Joint inversion of gravity and traveltime data using a level-set-based structural parameterization

Li, Wenbin; Qian, Jianliang

doi:10.1190/geo2015-0547.1

Cited by 26 publications

(6 citation statements)

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“…It is a viable extension as the slowness and density are structurally related (with limitations however [8]), and will share curves of discontinuity. Inversion is performed a weighted sum of the misfit functionals for slowness and gravity acceleration [39].…”

Section: Discussionmentioning

confidence: 99%

Binary recovery via phase field regularization for first-arrival traveltime tomography

Dunbar¹,

Elliott²

2019

Inverse Problems

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We propose a double obstacle phase field methodology for binary recovery of the slowness function of an Eikonal equation found in first traveltime tomography. We treat the inverse problem as an optimization problem with quadratic misfit functional added to a phase field relaxation of the perimeter penalization functional. Our approach yields solutions as we account for well posedness of the forward problem by choosing regular priors. We obtain a convergent finite difference and mixed finite element based discretization and a well defined descent scheme by accounting for the non-differentiability of the forward problem. We validate the phase field technique with a Γ -convergence result and numerically by conducting parameter studies for the scheme, and by applying it to a variety of test problems with different geometries, boundary conditions, and source -receiver locations.

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Section: Discussionmentioning

confidence: 99%

Binary recovery via phase field regularization for first-arrival traveltime tomography

Dunbar¹,

Elliott²

2019

Inverse Problems

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“…Impedance Tomography (EIT, also known as resistivity tomography, e.g. Chung et al 2005), hydrology (Cardiff & Kitanidis 2009;, and in various exploration geophysics contexts, especially crosswell seismic tomography and to a more limited extent gravity and magnetic applications (Isakov et al 2011;Zheglova et al 2013;Li et al 2014;Lu & Qian 2015;Li & Qian 2016;Li et al 2017;Zheglova et al 2018). Existing work has typically assumed piecewise constant fields, often of prescribed value, as this strong a priori knowledge is often available in exploration contexts.…”

Section: The Level Set Methodsmentioning

confidence: 99%

Geometric and level set tomography using ensemble Kalman inversion

Muir

Tsai

2019

Geophysical Journal International

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Summary Tomography is one of the cornerstones of geophysics, enabling detailed spatial descriptions of otherwise invisible processes. However, due to the fundamental ill-posedness of tomography problems, the choice of parametrizations and regularizations for inversion significantly affect the result. Parametrizations for geophysical tomography typically reflect the mathematical structure of the inverse problem. We propose, instead, to parametrize the tomographic inverse problem using a geologically motivated approach. We build a model from explicit geological units that reflect the a priori knowledge of the problem. To solve the resulting large-scale nonlinear inverse problem, we employ the efficient Ensemble Kalman Inversion scheme, a highly parallelizable, iteratively regularizing optimizer that uses the ensemble Kalman filter to perform a derivative-free approximation of the general iteratively-regularized Levenberg-Marquardt method. The combination of a model specification framework that explicitly encodes geological structure and a robust, derivative-free optimizer enables the solution of complex inverse problems involving non-differentiable forward solvers and significant a priori knowledge. We illustrate the model specification framework using synthetic and real data examples of near-surface seismic tomography using the factored eikonal fast marching method as a forward solver for first arrival travel times. The geometrical and level set framework allows us to describe geophysical hypotheses in concrete terms, and then optimize and test these hypotheses, helping us to answer targeted geophysical questions.

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“…Defining decoupled structures can represent a significant advantage in the joint interpretation of two or more observables relative to the same investigated volume. On one side, when total spatial (or temporal) coupling between two model parameters is assumed in widely used joint inversion schemes (e.g., Gallardo & Meju, ; Heincke et al, ; Li & Qian, ), structures belonging to weakly resolved physical properties can be misinterpreted. On the other hand, when results from two independent inversions (each one focused on one physical property) are compared, local coupling of the structures is only suggested based on interpretation of the single images (e.g., Meju et al, ).…”

Section: An Algorithm For Defining Decoupled Structuresmentioning

confidence: 99%

“…Joint inversion approaches that account for the level of spatial coupling between two or more properties have been proposed in the past years like cross‐gradients constraints (e.g., Gallardo & Meju, ), adaptive coupling strategy (e.g., Heincke et al, ), or level‐set‐based structural parameterization (e.g., Li & Qian, ). In these studies, the level coupling is directly imposed by the user through a penalty term in the objective function, in the first case, or in an iterative redefinition of the coupling constraints, in the latter cases.…”

Section: Introductionmentioning

confidence: 99%

“…In these studies, the level coupling is directly imposed by the user through a penalty term in the objective function, in the first case, or in an iterative redefinition of the coupling constraints, in the latter cases. Subjective choices are introduced in terms of weighting the relative contribution of different terms in objective function (Gallardo & Meju, ; Moorkamp, ) or selecting the number of set‐level perturbations to compute for the updating (Li & Qian, ). As a consequence, even if the fully coupled structure assumption is removed, the degree of coupling is still in the hands of the practitioner.…”

Section: Introductionmentioning

confidence: 99%

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Flexible Coupling in Joint Inversions: A Bayesian Structure Decoupling Algorithm

Agostinetti

Bodin

2018

JGR Solid Earth

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When different geophysical observables are sensitive to the same volume, it is possible to invert them simultaneously to jointly constrain different physical properties. The question addressed in this study is to determine which structures (e.g., interfaces) are common to different properties and which ones are separated. We present an algorithm for resolving the level of spatial coupling between physical properties and to enable both common and separate structures in the same model. The new approach, called structure decoupling (SD) algorithm, is based on a Bayesian trans‐dimensional adaptive parameterization, where models can display the full spectra of spatial coupling between physical properties, from fully coupled models, that is, where identical model geometries are imposed across all inverted properties, to completely decoupled models, where an independent parameterization is used for each property. We apply the algorithm to three 1‐D geophysical inverse problems, using both synthetic and field data. For the synthetic cases, we compare the SD algorithm to standard Markov chain Monte Carlo and reversible‐jump Markov chain Monte Carlo approaches that use either fully coupled or fully decoupled parameterizations. In case of coupled structures, the SD algorithm does not behave differently from methods that assume common interfaces. In case of decoupled structures, the SD approach is demonstrated to correctly retrieve the portion of profiles where the physical properties do not share the same structure. The application of the new algorithm to field data demonstrates its ability to decouple structures where a common stratification is not supported by the data.

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Joint inversion of gravity and traveltime data using a level-set-based structural parameterization

Cited by 26 publications

References 50 publications

Binary recovery via phase field regularization for first-arrival traveltime tomography

Binary recovery via phase field regularization for first-arrival traveltime tomography

Geometric and level set tomography using ensemble Kalman inversion

Flexible Coupling in Joint Inversions: A Bayesian Structure Decoupling Algorithm

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