Eigenvector models for solving the seismic inverse problem for the Helmholtz equation

Faucher, Florian; Scherzer, Otmar; Barucq, Hélène

doi:10.1093/gji/ggaa009

Cited by 13 publications

(10 citation statements)

References 87 publications

(126 reference statements)

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“…Here both the shapes and contrast in amplitude are accurately obtained. We notice some oscillatory noise in the reconstructed models, which could certainly be reduced by incorporating a regularization criterion in the minimization ( [19]).…”

Section: Reconstruction Using Fwimentioning

confidence: 99%

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Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion

Faucher¹,

Kirisits²,

Quellmalz³

et al. 2021

Preprint

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In this paper, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the scattered waves. Conventional DT relies on the Fourier diffraction theorem, which is applicable under the condition of weak scattering. However, if the object has high contrasts or is too large compared to the wavelength, it tends to produce multiple scattering, which complicates the reconstruction. We give a survey on diffraction tomography and compare the reconstruction of low and high contrast objects. We also implement and compare the reconstruction using the full waveform inversion method which, contrary to the Born and Rytov approximations, works with the total field and is more robust to multiple scattering.

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Section: Reconstruction Using Fwimentioning

confidence: 99%

“…For simplicity, we do not encode a regularization term in Equation 6.3 and refer the readers to, e.g., [19,27] and the reference therein.…”

Section: Reconstruction Using Full Waveform Inversionmentioning

confidence: 99%

Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion

Faucher¹,

Kirisits²,

Quellmalz³

et al. 2021

Preprint

Self Cite

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show abstract

“…where the choice of misfit function, depending on the data-sets and inverted parameters, is the subject of numerous studies, e.g., [58,28,9,63,35,21,26,23]. Per simplicity, we rely on the l 2 -distance of the difference, such that…”

Section: Reconstruction With Iterative Minimization Fwimentioning

confidence: 99%

Quantitative inverse problem in visco-acoustic media under attenuation model uncertainty

Faucher¹,

Scherzer²

2022

Preprint

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We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is performed by an iterative minimization algorithm. Firstly, we investigate the robustness of the algorithm with respect to attenuation model uncertainty, that is, when different attenuation models are used to simulate synthetic observation data and for the inversion, respectively. Secondly, to handle data-sets with multiple reflections generated by wall boundaries around the domain, we perform inversion using complex frequencies, and show that it offers a robust framework that alleviate the difficulties of multiple reflections. To illustrate the efficiency of the algorithm, we perform numerical simulations of ultrasound imaging experiments to reconstruct a synthetic breast sample that contains an inclusion of sharp contrast, in two and three dimensions, where the latter also serves to demonstrate the numerical feasibility in a large-scale configuration.

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“…Recently, it was extended to electromagnetic inverse scattering problems at fixed frequency [9] and also to time-dependent inverse scattering problems when the illuminating source is unknown [10]. In [11], AS decompositions were used for solving 2-D and 3-D seismic inverse problems for the Helmholtz equation. First theoretical estimates for AS decompositions together with an approach for adapting the dimension of the search space were derived in [5].…”

Section: Introductionmentioning

confidence: 99%

Error Estimates for Adaptive Spectral Decompositions

Baffet¹,

Gleichmann²,

Grote³

2021

Preprint

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Adaptive spectral (AS) decompositions associated with a piecewise constant function, u, yield small subspaces where the characteristic functions comprising u are well approximated. When combined with Newton-like optimization methods, AS decompositions have proved remarkably efficient in providing at each nonlinear iteration a lowdimensional search space for the solution of inverse medium problems. Here, we derive L 2 -error estimates for the AS decomposition of u, truncated after K terms, when u is piecewise constant and consists of K characteristic functions over Lipschitz domains and a background. Numerical examples illustrate the accuracy of the AS decomposition for media that either do, or do not, satisfy the assumptions of the theory.

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Eigenvector models for solving the seismic inverse problem for the Helmholtz equation

Cited by 13 publications

References 87 publications

Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion

Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion

Quantitative inverse problem in visco-acoustic media under attenuation model uncertainty

Error Estimates for Adaptive Spectral Decompositions

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