Bayesian Elastic Full‐Waveform Inversion Using Hamiltonian Monte Carlo

Gebraad, Lars; Boehm, Christian; Fichtner, Andreas

doi:10.1029/2019jb018428

Cited by 80 publications

(63 citation statements)

References 97 publications

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“…Furthermore, our inversion utilizes relatively coarse spherical harmonics, which ensure that at the finest resolutions tested the effective 'voxel' aspect ratio at the CMB induced by our assumption of a 300-km-thick layer is of order one, so that we are not inverting for an unrealistic vertically elongated parametrization. Current software developments are increasingly allowing for more complex, large scale non-linear Monte Carlo inversions (Gebraad et al 2020), however robust, well-tested implementations are currently limited to linear models such as the one considered here for performance reasons.…”

Section: Probabilistic Lowermost Mantle P-wave Tomography 1633mentioning

confidence: 99%

Probabilistic lowermost mantle P-wave tomography from hierarchical Hamiltonian Monte Carlo and model parametrization cross-validation

Muir

Tkalčić

2020

Geophysical Journal International

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Summary Bayesian methods, powered by Markov Chain Monte Carlo estimates of posterior densities, have become a cornerstone of geophysical inverse theory. These methods have special relevance to the deep Earth, where data is sparse and uncertainties are large. We present a strategy for efficiently solving hierarchical Bayesian geophysical inverse problems for fixed parametrisations using Hamiltonian Monte Carlo sampling, and highlight an effective methodology for determining optimal parametrisations from a set of candidates by using efficient approximations to leave-one-out cross-validation for model complexity. To illustrate these methods, we employ a case study of differential travel-time tomography of the lowermost mantle, using short period P-wave data carefully selected to minimize the contributions of the upper mantle and inner core. The resulting tomographic image of the lowermost mantle has a relatively weak degree 2 — instead there is substantial heterogeneity at all low spherical harmonic degrees less than 15. This result further reinforces the dichotomy in the lowermost mantle between relatively simple degree 2 dominated long-period S-wave tomographic models, and more complex short-period P-wave tomographic models.

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Section: Probabilistic Lowermost Mantle P-wave Tomography 1633mentioning

confidence: 99%

Probabilistic lowermost mantle P-wave tomography from hierarchical Hamiltonian Monte Carlo and model parametrization cross-validation

Muir

Tkalčić

2020

Geophysical Journal International

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“…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

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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.

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“…This alternative approach is based on the update direction (12), where the focus of argument is shifted from the weighting curves to the prior and likelihood vector components. With w = w x + w y all that is known is that the inequality w ≤ w x + w y holds, using the standard 2-norm z = i |z i | 2 1/2 .…”

Section: Norm Criteriamentioning

confidence: 99%

Batch seismic inversion using the iterative ensemble Kalman smoother

Gineste¹,

Eidsvik²

2021

Comput Geosci

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An ensemble-based method for seismic inversion to estimate elastic attributes is considered, namely the iterative ensemble Kalman smoother. The main focus of this work is the challenge associated with ensemble-based inversion of seismic waveform data. The amount of seismic data is large and, depending on ensemble size, it cannot be processed in a single batch. Instead a solution strategy of partitioning the data recordings in time windows and processing these sequentially is suggested. This work demonstrates how this partitioning can be done adaptively, with a focus on reliable and efficient estimation. The adaptivity relies on an analysis of the update direction used in the iterative procedure, and an interpretation of contributions from prior and likelihood to this update. The idea is that these must balance; if the prior dominates, the estimation process is inefficient while the estimation is likely to overfit and diverge if data dominates. Two approaches to meet this balance are formulated and evaluated. One is based on an interpretation of eigenvalue distributions and how this enters and affects weighting of prior and likelihood contributions. The other is based on balancing the norm magnitude of prior and likelihood vector components in the update. Only the latter is found to sufficiently regularize the data window. Although no guarantees for avoiding ensemble divergence are provided in the paper, the results of the adaptive procedure indicate that robust estimation performance can be achieved for ensemble-based inversion of seismic waveform data.

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Bayesian Elastic Full‐Waveform Inversion Using Hamiltonian Monte Carlo

Cited by 80 publications

References 97 publications

Probabilistic lowermost mantle P-wave tomography from hierarchical Hamiltonian Monte Carlo and model parametrization cross-validation

Probabilistic lowermost mantle P-wave tomography from hierarchical Hamiltonian Monte Carlo and model parametrization cross-validation

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

Batch seismic inversion using the iterative ensemble Kalman smoother

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