Transdimensional and Hamiltonian Monte Carlo inversions of Rayleigh‐wave dispersion curves: a comparison on synthetic datasets

Aleardi, Mattia; Salusti, Alessandro; Pierini, S.

doi:10.1002/nsg.12100

Cited by 20 publications

(11 citation statements)

References 72 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another viable strategy to reduce the burn‐in period could be starting the MCMC sampling from the model predicted by a local inversion. More advanced MCMC algorithms that incorporate the principles of Hamiltonian dynamics into the standard Metropolis–Hasting method (Betancourt, 2017; Fichtner et al ., 2019; Gebraad et al ., 2020; Aleardi et al ., 2020; Aleardi and Salusti, 2020b) could be useful to speed up the probabilistic ERT inversion. The major computational requirement of the Hamiltonian Monte Carlo algorithm is the need for computing the derivative (i.e.…”

Section: Discussionmentioning

confidence: 99%

A geostatistical Markov chain Monte Carlo inversion algorithm for electrical resistivity tomography

Aleardi

Vinciguerra

Hojat

2020

Near Surface Geophysics

Self Cite

View full text Add to dashboard Cite

Electrical resistivity tomography is an ill‐posed and nonlinear inverse problem commonly solved through deterministic gradient‐based methods. These methods guarantee a fast convergence towards the final solution, but the local linearization of the inverse operator impedes accurate uncertainty assessments. On the contrary, numerical Markov chain Monte Carlo algorithms allow for accurate uncertainty appraisals, but appropriate Markov chain Monte Carlo recipes are needed to reduce the computational effort and make these approaches suitable to be applied to field data. A key aspect of any probabilistic inversion is the definition of an appropriate prior distribution of the model parameters that can also incorporate spatial constraints to mitigate the ill conditioning of the inverse problem. Usually, Gaussian priors oversimplify the actual distribution of the model parameters that often exhibit multimodality due to the presence of multiple litho‐fluid facies. In this work, we develop a novel probabilistic Markov chain Monte Carlo approach for inversion of electrical resistivity tomography data. This approach jointly estimates resistivity values, litho‐fluid facies, along with the associated uncertainties from the measured apparent resistivity pseudosection. In our approach, the unknown parameters include the facies model as well as the continuous resistivity values. At each spatial location, the distribution of the resistivity value is assumed to be multimodal and non‐parametric with as many modes as the number of facies. An advanced Markov chain Monte Carlo algorithm (the differential evolution Markov chain) is used to efficiently sample the posterior density in a high‐dimensional parameter space. A Gaussian variogram model and a first‐order Markov chain respectively account for the lateral continuity of the continuous and discrete model properties, thereby reducing the null‐space of solutions. The direct sequential simulation geostatistical method allows the generation of sampled models that honour both the assumed marginal prior and spatial constraints. During the Markov chain Monte Carlo walk, we iteratively sample the facies, by moving from one mode to another, and the resistivity values, by sampling within the same mode. The proposed method is first validated by inverting the data calculated from synthetic models. Then, it is applied to field data and benchmarked against a standard local inversion algorithm. Our experiments prove that the proposed Markov chain Monte Carlo inversion retrieves reliable estimations and accurate uncertainty quantifications with a reasonable computational effort.

show abstract

Section: Discussionmentioning

confidence: 99%

A geostatistical Markov chain Monte Carlo inversion algorithm for electrical resistivity tomography

Aleardi

Vinciguerra

Hojat

2020

Near Surface Geophysics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Molnar et al (2010) employed a Bayesian framework and Markov Chain Monte Carlo (MCMC) method to cast the surface wave DCs data inversion into a solid probabilistic statement for accurate estimation of a posterior probability density (PPD). Aleardi et al (2020) performed a rigorous study and comparison of transdimensional and reversible-jump MCMC inversions of Rayleigh-wave DCs. Aleardi and Stucchi (2021) state MCMC methods are computationally expensive due to the huge number of samples needed to attain stable PPDs.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty quantification of multi-modal surface wave inversion using artificial neural networks

Yablokov¹,

Lugovtsova²,

Serdyukov³

2022

Preprint

View full text Add to dashboard Cite

An inversion of surface waves dispersion curves is a non-unique and ill-conditioned problem. The inversion result has a probabilistic nature, what becomes apparent when simultaneously restoring the shear wave (S-wave) velocity and layer thickness. Therefore, the problem of uncertainty quantification is relevant. Existing methods through deterministic or global optimization approaches of uncertainty quantification via posterior probability density (PPD) of the model parameters are not computationally efficient since they demand multiple solutions of the inverse problem. We present an alternative method based on a multi-layer fully connected artificial neural network (ANN). We improve the previous approach from uni-modal to multi-modal inversion and use the existing algorithm to determine optimal parametrization (number of layers) and the ranges of possible model parameters. We uniformly draw training data sets within estimated ranges and train the ANN. Saved ANN's weights map the phase velocity dispersion curves to values of the S-wave velocity and layers thickness. To estimate the uncertainties, we adapt the Monte-Carlo simulation strategy and project onto the resulting velocity model both frequency-dependent data noise and inverse operator errors, which are evaluated by the prediction of the training data set. We first test our approach on synthetic experiments for various velocity models: a positive velocity gradient, a low-velocity layer and a high-velocity layer. This is done considering uni-modal inversion at first and then compared to the multi-modal inversion. Afterwards, we apply our approach to field data and compare resulting models with the body S-wave processing by the generalized reciprocal method. The experiments show high-potential results - using ANN yields the possibility to accurately estimate PPD of restored model parameters without a significant computational effort. The PPD-based comparison demonstrates advantages of a multi-modal inversion over uni-modal inversion. The trained ANN provides reasonable model parameters predictions and related uncertainties in real-time.

show abstract

“…These algorithms transform the Bayesian inversion process into a sampling problem in which the sampling density is proportional to the PPD. Although the increasing computational power provided by modern parallel architectures has considerably encouraged the applications of MCMC methods to solve geophysical problems (Fichtner and Zunino et al ., 2019; Stuart et al ., 2019; Aleardi et al ., 2020; Aleardi, 2020a), it is always crucial adopting specific recipes to guarantee an accurate and computationally efficient sampling of the PPD. For example, many MCMC algorithms (e.g.…”

Section: Introductionmentioning

confidence: 99%

Discrete cosine transform for parameter space reduction in Bayesian electrical resistivity tomography

Vinciguerra

Aleardi

Hojat

et al. 2021

Geophysical Prospecting

View full text Add to dashboard Cite

Electrical 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 model which 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.

show abstract

Transdimensional and Hamiltonian Monte Carlo inversions of Rayleigh‐wave dispersion curves: a comparison on synthetic datasets

Cited by 20 publications

References 72 publications

A geostatistical Markov chain Monte Carlo inversion algorithm for electrical resistivity tomography

A geostatistical Markov chain Monte Carlo inversion algorithm for electrical resistivity tomography

Uncertainty quantification of multi-modal surface wave inversion using artificial neural networks

Discrete cosine transform for parameter space reduction in Bayesian electrical resistivity tomography

Contact Info

Product

Resources

About