On Estimation of Fracture Aperture with Ground Penetrating Radar

Ground penetrating radar (GPR) is an excellent tool for fracture imaging, but GPR-assisted estimation of fracture aperture is a largely unresolved challenge. The main reason for this is that traditional modeling techniques face severe limitations in fractured rock environments. For example, finite-difference time-domain (FDTD) formulations of Maxwell's equations are poorly adapted to deal with fractures of arbitrary orientations and apertures that are three-five orders of magnitude smaller than the modeling domain. An alternative is to use analytical solutions for thin-bed responses, but they are based on strong assumptions that often do not apply in practise. We have recently developed an efficient modeling approach to simulate GPR propagation and reflection in fractured rock. Here, we first use this modeling formulation to examine the ability of the thin-bed solution to infer the aperture of a homogeneous fracture. We then consider a suite of synthetic examples with heterogeneous fracture aperture fields of varying fractal (Hurst) exponents and spatial correlation lengths. We then use a global optimization algorithm to infer a mean (effective) fracture aperture in each case using the noise-contaminated synthetic data. The thin-bed solution leads to biased aperture estimates even if the fracture has a constant aperture and all other modeling parameters are known. With our modeling approach, we find that appropriate mean apertures are estimated in the homogeneous case, and when the correlation length of the aperture distribution is of similar scale (or larger) than the dominant GPR wavelength.