Time-reversal algorithms in viscoelastic media

Ammari, Habib; Bretin, Élie; Garnier, Josselin; Wahab, Abdul

doi:10.1017/s0956792513000107

Cited by 42 publications

(53 citation statements)

References 46 publications

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“…Moreover, causality condition (A3) is satisfied for α ksb * defined as in (2), but not for α tv * defined as in (3). Proof.…”

Section: Waves Forward In Timementioning

confidence: 99%

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On Time Reversal in Photoacoustic Tomography for Tissue Similar to Water

Kowar¹

2014

SIAM J. Imaging Sci.

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This paper is concerned with time reversal in photoacoustic tomography (PAT) of dissipative media that are similar to water. Under an appropriate condition, it is shown that the time reversal method in [23,2] based on the non-causal thermo-viscous wave equation can be used if the non-causal data is replaced by a time shifted set of causal data. We investigate a similar imaging functional for time reversal and an operator equation with the time reversal image as right hand side. If required, an enhanced image can be obtained by solving this operator equation. Although time reversal (for noise-free data) does not lead to the exact initial pressure function, the theoretical and numerical results of this paper show that regularized time reversal in dissipative media similar to water is a valuable method. We note that the presented time reversal method can be considered as an alternative to the causal approach in [11] and a similar operator equation may hold for their approach.

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“…Moreover, causality condition (A3) is satisfied for α ksb * defined as in (2), but not for α tv * defined as in (3). Proof.…”

Section: Waves Forward In Timementioning

confidence: 99%

“…In this paper we focus on a time reversal method in dissipative media [2,3,5,9,11,14,16,20,22,23] and show that under an appropriate condition…”

Section: Introductionmentioning

confidence: 99%

On Time Reversal in Photoacoustic Tomography for Tissue Similar to Water

Kowar¹

2014

SIAM J. Imaging Sci.

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“…Many dedicated mathematical and computational algorithms for the reconstruction of location and parameters of anomalies of different geometrical nature (cavities, cracks, and inclusions) have been proposed over the past few decades (see, for instance, [1,4,6,12,13,14,15,21,26,27,29,31,33,34,42,43,55], the survey articles [16,11], and the monograph [5]). Most of the classical techniques are suited to continuous measurements, in other words, to experimental setups allowing to measure continuum deformations inside the elastic body or on a substantial part of its boundary.…”

Section: Introductionmentioning

confidence: 99%

A Joint Sparse Recovery Framework for Accurate Reconstruction of Inclusions in Elastic Media

Yoo¹,

Jung²,

Lim³

et al. 2017

SIAM J. Imaging Sci.

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A robust algorithm is proposed to reconstruct the spatial support and the Lamé parameters of multiple inclusions in a homogeneous background elastic material using a few measurements of the displacement field over a finite collection of boundary points. The algorithm does not require any linearization or iterative update of Green's function but still allows very accurate reconstruction. The breakthrough comes from a novel interpretation of Lippmann-Schwinger type integral representation of the displacement field in terms of unknown densities having common sparse support on the location of inclusions. Accordingly, the proposed algorithm consists of a two-step approach. First, the localization problem is recast as a joint sparse recovery problem that renders the densities and the inclusion support simultaneously. Then, a noise robust constrained optimization problem is formulated for the reconstruction of elastic parameters. An efficient algorithm is designed for numerical implementation using the Multiple Sparse Bayesian Learning (M-SBL) for joint sparse recovery problem and the Constrained Split Augmented Lagrangian Shrinkage Algorithm (C-SALSA) for the constrained optimization problem. The efficacy of the proposed framework is manifested through extensive numerical simulations. To the best of our knowledge, this is the first algorithm tailored for parameter reconstruction problems in elastic media using highly under-sampled data in the sense of Nyquist rate.

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“…In order to perform the convolution involved in the calculation of the kernels (1) and (2), simultaneous access to the forward wavefield s at time t and the adjoint wavefield s † at time T − t is required (or conversely, since…”

Section: Introductionmentioning

confidence: 99%

Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion

Komatitsch¹,

Xie

Bozdag

et al. 2016

Geophys. J. Int.

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We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the K α sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersion-only kernels. *** This manuscript is now published as a paper in the Geophysical JournalInternational, 2016. *** I IntroductionEfficient numerical methods for simulating the propagation of acoustic, elastic, or anelastic waves in the time domain are widely available, for instance based on finite-difference methods see e.g., 63 for a review, spectral-element methods e.g., 32;61;30;31 , or standard finiteelement methods e.g., 28 . Nowadays, these techniques are heavily used for imaging based on full waveform inversion (FWI) or adjoint tomography e.g., 59;44;60;63;20;41 . FWI involves fitting band-pass filtered versions of observed seismograms by minimizing least-squared differences between observed and synthetic seismograms. Adjoint tomography generalizes FWI by considering arbitrary measures of misfit, e.g., cross-correlation traveltimes, multi-taper phase and amplitude anomalies, or instantaneous phase measurements.In the context of imaging, it is useful to resort to the concept of sensitivity kernels e.g., 56;57;58;59;60;39;20;21 . Let s denote the forward displacement wavefield and s † the adjoint wavefield. In an isotropic Earth model, the kernels K κ and K µ represent Fréchet derivatives with respect to relative bulk and shear moduli perturbations, respectively. These kernels are given by e.g.,whereanddenote the traceless strain deviator and its adjoint, respectively, x is the position vector, and κ and µ are the bulk and shear moduli, respectively. Their expression remains valid for elastic perturbations superimposed on an anelastic Earth model 39 if the regular and adjoint wavefields are computed in that anelastic reference model. In practical applications, it is often useful to define compressional and shear wavespeed sensitivity kernels, namely 59;60andIn order to perform the convolution involved in the calculation of the kernels (1) and (2), simultaneous access to the forward wavefield s at time t and the adjoint wavefield s † at time T − t is required (or conversely, sinceconvolving two funct...

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Time-reversal algorithms in viscoelastic media

Cited by 42 publications

References 46 publications

On Time Reversal in Photoacoustic Tomography for Tissue Similar to Water

On Time Reversal in Photoacoustic Tomography for Tissue Similar to Water

A Joint Sparse Recovery Framework for Accurate Reconstruction of Inclusions in Elastic Media

Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion

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