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

Qin, Hui; Vrugt, Jasper A.; Xie, Xuansong; Zhou, Yi

doi:10.1016/j.autcon.2018.08.014

Cited by 23 publications

(11 citation statements)

References 51 publications

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“…The choice of the number of DCT-coefficients is a trade-off between spatial resolution and uncertainty in the inversion results. In previous work we have introduced a method to determine the number of DCT-coefficients by examining the similarity between the reference model and its reduced order DCT representations [28]. If some structural features of the subsurface can be used as prior information, a set of realizations can be generated from the training image (TI) and the DCT-coefficients with the occurrence probabilities larger than the threshold are considered as unknown model parameters in the inversion [49].…”

Section: Straight-ray Model With Modeling Error Correctedmentioning

confidence: 99%

“…They provide only a single realization and are not able to quantify the result uncertainties. On the contrary, probabilistic inversion methods treat different sources of error explicitly and provide a set of solutions drawn from the posterior distribution of model parameters [24][25][26][27][28]. In previous work we have developed a Bayesian inversion method to determine the relative permittivity fields, ε r (ε r = ε/ε 0 , where ε 0 signifies the dielectric permittivity in free space) from crosshole GPR waveform data [29].…”

Section: Introductionmentioning

confidence: 99%

“…We employ a 2D finite-difference time-domain (FDTD) solver of the Maxwell's equations for forward computing [31,32], and resort to the Markov-chain Monte Carlo (MCMC) simulation with the DREAM (ZS) algorithm to explore the posterior distribution of model parameters (DCT-coefficients) [33][34][35]. The usefulness of the proposed inversion method was demonstrated on both numerical and real-world applications [28,29]. However, we find the use of the CPU-intensive FDTD forward modeling leads to the inversion work a daunting task as the MCMC iteration requires thousands to millions of model evaluations.…”

Section: Introductionmentioning

confidence: 99%

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

2019

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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.

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Section: Straight-ray Model With Modeling Error Correctedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2019

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“…To invert GPR data, both deterministic inversion algorithms and probabilistic inversion methods have been proposed [10][11][12][13][14][15]. Most deterministic inversion methods depend on an accurate prior model.…”

Section: Introductionmentioning

confidence: 99%

“…FWI was tested on synthetic crosshole data, and proved successful for characterizing a gravel aquifer [27]. Qin proposed two-stage Bayesian inversion to decrease the computational cost using crosshole GPR data [15]. Cordua implemented the first inversion example, which used full-waveform data to get a solution of a posteriori probability density [28].…”

Section: Introductionmentioning

confidence: 99%

Full-Waveform Inversion of Time-Lapse Crosshole GPR Data Using Markov Chain Monte Carlo Method

et al. 2021

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Crosshole ground-penetrating radar (GPR) is an important tool for a wide range of geoscientific and engineering investigations, and the Markov chain Monte Carlo (MCMC) method is a heuristic global optimization method that can be used to solve the inversion problem. In this paper, we use time-lapse GPR full-waveform data to invert the dielectric permittivity. An inversion based on the MCMC method does not rely on an accurate initial model and can introduce any complex prior information. Time-lapse ground-penetrating radar has great potential to monitor the properties of a subsurface. For the time-lapse inversion, we used the double difference method to invert the time-lapse target area accurately and full-waveform data. We propose a local sampling strategy taking advantage of the a priori information in the Monte Carlo method, which can sample only the target area with a sequential Gibbs sampler. This method reduces the calculation and improves the inversion accuracy of the target area. We have provided inversion results of the synthetic time-lapse waveform data that show that the proposed method significantly improves accuracy in the target area.

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Parasite inversion for determining the coefficients and time‐validity of Philip's two‐term infiltration equation

Jaiswal

Gao

Rahmati

et al. 2022

Vadose Zone Journal

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Many different equations have been proposed to describe quantitatively onedimensional soil water infiltration. The unknown coefficients of these equations characterize soil hydraulic properties and may be estimated from a n record, { t𝑖 , Ĩ𝑖 } 𝑛 𝑖=1 , of cumulative infiltration measurements using curve fitting techniques. The two-term infiltration equation, 𝐼(𝑡) = 𝑆 √ 𝑡 + 𝑐𝐾 s 𝑡, of Philip has been widely used to describe measured infiltration data. This function enjoys a solid mathematical-physical underpinning and admits a closed-form solution for the soil sorptivity, S [L T −1/2 ], and multiple, 𝑐 [−], of the saturated hydraulic conductivity, 𝐾 s [L T −1 ]. However, Philip's two-term equation has a limited time validity, 𝑡 valid [T], and thus cumulative infiltration data, Ĩ( t), beyond 𝑡 = 𝑡 valid will corrupt the estimates of S and 𝐾 s . This paper introduces a novel method for estimating S, c, 𝐾 s , and 𝑡 valid of Philip's twoterm infiltration equation. This method, coined parasite inversion, use as vehicle Parlange's three-parameter infiltration equation. As prerequisite to our method, wepresent as secondary contribution an exact, robust and efficient numerical solution of Parlange's infiltration equation. This solution admits Bayesian parameter estimation with the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm and yields as byproduct the marginal distribution of Parlange's β parameter. We evaluate our method for 12 USDA soil types using synthetic infiltration data simulated with HYDRUS-1D. An excellent match is observed between the inferred values of S and 𝐾 s and their "true" values known beforehand. Furthermore, our estimates of c and 𝑡 valid correlate well with soil texture, corroborate linearity of the 𝑐(β) relationship for 0 ≤ 𝑡 ≤ 𝑡 valid , and fall within reported ranges. A cumulative vertical infiltration of about 2.5 cm may serve as guideline for the time-validity of Philip's two-term infiltration equation.

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

Cited by 23 publications

References 51 publications

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

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

Full-Waveform Inversion of Time-Lapse Crosshole GPR Data Using Markov Chain Monte Carlo Method

Parasite inversion for determining the coefficients and time‐validity of Philip's two‐term infiltration equation

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