Evaluation of a Straight-Ray Forward Model for Bayesian Inversion of Crosshole Ground Penetrating Radar Data

Abstract

Bayesian inversion of crosshole ground penetrating radar (GPR) data is capable of characterizing the subsurface dielectric properties and qualifying the associated uncertainties. Markov chain Monte Carlo (MCMC) simulations within the Bayesian inversion usually require thousands to millions of forward model evaluations for the parameters to hit their posterior distributions. Therefore, the CPU cost of the forward model is a key issue that influences the efficiency of the Bayesian inversion method. In this paper we implement a widely used straight-ray forward model within our Bayesian inversion framework. Based on a synthetic unit square relative permittivity model, we simulate the crosshole GPR first-arrival traveltime data using the finite-difference time-domain (FDTD) and straight-ray solver, respectively, and find that the straight-ray simulator runs 450 times faster than its FDTD counterpart, yet suffers from a modeling error that is more than 7 times larger. We also perform a series of numerical experiments to evaluate the performance of the straight-ray model within the Bayesian inversion framework. With modeling error disregarded, the inverted posterior models fit the measurement data nicely, yet converge to the wrong set of parameters at the expense of unreasonably large number of iterations. When the modeling error is accounted for, with a quarter of the computational burden, the main features of the true model can be identified from the posterior realizations although there still exist some unwanted artifacts. Finally, a smooth constraint on the model structure improves the inversion results considerably, to the extent that it enhances the inversion accuracy approximating to those of the FDTD model, and further reduces the CPU demand. Our results demonstrate that the use of the straight-ray forward model in the Bayesian inversion saves computational cost tremendously, and the modeling error correction together with the model structure constraint are the necessary amendments that ensure that the model parameters converge correctly.

GAN-Based Inversion of Crosshole GPR Data to Characterize Subsurface Structures

“…Quantitatively, our method had the lowest MSE (981. 19) and the highest SSIM (0.92), which were superior to those of ray-based tomography (MSE: 5547.35; SSIM: 0.80) and FWI (MSE: 5727.27; SSIM: 0.84). Since FWI requires the correct selection of initial model and source wavelet, which is easy to implement in a numerical simulation dataset but difficult to achieve in a measured dataset, although FWI had the best performance in the inversion of simulated data, it performed worse than the proposed method when inverting real-world crosshole GPR data.…”

“…They are capable of preventing the inversion results from being trapped in the local minimum and able to quantify the uncertainties of the inversion results. Nevertheless, the probabilistic inversion methods involve thousands to millions of forward simulations to ensure the inversion results are converged to the posterior distribution, which leads to the consumption of considerable computing resources [19,20].…”

Special Issue on “Advanced Technology Related to Radar Signal, Imaging, and Radar Cross-Section Measurement”

“…After a very careful peer-review process, a total of 32 papers were accepted. These works include SAR/ISAR [2][3][4][5][6][7][8][9], polarimetry [10][11][12], MIMO [13,14], direction of arrival (DOA)/direction of departure (DOD) [13][14][15], sparse sensing [5,14,16], ground-penetrating radar (GPR) [17][18][19], through-wall radar [20,21], coherent integration [22,23], clutter suppression [24,25], and meta-materials, among others [26][27][28][29][30][31]. All of these accepted papers are the latest research results and are expected to be further advanced, applied, and diverted.…”

Elastic prestack seismic inversion through discrete cosine transform reparameterization and convolutional neural networks

“…After such reparameterization, the unknown parameters become the numerical coefficients that multiply the basis functions. Some examples of applications of these methods to geophysical problems can be found in Fernández Martínez et al (2011), Dejtrakulwong et al (2012), Satija andCaers (2015), Fernández Martínez et al (2017), Lochbühler et al (2018), Aleardi (2019), Szabó and Dobróka (2019), Qin et al (2019), Aleardi (2020). These compression techniques must be applied taking in mind that part of the information in the original (unreduced) parameter space could be lost in the reduced space and for this reason, the model parameterization must always constitute a compromise between model resolution and model uncertainty (Malinverno, 2000;Grana et al 2019).…”