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.
Highlights
The crosshole ground penetrating radar (GPR) is an effective tool to map the subsurface properties, and found widespread application in soil moisture estimation [1,2], hydraulic parameter qualification [3,4], geological investigation [5,6,7], and civil structure inspection [8,9]
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
In Bayesian inversion of crosshole GPR data, the use of finite-difference time-domain (FDTD) forward model with waveform data can generate posterior realizations with high accuracy, yet thousands to millions of model evaluations required by Markov chain Monte Carlo (MCMC) iterations are always computationally infeasible
Summary
The crosshole ground penetrating radar (GPR) is an effective tool to map the subsurface properties, and found widespread application in soil moisture estimation [1,2], hydraulic parameter qualification [3,4], geological investigation [5,6,7], and civil structure inspection [8,9] This method uses a transmitting antenna in one borehole to emit high-frequency (10 MHz to 1 GHz) electromagnetic (EM) waves and a receiving antenna in an adjacent borehole to receive them. Perhaps the most popular methods are the ray-based tomographic algorithms that simplify the EM wave propagation to a straight or bending ray from the transmitter to receiver [11,12] These approaches that use the information of first-arrival traveltimes and maximum first-cycle amplitudes solve iteratively for the EM wave velocity and attenuation fields [13,14,15,16]. The main challenges lie in generating a large training data and training the neural network
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