Estimation of velocity macro-models using stochastic full-waveform inversion

Near Surface Geophysics

Tognarelli

Mazzotti

2016

Self Cite

We estimate the elastic properties of marine sediments beneath the seabed by means of high‐resolution velocity analysis and one‐dimensional elastic full‐waveform inversion performed on two‐dimensional broad‐band seismic data of a well‐site survey. A high‐resolution velocity function is employed to exploit the broad frequency band of the data and to derive the P‐wave velocity field with a high degree of accuracy. To derive a complete elastic characterisation in terms of P‐wave and S‐wave velocities (Vp, Vs) and density of the subsurface, and to increase the resolution of the Vp estimates, we apply a one‐dimensional elastic full‐waveform inversion in which the outcomes derived from the velocity analysis are used as a priori information to define the Vp search range. The one‐dimensional inversion is done using genetic algorithm as the optimisation method. It is performed by considering two misfit functions: the first uses the entire waveform to compute the misfit between modelled and observed seismograms, and the second considers the envelope of the seismograms, thus relaxing the requirement of an exact estimation of the wavelet phase. The full‐waveform inversion and the high‐resolution velocity analysis yield comparable Vp profiles, but the full‐waveform inversion reconstruction is much more detailed. Regarding the full‐waveform inversion results, the final depth models of P‐ and S‐wave velocities and density show a fine‐layered structure with a significant increase in velocities and density at shallow depth, which may indicate the presence of a consolidated layer. The very similar velocities and density‐depth trends obtained by employing the two different misfit functions increase our confidence in the reliability of the predicted subsurface models.

Section: Field Data Processingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Characterisation of shallow marine sediments using high‐resolution velocity analysis and genetic‐algorithm‐driven 1D elastic full‐waveform inversion

Near Surface Geophysics

Tognarelli

Mazzotti

2016

Self Cite

“…For many practical applications, the stochastic approach to elastic FWI is usually limited to horizontally stratified media using reflectivity method (Mallick 1999;Mallick and Dutta 2002;Mallick et al 2010;Fliedner et al 2012;Li and Mallick 2015). However, due to the recent growth of high-performance computing, the stochastic approach to FWI begins to be used to derive accurate and low-resolution 2D or 3D compressional velocity fields that are well suited to play the role of starting models for gradient-based acoustic FWI (Sajeva et al 2014a;Gao et al 2014;Tognarelli et al 2015;Datta 2015). Such scaling problem is sometimes referred to as the "curse of dimensionality" (Bellman 1957), and it makes the stochastic and elastic FWI unfeasible for 2D or 3D applications in which thousands or even millions of unknowns are considered.…”

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confidence: 99%

“…It is known that the computational cost of stochastic methods grows exponentially with the number of unknowns. In these applications, a method to reduce the number of unknown parameters and a highly efficient parallel implementation are crucial to make the computational cost of the stochastic inversion affordable (Diouane et al 2014;Sajeva et al 2014a). However, due to the recent growth of high-performance computing, the stochastic approach to FWI begins to be used to derive accurate and low-resolution 2D or 3D compressional velocity fields that are well suited to play the role of starting models for gradient-based acoustic FWI (Sajeva et al 2014a;Gao et al 2014;Tognarelli et al 2015;Datta 2015).…”

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confidence: 99%

1D elastic full‐waveform inversion and uncertainty estimation by means of a hybrid genetic algorithm–Gibbs sampler approach

Geophysical Prospecting

Mazzotti

2016

Stochastic optimization methods, such as genetic algorithms, search for the global minimum of the misfit function within a given parameter range and do not require any calculation of the gradients of the misfit surfaces. More importantly, these methods collect a series of models and associated likelihoods that can be used to estimate the posterior probability distribution. However, because genetic algorithms are not a Markov chain Monte Carlo method, the direct use of the genetic-algorithm-sampled models and their associated likelihoods produce a biased estimation of the posterior probability distribution. In contrast, Markov chain Monte Carlo methods, such as the Metropolis-Hastings and Gibbs sampler, provide accurate posterior probability distributions but at considerable computational cost. In this paper, we use a hybrid method that combines the speed of a genetic algorithm to find an optimal solution and the accuracy of a Gibbs sampler to obtain a reliable estimation of the posterior probability distributions. First, we test this method on an analytical function and show that the genetic algorithm method cannot recover the true probability distributions and that it tends to underestimate the true uncertainties. Conversely, combining the genetic algorithm optimization with a Gibbs sampler step enables us to recover the true posterior probability distributions. Then, we demonstrate the applicability of this hybrid method by performing one-dimensional elastic full-waveform inversions on synthetic and field data. We also discuss how an appropriate genetic algorithm implementation is essential to attenuate the "genetic drift" effect and to maximize the exploration of the model space. In fact, a wide and efficient exploration of the model space is important not only to avoid entrapment in local minima during the genetic algorithm optimization but also to ensure a reliable estimation of the posterior probability distributions in the subsequent Gibbs sampler step

Stochastic electrical resistivity tomography with ensemble smoother and deep convolutional autoencoders

Near Surface Geophysics

Vinciguerra

Stucchi

et al. 2022

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.