Recovery of wave speeds and density of mass across a heterogeneous smooth interface from acoustic and elastic wave reflection operators

Bhattacharyya, Sombuddha; Hoop, Maarten V. de; Katsnelson, Vitaly; Uhlmann, Günther

doi:10.1007/s13137-022-00199-1

Cited by 3 publications

(1 citation statement)

References 32 publications

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“…Analyzing these problems under realistic assumptions is subject to current research and often requires the use of sophisticated mathematical tools, see e.g. Rachele (2000), Stefanov et al (2021), Bhattacharyya et al (2022) for the application of microlocal techniques to the recovery of material parameters from certain type of boundary measurements. Furthermore, numerical methods which make optimal use of the latest analytical results and lead to provably convergent and reliable solutions of the inverse problems are in high demand.…”

Section: Introductionmentioning

confidence: 99%

Unique continuation for the Lamé system using stabilized finite element methods

Burman

Preuß

2023

Int J Geomath

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We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove convergence rates for the proposed method which take into account the noise level and the polynomial degree. A series of numerical experiments corroborates our theoretical results and explores additional aspects, e.g. how the quality of the reconstruction depends on the geometry of the involved domains. We find that certain convexity properties are crucial to obtain a good recovery of the wave displacement outside the data domain and that higher polynomial orders can be more efficient but also more sensitive to the ill-conditioned nature of the problem.

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Section: Introductionmentioning

confidence: 99%

Unique continuation for the Lamé system using stabilized finite element methods

Burman

Preuß

2023

Int J Geomath

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The solid-fluid transmission problem

Eptaminitakis,

Stefanov

2024

Trans. Amer. Math. Soc.

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We study microlocally the transmission problem at the interface between an isotropic linear elastic solid and a linear inviscid fluid. We set up a system of evolution equations describing the particle displacement and velocity in the solid, and pressure and velocity in the fluid, coupled by suitable transmission conditions at the interface. We show well-posedness for the coupled system and study the problem microlocally, constructing a parametrix for it using geometric optics. This construction describes the reflected and transmitted waves, including mode converted ones, related to incoming waves from either side. We also study formation of surface Scholte waves. Finally, we prove that under suitable assumptions, we can recover the s- and the p-speeds, as well as the speed of the liquid, from boundary measurements.

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