3D Probabilistic Full Waveform Inversion: Application to Gulf of Mexico Field Data

Lomas, Angus; Luo, Simon; Irakarama, Modeste; Johnston, Rodney; Vyas, Madhav; Shen, Xuan

doi:10.3997/2214-4609.202310720

Cited by 7 publications

(4 citation statements)

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“…In such cases, we can simply use the representative samples obtained from BVI components for analysis. Moreover, storing a large set of posterior samples on disk and loading them into memory can be extremely demanding, especially for 3D FWI problems (Lomas et al., 2023; X. Zhang et al., 2023), to which the use of representative samples or the fully analytic and parametric posterior expression from BVI results provides a practical solution, as demonstrated in Scheiter et al. (2022).…”

Section: Discussionmentioning

confidence: 99%

“…Zhao & Sen, 2021). Alternatively, in recent years variational methods have also been introduced to address the computational challenges of Bayesian FWI (Lomas et al, 2023;W. Wang et al, 2023;X.…”

Section: Bayesian Fwi Implementationmentioning

confidence: 99%

“…To address these challenges, several efficient Monte Carlo methods have been applied to FWI (Biswas & Sen, 2022; de Lima et al., 2023; Ely et al., 2018; Gebraad et al., 2020; P. Guo et al., 2020; Kotsi et al., 2020; Qin et al., 2016; A. Ray et al., 2016; Visser et al., 2019; Z. Zhao & Sen, 2021). Alternatively, in recent years variational methods have also been introduced to address the computational challenges of Bayesian FWI (Lomas et al., 2023; W. Wang et al., 2023; X. Zhang & Curtis, 2021a; X. Zhang et al., 2023). However, none of these methods provide an accurate and analytic approximation to the posterior probability distribution.…”

Section: Full Waveform Inversionmentioning

confidence: 99%

“…(2020). Since then variational methods have been applied to a variety of problems including travel time tomography (Levy, Laloy, & Linde, 2022; X. Zhang & Curtis, 2020a; X. Zhao et al., 2021), seismic denoising (Siahkoohi et al., 2021, 2023), seismic amplitude inversion (Zidan et al., 2022), earthquake hypocenter inversion (Smith et al., 2022), slip distribution inversion (Sun et al., 2023), full waveform inversion in 2D (Urozayev et al., 2022; W. Wang et al., 2023; X. Zhang & Curtis, 2020b) and in 3D (Lomas et al., 2023; X. Zhang et al., 2023), and survey or experimental design (Strutz & Curtis, 2024). In addition, various types of neural networks produce probabilistic outputs and can be considered variational methods (Bishop, 1994), and these have been applied to subsurface imaging problems for more than two decades (Bloem et al., 2023; Cao et al., 2020; Devilee et al., 1999; de Wit et al., 2013; Earp & Curtis, 2020; Earp et al., 2020; Hansen & Finlay, 2022; Käufl et al., 2014, 2016; Lubo‐Robles et al., 2021; Meier et al., 2007a, 2007b; A. K. Ray & Biswal, 2010; Shahraeeni & Curtis, 2011; Shahraeeni et al., 2012; Siahkoohi et al., 2022; X. Zhang & Curtis, 2021b; X. Zhao et al., 2021).…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Inversion, Uncertainty Analysis and Interrogation Using Boosting Variational Inference

Zhao,

Curtis

2024

JGR Solid Earth

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Geoscientists use observed data to estimate properties of the Earth's interior. This often requires non‐linear inverse problems to be solved and uncertainties to be estimated. Bayesian inference solves inverse problems under a probabilistic framework, in which uncertainty is represented by a so‐called posterior probability distribution. Recently, variational inference has emerged as an efficient method to estimate Bayesian solutions. By seeking the closest approximation to the posterior distribution within any chosen family of distributions, variational inference yields a fully probabilistic solution. It is important to define expressive variational families so that the posterior distribution can be represented accurately. We introduce boosting variational inference (BVI) as a computationally efficient means to construct a flexible approximating family comprising all possible finite mixtures of simpler component distributions. We use Gaussian mixture components due to their fully parametric nature and the ease with which they can be optimized. We apply BVI to seismic travel time tomography and full waveform inversion, comparing its performance with other methods of solution. The results demonstrate that BVI achieves reasonable efficiency and accuracy while enabling the construction of a fully analytic expression for the posterior distribution. Samples that represent major components of uncertainty in the solution can be obtained analytically from each mixture component. We demonstrate that these samples can be used to solve an interrogation problem: to assess the size of a subsurface target structure. To the best of our knowledge, this is the first method in geophysics that provides both analytic and reasonably accurate probabilistic solutions to fully non‐linear, high‐dimensional Bayesian full waveform inversion problems.

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Section: Discussionmentioning

confidence: 99%

Section: Bayesian Fwi Implementationmentioning

confidence: 99%

Section: Full Waveform Inversionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian Inversion, Uncertainty Analysis and Interrogation Using Boosting Variational Inference

Zhao,

Curtis

2024

JGR Solid Earth

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Physically Structured Variational Inference for Bayesian Full Waveform Inversion

Zhao,

Curtis

2024

JGR Solid Earth

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Full waveform inversion (FWI) creates high resolution models of the Earth's subsurface structures from seismic waveform data. Due to the non‐linearity and non‐uniqueness of FWI problems, finding globally best‐fitting model solutions is not necessarily desirable since they fit noise as well as the desired signal in data. Bayesian FWI calculates a so‐called posterior probability distribution function, which describes all possible model solutions and their uncertainties. In this paper, we solve Bayesian FWI using variational inference, and propose a new methodology called physically structured variational inference, in which a physics‐based structure is imposed on the variational distribution. In a simple example motivated by prior information from imaging inverse problems, we include parameter correlations between pairs of spatial locations within a dominant wavelength of each other, and set other correlations to zero. This makes the method far more efficient compared to other variational methods in terms of both memory requirements and computation, at the cost of some loss of generality in the solution found. We demonstrate the proposed method with a 2D acoustic FWI scenario, and compare the results with those obtained using other methods. This verifies that the method can produce accurate statistical information about the posterior distribution with hugely improved efficiency (in our FWI example, 1 order of magnitude reduction in computation). We further demonstrate that despite the possible reduction in generality of the solution, the posterior uncertainties can be used to solve post‐inversion interrogation problems connected to estimating volumes of subsurface reservoirs and of stored , with minimal bias, creating a highly efficient FWI‐based decision‐making workflow.

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Variational prior replacement in Bayesian inference and inversion

Zhao,

Curtis

2024

Geophysical Journal International

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Summary Many scientific investigations require that the values of a set of model parameters are estimated using recorded data. In Bayesian inference, information from both observed data and prior knowledge is combined to update model parameters probabilistically by calculating the posterior probability distribution function. Prior information is often described by a prior probability distribution. Situations arise in which we wish to change prior information during the course of a scientific project. However, estimating the solution to any single Bayesian inference problem is often computationally costly, as it typically requires many model samples to be drawn, and the data set that would have been recorded if each sample was true must be simulated. Recalculating the Bayesian inference solution every time prior information changes can therefore be extremely expensive. We develop a mathematical formulation that allows the prior information that is embedded within a solution, to be changed using variational methods, without recalculating the original Bayesian inference. In this method, existing prior information is removed from a previously obtained posterior distribution and is replaced by new prior information. We therefore call the methodology variational prior replacement (VPR). We demonstrate VPR using a 2D seismic full waveform inversion example, in which VPR provides similar posterior solutions to those obtained by solving independent inference problems using different prior distributions. The former can be completed within minutes on a laptop computer, whereas the latter requires days of computations using high-performance computing resources. We demonstrate the value of the method by comparing the posterior solutions obtained using three different types of prior information: uniform, smoothing and geological prior distributions.

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3D Probabilistic Full Waveform Inversion: Application to Gulf of Mexico Field Data

Cited by 7 publications

References 0 publications

Bayesian Inversion, Uncertainty Analysis and Interrogation Using Boosting Variational Inference

Bayesian Inversion, Uncertainty Analysis and Interrogation Using Boosting Variational Inference

Physically Structured Variational Inference for Bayesian Full Waveform Inversion

Variational prior replacement in Bayesian inference and inversion

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