52 research outputs found
An Iterative 3D Correction plus 2D Inversion Procedure to Remove 3D Effects from 2D ERT Data along Embankments
No full textThis paper addresses the problem of removing 3D effects as one of the most challenging problems related to 2D electrical resistivity tomography (ERT) monitoring of embankment structures. When processing 2D ERT monitoring data measured along linear profiles, it is fundamental to estimate and correct the distortions introduced by the non-uniform 3D geometry of the embankment. Here, I adopt an iterative 3D correction plus 2D inversion procedure to correct the 3D effects and I test the validity of the proposed algorithm using both synthetic and real data. The modelled embankment is inspired by a critical section of the Parma River levee in Colorno (PR), Italy, where a permanent ERT monitoring system has been in operation since November 2018. For each model of the embankment, reference synthetic data were produced in Res2dmod and Res3dmod for the corresponding 2D and 3D models. Using the reference synthetic data, reference 3D effects were calculated to be compared with 3D effects estimated by the proposed algorithm at each iteration. The results of the synthetic tests showed that even in the absence of a priori information, the proposed algorithm for correcting 3D effects converges rapidly to ideal corrections. Having validated the proposed algorithm through synthetic tests, the method was applied to the ERT monitoring data in the study site to remove 3D effects. Two real datasets from the study site, taken after dry and rainy periods, are discussed here. The results showed that 3D effects cause about ±50% changes in the inverted resistivity images for both periods. This is a critical artifact considering that the final objective of ERT monitoring data for such studies is to produce water content maps to be integrated in alarm systems for hydrogeological risk mitigation. The proposed algorithm to remove 3D effects is thus a rapid and validated solution to satisfy near-real-time data processing and to produce reliable results
Probabilistic inversions of electrical resistivity tomography data with a machine learning‐based forward operator
No full textCasting a geophysical inverse problem into a Bayesian setting is often discouraged by the computational workload needed to run many forward modeling evaluations. Here we present probabilistic inversions of electrical resistivity tomography data in which the forward operator is replaced by a trained residual neural network that learns the non-linear mapping between the resistivity model and the apparent resistivity values. The use of this specific architecture can provide some advantages over standard convolutional networks as it mitigates the vanishing gradient problem that might affect deep networks. The modeling error introduced by the network approximation is properly taken into account and propagated onto the estimated model uncertainties. One crucial aspect of any machine learning application is the definition of an appropriate training set. We draw the models forming the training and validation sets from previously defined prior distributions, while a finite element code provides the associated datasets. We apply the approach to two probabilistic inversion frameworks: a Markov Chain Monte Carlo algorithm is applied to synthetic data, while an ensemble-based algorithm is employed for the field measurements. For both the synthetic and field tests, the outcomes of the proposed method are benchmarked against the predictions obtained when the finite element code constitutes the forward operator. Our experiments illustrate that the network can effectively approximate the forward mapping even when a relatively small training set is created. The proposed strategy provides a forward operator three that is orders of magnitude faster than the accurate but computationally expensive finite element code. Our approach also yields most likely solutions and uncertainty quantifications comparable to those estimated when the finite element modeling is employed. The presented method allows solving the Bayesian electrical resistivity tomography with a reasonable computational cost and limited hardware resources
Stochastic electrical resistivity tomography with ensemble smoother and deep convolutional autoencoders
No full textTo reduce both the computational cost of probabilistic inversions and the ill-posedness of geophysical problems, model and data spaces can be re-parameterized into low-dimensional domains where the inverse solution can be computed more efficiently. Among the many compression methods, deep learning algorithms based on deep generative models provide an efficient approach for model and data space reduction. We present a probabilistic electrical resistivity tomography inversion in which the data and model spaces are compressed through deep convolutional variational autoencoders, while the optimization procedure is driven by the ensemble smoother with multiple data assimilation, an iterative ensemble-based algorithm. This method iteratively updates an initial ensemble of models that are generated according to a previously defined prior model. The inversion outcome consists of the most likely solution and a set of realizations of the variables of interest from which the posterior uncertainties can be numerically evaluated. We test the method on synthetic data computed over a schematic subsurface model, and then we apply the inversion to field measurements. The model predictions and the uncertainty assessments provided by the presented approach are also compared with the results of an MCMC sampling working in the compressed domains, a gradient-based algorithm, and with the outcomes of an ensemble-based inversion running in the uncompressed spaces. A finite-element code constitutes the forward operator. Our experiments show that the implemented inversion provides most likely solutions and uncertainty quantifications comparable to those yielded by the ensemble-based inversion running in the full model and data spaces, and the MCMC sampling, but with a significant reduction of the computational cost
Discrete Cosine Transform Reparameterization for Bayesian Time-Lapse ERT Inversion
No full textTime-Lapse electrical resistivity tomography (TL-ERT) is used to monitor dynamic processes through mapping the resistivity variations in the subsurface. Inversion of TL-ERT data is a highly non-linear and ill-conditioned problem characterized by non-unique solutions. For this reason, an accurate uncertainty appraisal is essential to quantify the ambiguity affecting the estimated resistivity model. We present a probabilistic TL-ERT inversion in which the Differential Evolution Markov Chain (DEMC) algorithm samples the posterior probability density function, while the Discrete Cosine Transform (DCT) is used to compress the model space. The model compression aims at mitigating both the ill-conditioned nature of the inversion problem and the curse of dimensionality issue. On the other hand, the DEMC combines principles coming from metaheuristic optimisation methods and Markov Chain Monte Carlo algorithms to speed up the probabilistic sampling. To draw essential conclusions about the reliability and applicability of the implemented algorithm, we focus on synthetic inversion experiments in which we simulate two data acquisitions at different time instants (t0 and t1) and we jointly estimate the resistivity model at t0 along with the resistivity changes at t1. The results demonstrate that the implemented method provides accurate model predictions and uncertainty estimations with an affordable computational cost
Discrete Cosine Transform for Parameter Space Reduction in Bayesian ERT Inversion
No full textMarkov Chain Monte Carlo (MCMC) algorithms are employed for accurate uncertainty assessments in non-linear geophysical inverse problems. However, one of their main drawbacks is the considerable number of sampled models needed to attain stable posterior estimations, especially in high-dimensional parameter spaces. We use the Discrete Cosine Transform (DCT) to reparametrize a Bayesian Electrical Resistivity Tomography (ERT) inversion solved through an MCMC sampling. In this framework, the unknown parameters become the series of coefficients associated with the retained DCT base functions. We employ the Differential Evolution Markov Chain (DEMC) algorithm that guarantees a more accurate and rapid sampling of the posterior density than more standard MCMC algorithms (such as the random walk Metropolis). To draw essential conclusions about the reliability of the implemented algorithm, we focus on inversions of a synthetic subsurface block model. We assess the benefits provided by the DCT compression of the model space by comparing the outcomes of the implemented inversion approach with those provided by a DEMC algorithm running in the full, un-reduced model space. Although preliminary, our results are promising and prove that the implemented inversion approach guarantees rapid convergence toward the stationary regime, thereby preserving an accurate sampling of the posterior model
GPR measurements to detect major discontinuities at Cheshmeh-Shirdoosh limestone quarry, Iran
No full textIn recent years, the Iranian rich quarry industry has been looking for efficient scientific investigations to improve the extraction operations in different dimension stone quarries. Kerman Province is one of the most potential zones with a variety of dimension stone quarries near the city of Kerman. In this research, GPR measurements were carried out to detect major discontinuities at Cheshmeh-Shirdoosh limestone quarry, northeast of Kerman city. This quarry is being extracted by the diamond wire sawing method. As the first GPR study in Iranian quarries, a total length of about 1200 m was surveyed with 50 MHz and 250 MHz GPR antennas collecting data on the surface of the three extraction benches of the quarry. A 800 MHz antenna was also used to map the main defects of a block, which was extracted from a fractured section of the quarry. Six parallel profiles at 10 cm intervals were measured along one side of the block. The results obtained from the 250 MHz dataset were very encouraging and could detect all the major discontinuities. Interpreted profiles were also used to prepare depth slices of the density of joints for two main survey areas. As expected, GPR sections obtained from the 50 MHz antenna had a lower resolution but could clearly detect fault zones. The 800 MHz antenna could map the main defects of the extracted block. However, a higher frequency antenna (e.g., 2GHz or more) is recommended for mapping thin fractures
Discrete cosine transform for parameter space reduction in Bayesian electrical resistivity tomography
No full textElectrical resistivity tomography is a non-linear and ill-posed geophysical inverse problem that is usually solved through gradient-descent methods. This strategy is computationally fast and easy to implement but impedes accurate uncertainty appraisals. We present a probabilistic approach to two-dimensional electrical resistivity
tomography in which a Markov chain Monte Carlo algorithm is used to numerically evaluate the posterior probability density function that fully quantifies the uncertainty affecting the recovered solution. The main drawback of Markov chain Monte Carlo approaches is related to the considerable number of sampled models needed to achieve accurate posterior assessments in high-dimensional parameter spaces. Therefore, to reduce the computational burden of the inversion process, we employ the differential evolution Markov chain, a hybrid method between non-linear optimization and Markov chain Monte Carlo sampling, which exploits multiple and interactive chains to speed up the probabilistic sampling. Moreover, the discrete cosine transform reparameterization is employed to reduce the dimensionality of the parameter space removing the high-frequency components of the resistivity modelwhich are not sensitive to data. In this framework, the unknown parameters become the series of coefficients associated with the retained discrete cosine transform basis functions. First, synthetic data inversions are used to validate the proposed method and to demonstrate the benefits provided by the discrete cosine transform compression. To this end, we compare the outcomes of the implemented approach with those provided by a differential evolution Markov chain algorithm running in the full, un-reduced model space. Then, we apply the method to invert field data acquired along a river embankment. The results yielded by the implemented approach are also benchmarked against a standard local inversion algorithm. The proposed Bayesian inversion provides posterior mean models in agreement with the predictions achieved by the gradient-based inversion, but it also provides model uncertainties, which can be used for penetration depth and resolution limit identification
Experimenting a permanent geoelectrical monitoring system for stability assessment of levees
No full textSperimentazione di un sistema di monitoraggio geoelettrico permanente per la valutazione della stabilità arginale
No full textGli argini sono l’ultima difesa per salvaguardare le vite umane e i beni materiali dalla potenza distruttrice delle inondazioni. Sfortunatamente ad oggi in Italia non è prevista per legge una procedura sistematica e oggettiva di valutazione della stabilità degli argini. I consorzi di Bonifica, enti preposti alla manutenzione dei rilevati arginali, eseguono infatti ispezioni visuali delle strutture, operazioni soggettive che dipendono fortemente dall’operatore che realizza il sopralluogo. Negli ultimi decenni le metodologie geofisiche sono state utilizzate di frequente per valutare lo stato di salute dei rilevati in terra (Kim et al., 2007; Cardarelli et al., 2014) e in particolar modo la geoelettrica è stata utilizzata per il riconoscimento di zone di filtrazione preferenziale e per valutare la saturazione differenziale all’interno delle strutture (Takakura et al., 2013; Perri et al., 2014; Loperte et al., 2016). Solo in pochi casi, però, sono stati implementati sistemi di monitoraggio permanenti (Hilbich et al., 2011; Supper et al., 2011). L’obiettivo di questo lavoro è la valutazione della stabilità dei rilevati arginali in terra in tempo reale, in una maniera indiretta, economica e efficace, grazie all’implementazione di un monitoraggio geoelettrico per il riconoscimento di vie preferenziali di filtrazione e zone a contenuto d’acqua non omogeneo
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