR simulations were performed with a newly developed algorithm [ Shakas and Linde , ] and the flow‐and‐transport simulation was done with MaFloT 2‐D.…”

Probabilistic inference of fracture-scale flow paths and aperture distribution from hydrogeophysically-monitored tracer tests

“…In all the results that follow we discretize a single fracture of 16 m × 16 m into cells of 20 cm × 20 cm (in accordance with modeling recommendations for a 100 MHz antenna, see Shakas and Linde (2015)) leading to aperture fields consisting of 6400 cells. We use a dimensionality-reduction algorithm (Laloy et al, 2015;Hunziker et al, 2017) that allows us to represent each aperture realization with 100 dimension-reduction (DR) variables and 5 global geostatistical variables.…”

“…A widely used method in this regard is the ground penetrating radar (GPR) method, in which a high-frequency radar antenna emits an electromagnetic wave that propagates through the rock matrix and is scattered at fracture locations. The recorded scattered field carries information about fracture properties, namely the aperture and orientation of the fracture as well as the electrical properties of the fracture filling (e.g., Bradford and Deeds, 2006;Tsoflias and Becker, 2008;Shakas and Linde, 2015). In low-loss (i.e., electrically-resistive) media, the GPR propagation distances can span several tens of meters.…”

“…Instead, most fracture-related GPR studies have relied on an analytical solution, namely the thin-bed approximation, to model EM interaction with fractures (Tsoflias and Hoch, 2006;Bradford and Deeds, 2006;Deparis and Garambois, 2008;Sassen and Everett, 2009;Sambuelli and Calzoni, 2010;Babcock and Bradford, 2015). Shakas and Linde (2015) introduced a new methodology (the so-called effective-dipole approach) to model GPR scattering from heterogeneous fractures that is inspired by a microscopic treatment of Maxwell's equations. It is capable of modeling reflections arising from fractures with spatially-varying electrical properties and aperture along the fracture plane.…”

“…In this study, we develop a methodology to invert GPR reflection monitoring data from push-pull tracer tests to infer fracture-scale aperture variations and flow paths. For this, we combine simulations of flow and transport of an electrically-conductive tracer within a single heterogeneous fracture with the associated GPR response using the effective-dipole approach by Shakas and Linde (2015). More specifically, we use the local cubic law to simulate fluid flow by assigning the local fracture transmissivity based on the local aperture, while the GPR-response is determined by a semi-analytical formulation that is strongly dependent on aperture, as well as electrical conductivity and permittivity.…”