Underground structure defect detection and reconstruction using crosshole GPR and Bayesian waveform inversion

Abstract

A B S T R A C TCrosshole ground-penetrating radar (GPR) is a widely used measurement technique to help inspect the structural integrity of man-made underground structures, yet the resulting waveform and travel-time data can be difficult, complex and challenging to interpret. Here, we introduce the elements of a Bayesian inversion method for analyzing crosshole GPR data to guide detection of defects (weakness zones) in underground concrete structures. This framework uses as main building blocks the two-dimensional finite-difference time-domain (FDTD) simulator, the discrete cosine transform (DCT) method, and the DREAM (ZS) algorithm to reconstruct the relative permittivity field of an underground concrete structure from full-waveform GPR inversion. The FDTD simulator solves numerically Maxwell's equations in the time and space domain of the crosshole GPR experiment and simulates iteratively the electromagnetic (EM) waveforms. The DCT algorithm transforms the Cartesian parameterization to the frequency domain and reduces drastically the dimensionality of the parameter space by retaining only the low-frequency DCT-coefficients. Markov chain Monte Carlo (MCMC) simulation with the DREAM (ZS) algorithm is used to estimate the posterior distribution of the DCT-coefficients. The usefulness and applicability of the FDTD−DCT−DREAM (ZS) framework is demonstrated on a synthetic test example involving a unit square concrete structure with a small defect. Our results demonstrate that the proposed method successfully detects and locates defects in concrete structures. The inversion results appear rather insensitive to the noise level of the measured GPR waveforms, and the amount of data used (number of receiving antenna positions), as long as a sufficient number of measurements is available. The more DCT-coefficients that are used to characterize the concrete structure, the more accurate the results, yet the larger the posterior uncertainty of the reconstructed permittivity fields.

Improved characterization of underground structure defects from two-stage Bayesian inversion using crosshole GPR data

“…Numerical examples have proven the usefulness and applicability of the FDTD-DCT-DREAM (ZS) framework in our previous work [41]. We now evaluate the merits of this inversion method by application to waveform data measured by crosshole GPR in a field diaphragm wall model experiment.…”

“…We propose herein a simple refinement of the FDTD-DCT-DREAM (ZS) framework of [41] which guarantees a sufficient spatial detail of the structure defects at reasonable computational cost. This alternative implementation uses a two-stage approach, where in the first step only a sufficient number of lower-order DCT-coefficients is used to detect the presence of areas with anomalous permittivity values, followed by a second step in which the spatial resolution of the model is enhanced significantly in these anomalous areas to delineate exactly the location and shape of each structure defect.…”

“…This inversion method combines two-dimensional FDTD solution of the Maxwell's equations, parameter dimensionality reduction with the DCT, and the DREAM (ZS) algorithm to facilitate a rapid and efficient characterization of the relative permittivity distribution of the underground structure of interest. A detailed description of this method appears in [41] and so will not be repeated herein. Instead, we only briefly summarize the main building blocks of this framework.…”

“…In a previous paper, we have developed a Bayesian inversion methodology to infer the relative permittivity distribution, ε r of underground structures from crosshole GPR waveform data [41]. The relative permittivity is related to the permittivity as follows, ε r = ε/ε 0 , where ε 0 denotes the free space dielectric permittivity.…”

“…MCMC simulation with the DREAM (ZS) algorithm is used to estimate the posterior distribution of the DCTcoefficients. Numerical experiments with synthetic waveform data were used by [41] to demonstrate the ability of the FDTD-DCT-DREAM (ZS) framework to successfully back out structure defects. Indeed, the DCT approach sacrifices model resolution and may not recover correctly with sufficient fidelity structure defects, particularly if these anomalous areas appear relatively small in comparison to the surrounding structure.…”