Stochastic electrical resistivity tomography with ensemble smoother and deep convolutional autoencoders

Abstract

To reduce both the computational cost of probabilistic inversions and the ill‐posedness of geophysical problems, model and data spaces can be reparameterized 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 a Markov Chain Monte Carlo 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 Markov Chain Monte Carlo sampling, but with a significant reduction of the computational cost.

Application of a global–local full‐waveform inversion of Rayleigh wave to estimate the near‐surface shear wave velocity model

“…Although some studies have been done in this direction (Aleardi & Mazzotti, 2017; Sajeva et al., 2017; Gebraad et al., 2020; Zhao & Sen, 2021), we are still working on this topic, especially to make the probabilistic FWI of surface waves computationally affordable. Deep generative models and compression techniques could be adopted to reduce the dimension of data and model spaces, thus also decreasing the computational workload of the probabilistic inversion (Aleardi et al., 2021, 2022).…”

“…The recorded Rayleigh waves can be inverted using different techniques, among which the most widely used is the multichannel analysis of surface waves (MASW) (Park et al, 1999;Bohlen et al, 2004;Socco & Strobbia, 2004;Cercato, 2009;Maraschini et al, 2010;Socco et al, 2010;Aleardi & Stucchi, 2021), in which the dispersion curves are picked on the velocity-frequency spectra. The main advantage of this method lies in its limited computational demand, but it is also affected by many downsides and limitations.…”