# Numerical inverse wave problem in anisotropic elastic media

Florian Faucher, Ha Pham, Otmar Scherzer, Hélène Barucq

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Florian Faucher, Ha Pham, Otmar Scherzer, Hélène Barucq. Numerical inverse wave problem in anisotropic elastic media. Workshop on Computational methods for Inverse and Ill-posed problems, University College London, Nov 2024, Londres, United Kingdom. hal-04854278

HAL Id: hal-04854278

https://inria.hal.science/hal-04854278v1

Submitted on 23 Dec 2024

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Numerical inverse wave problem in anisotropic elastic media

Florian Faucher<fnref n="1" />, Ha Pham<fnref n="1" />, Otmar Scherzer<fnref n="2" />, Hélène Barucq<fnref n="1" />

We consider the quantitative inverse problem for the reconstruction of physical properties of a medium are from wave measurements. We consider linear viscoelasticity to model the propagation of waves in solid materials, taking into account attenuation and anisotropy of the media. In this work, we employ the time-harmonic wave equations to facilitate working with different attenuation models, which are frequency-dependent. For numerical discretization, we use the hybridizable discontinuous Galerkin (HDG) method which employs static condensation to reduce the computational cost. We perform quantitative inversion by following a minimization algorithm where the elastic properties are iteratively updated. We carry out reconstructions with attenuation model uncertainty, and highlight the importance of considering anisotropy in the model. We provide synthetic experiments for ultrasound imaging of breast samples.

<footnote n="1">¹ Team Makutu, Inria, University of Pau and Pays de l'Adour, TotalEnergies, CNRS UMR 5142, France;</footnote>

<footnote n="2">² Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria</footnote>