Uniqueness for the inverse boundary value problem of piecewise homogeneous anisotropic elasticity in the time domain

Cârstea, Cătălin I.; Nakamura, Gen; Oksanen, Lauri

doi:10.1090/tran/8014

Cited by 5 publications

(3 citation statements)

References 37 publications

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“…In [5], it is assumed that the density ρ was trivial, but with similar yet more sophisticated arguments, it was proved in [23] that this assumption can be dispensed with, and that both piecewise smooth wavespeeds can be recovered from exterior measurements even when the density is piecewise smooth. The simpler case of piecewise analytic and piecewise constant coefficients is considered in [8,7] and the arguments are quite different than our approach here. In our approach, low frequencies are not required in the data.…”

Section: Introductionmentioning

confidence: 99%

Recovery of piecewise smooth density and Lamé parameters from high-frequency exterior Cauchy data

Bhattacharyya¹,

Hoop²,

Katsnelson³

et al. 2022

Preprint

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We consider an isotropic elastic medium occupying a bounded domain Ω ⊂ R 3 whose density and Lamé parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave equation, but only outside Ω and only for initial data supported outside Ω, and we study the recovery of the density and Lamé parameters. For known density, results have recently been obtained using the scattering control method to recover wave speeds. Here, we extend this result to include the recovery of the density in addition to the Lamé parameters under certain geometric conditions using techniques from microlocal analysis and a connection to local tensor tomography.

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Section: Introductionmentioning

confidence: 99%

Recovery of piecewise smooth density and Lamé parameters from high-frequency exterior Cauchy data

Bhattacharyya¹,

Hoop²,

Katsnelson³

et al. 2022

Preprint

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“…inverse source problems [4,5,31], inverse obstacle scattering [20,32,33], seismic inverse scattering [41], and see e.g. [6,8,15,16,22,34,35,36,37,46] for inverse boundary value problems of determining the elastic body, [19,45] for inverse problems for nonlinear elastic wave equations, and [9,27,38,39] for identifying inclusions or cracks.…”

Section: Introductionmentioning

confidence: 99%

Quantitative unique continuation for the elasticity system with application to the kinematic inverse rupture problem

Hoop¹,

Lassas²,

Lu³

et al. 2022

Preprint

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We obtain explicit estimates on the stability of the unique continuation for a linear system of hyperbolic equations. In particular our result applies to the elasticity and Maxwell systems. As an application, we study the kinematic inverse rupture problem of determining the jump in displacement and the friction force at the rupture surface, and we obtain new features on the stable unique continuation up to the rupture surface.

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“…Once having this, we note that we can also have it even if we weaken the regularity assumption "analytic" to "piecewise analytic". Then, it can be applied more widely to inverse problems (see [3], [9]).…”

mentioning

confidence: 99%

Global unique continuation from the boundary for a system of viscoelasticity with analytic coefficients and a memory term

Eller¹,

Honda²,

Lin³

et al. 2022

IPI

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<p style='text-indent:20px;'>A global unique continuation property (UCP) from the boundary for solutions to a viscoelastic system with a memory term is presented. The density and elasticity tensors are assumed to be real analytic. The tensors can be anisotropic and satisfy physically natural conditions such as full symmetry and strong convexity. The global UCP is given in terms of the travel time of the slowest wave of the viscoelastic system, which is the optimal description for the global UCP in our setup.</p>

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Uniqueness for the inverse boundary value problem of piecewise homogeneous anisotropic elasticity in the time domain

Cited by 5 publications

References 37 publications

Recovery of piecewise smooth density and Lamé parameters from high-frequency exterior Cauchy data

Recovery of piecewise smooth density and Lamé parameters from high-frequency exterior Cauchy data

Quantitative unique continuation for the elasticity system with application to the kinematic inverse rupture problem

Global unique continuation from the boundary for a system of viscoelasticity with analytic coefficients and a memory term

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