Using orthogonal Legendre polynomials to parameterize global geophysical optimizations: Applications to seismic‐petrophysical inversion and 1D elastic full‐waveform inversion

Aleardi, Mattia

doi:10.1111/1365-2478.12726

Cited by 19 publications

(13 citation statements)

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“…It is also possible to use basis functions in order to decrease the number of parameters and to unburden the computational load of the forward modeling. For example, in Aleardi ( 2019 ), orthogonal Legendre polynomials are used as basis functions to reparameterize the model space. The expansion coefficients associated with each Legendre polynomial are determined via PSO.…”

Section: Best Practices With Psomentioning

confidence: 99%

“…Furthermore, due to the striking computational improvements of the last decade, PSO began to be applied to complex geophysical problems. Original works include 3-D gravity inversion (Pallero et al 2015 ), microseismic event location (Lagos and Velis 2018 ), 2-D MT optimization (Pace et al 2019a ), full waveform inversion (Aleardi 2019 ) and joint inversion of multiple data sets (Paasche and Tronicke 2014 ).…”

Section: Introductionmentioning

confidence: 99%

“…The main applications of PSO to the geophysical inverse problem include the interpretation of: vertical electrical sounding (VES) (Fernández-Álvarez et al 2006 ; Fernández Martínez et al 2010a ; Pekşen et al 2014 ; Cheng et al 2015 ; Pace et al 2019b ); gravity data (Yuan et al 2009 ; Pallero et al 2015 , 2017 , 2021 ; Darisma et al 2017 ; Jamasb et al 2019 ; Essa and Munschy 2019 ; Anderson et al 2020 ; Essa and Géraud 2020 ; Essa et al 2021 ); magnetic data (Liu et al 2018 ; Essa and Elhussein 2018 , 2020 ); multi-transient electromagnetic data (Olalekan and Di 2017 ); time-domain EM data (Cheng et al 2015 , 2019 ; Santilano et al 2018 ; Pace et al 2019c ; Li et al 2019 ; Amato et al 2021 ); MT data (Shaw and Srivastava 2007 ; Pace et al 2017 , 2019a , c ; Godio and Santilano 2018 ; Santilano et al 2018 ) and radio-MT data (Karcıoğlu and Gürer 2019 ); self-potential data (Santos 2010 ; Pekşen et al 2011 ; Göktürkler and Balkaya 2012 ; Essa 2019 , 2020 ) and induced polarization (Vinciguerra et al 2019 ); Rayleigh wave dispersion curve (Song et al 2012 ) and full waveform inversion (Aleardi 2019 ). …”

Section: Introductionmentioning

confidence: 99%

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A Review of Geophysical Modeling Based on Particle Swarm Optimization

2021

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This paper reviews the application of the algorithm particle swarm optimization (PSO) to perform stochastic inverse modeling of geophysical data. The main features of PSO are summarized, and the most important contributions in several geophysical fields are analyzed. The aim is to indicate the fundamental steps of the evolution of PSO methodologies that have been adopted to model the Earth’s subsurface and then to undertake a critical evaluation of their benefits and limitations. Original works have been selected from the existing geophysical literature to illustrate successful PSO applied to the interpretation of electromagnetic (magnetotelluric and time-domain) data, gravimetric and magnetic data, self-potential, direct current and seismic data. These case studies are critically described and compared. In addition, joint optimization of multiple geophysical data sets by means of multi-objective PSO is presented to highlight the advantage of using a single solver that deploys Pareto optimality to handle different data sets without conflicting solutions. Finally, we propose best practices for the implementation of a customized algorithm from scratch to perform stochastic inverse modeling of any kind of geophysical data sets for the benefit of PSO practitioners or inexperienced researchers.

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Section: Best Practices With Psomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Review of Geophysical Modeling Based on Particle Swarm Optimization

2021

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“…To reduce the ill-conditioning and the number of unknown of inversion problems, several compression strategies could be adopted such as wavelet transform (Li & Oldenburg, 2003), singular value decomposition (Liu & Grana, 2018b), Legendre polynomials (Aleardi, 2019), convolutional autoencoder (Liu & Grana, 2018a). Here we reduce both the ill-conditioning of the ERT problem and the number of ensemble members needed for reliable uncertainty through a discrete cosine transform (DCT) reparameterization that is a very common method extensively used for image compression (Britanak et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Ensemble-Based Electrical Resistivity Tomography with Data and Model Space Compression

Aleardi

Vinciguerra

Hojat

2021

Pure Appl. Geophys.

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Inversion of electrical resistivity tomography (ERT) data is an ill-posed problem that is usually solved through deterministic gradient-based methods. These methods guarantee a fast convergence but hinder accurate assessments of model uncertainties. On the contrary, Markov Chain Monte Carlo (MCMC) algorithms can be employed for accurate uncertainty appraisals, but they remain a formidable computational task due to the many forward model evaluations needed to converge. We present an alternative approach to ERT that not only provides a best-fitting resistivity model but also gives an estimate of the uncertainties affecting the inverse solution. More specifically, the implemented method aims to provide multiple realizations of the resistivity values in the subsurface by iteratively updating an initial ensemble of models based on the difference between the predicted and measured apparent resistivity pseudosections. The initial ensemble is generated using a geostatistical method under the assumption of log-Gaussian distributed resistivity values and a Gaussian variogram model. A finite-element code constitutes the forward operator that maps the resistivity values onto the associated apparent resistivity pseudosection. The optimization procedure is driven by the ensemble smoother with multiple data assimilation, an iterative ensemble-based algorithm that performs a Bayesian updating step at each iteration. The main advantages of the proposed approach are that it can be applied to nonlinear inverse problems, while also providing an ensemble of models from which the uncertainty on the recovered solution can be inferred. The ill-conditioning of the inversion procedure is decreased through a discrete cosine transform reparameterization of both data and model spaces. The implemented method is first validated on synthetic data and then applied to field data. We also compare the proposed method with a deterministic least-square inversion, and with an MCMC algorithm. We show that the ensemble-based inversion estimates resistivity models and associated uncertainties comparable to those yielded by a much more computationally intensive MCMC sampling.

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“…Several methods have been proposed using different orthogonal basis functions (e.g. principal component analysis, wavelet transforms, Legendre polynomials, discrete cosine transform; Fernández‐Martínez et al ., 2011; Dejtrakulwong et al ., 2012; Satija and Caers, 2015; Fernández‐Martínez et al ., 2017; Aleardi, 2019, 2020; Szabó and Dobróka, 2019; Qin et al ., 2019). After such reparameterization, the unknown parameters become the numerical coefficients that multiply the basis functions.…”

Section: Introductionmentioning

confidence: 99%

Combining discrete cosine transform and convolutional neural networks to speed up the Hamiltonian Monte Carlo inversion of pre‐stack seismic data

Aleardi

2020

Geophysical Prospecting

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Markov chain Monte Carlo algorithms are commonly employed for accurate uncertainty appraisals in non-linear inverse problems. The downside of these algorithms is the considerable number of samples needed to achieve reliable posterior estimations, especially in high-dimensional model spaces. To overcome this issue, the Hamiltonian Monte Carlo algorithm has recently been introduced to solve geophysical inversions. Different from classical Markov chain Monte Carlo algorithms, this approach exploits the derivative information of the target posterior probability density to guide the sampling of the model space. However, its main downside is the computational cost for the derivative computation (i.e. the computation of the Jacobian matrix around each sampled model). Possible strategies to mitigate this issue are the reduction of the dimensionality of the model space and/or the use of efficient methods to compute the gradient of the target density. Here we focus the attention to the estimation of elastic properties (P-, S-wave velocities and density) from pre-stack data through a non-linear amplitude versus angle inversion in which the Hamiltonian Monte Carlo algorithm is used to sample the posterior probability. To decrease the computational cost of the inversion procedure, we employ the discrete cosine transform to reparametrize the model space, and we train a convolutional neural network to predict the Jacobian matrix around each sampled model. The training data set for the network is also parametrized in the discrete cosine transform space, thus allowing for a reduction of the number of parameters to be optimized during the learning phase. Once trained the network can be used to compute the Jacobian matrix associated with each sampled model in real time. The outcomes of the proposed approach are compared and validated with the predictions of Hamiltonian Monte Carlo inversions in which a quite computationally expensive, but accurate finitedifference scheme is used to compute the Jacobian matrix and with those obtained by replacing the Jacobian with a matrix operator derived from a linear approximation of the Zoeppritz equations. Synthetic and field inversion experiments demonstrate that the proposed approach dramatically reduces the cost of the Hamiltonian Monte Carlo inversion while preserving an accurate and efficient sampling of the posterior probability.

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Using orthogonal Legendre polynomials to parameterize global geophysical optimizations: Applications to seismic‐petrophysical inversion and 1D elastic full‐waveform inversion

Cited by 19 publications

References 50 publications

A Review of Geophysical Modeling Based on Particle Swarm Optimization

A Review of Geophysical Modeling Based on Particle Swarm Optimization

Ensemble-Based Electrical Resistivity Tomography with Data and Model Space Compression

Combining discrete cosine transform and convolutional neural networks to speed up the Hamiltonian Monte Carlo inversion of pre‐stack seismic data

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