Related papers: Semiclassical inverse spectral problem for elastic…

We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we extend the treatment of Love waves [arXiv: 1908.10529] to Rayleigh waves. Under certain conditions, and assuming that the Poisson ratio…

In this paper we study Love waves in a layered, elastic half-space. We first address the direct problem and we characterize the existence of Love waves through the dispersion relation. We then address the inverse problem and we show how to…

In this paper we solve an inverse resonance problem for the half-solid with vanishing stresses on the surface: Lamb's problem. Using a semi-classical approach we are able to simplify this three-dimensional problem of the elastic wave…

In this work we present a semi-classical approach to solve the inverse spectrum problem for one-dimensional wave equations for a specific class of potentials that admits quasi-stationary states. We show how inverse methods for potential…

In this paper we prove an inverse resonance theorem for the half-solid with vanishing stresses on the surface via Weyl-Titchmarsh function. Using a semi-classical approach it is possible to simplify this three-dimensional problem of the…

In this paper, we present a semiclassical description of surface waves or modes in an elastic medium near a boundary, in spatial dimension three. The medium is assumed to be essentially stratified near the boundary at some scale comparable…

We consider in a simple and general way elastic waves in isotropic and anisotropic media, their polarization, speeds, reflection from interfaces with mode conversion, and surface waves. Reflection of quasi transverse waves in anisotropic…

It is shown that a slip wave solution exists for anti-plane sliding of an elastic layer on an elastic half-space. It is a companion solution to the well-known Love wave solution.

The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…

We consider the problem of reconstructing the seabed topography from observations of surface gravity waves. We formulate the problem as a classical inverse scattering problem using the mild-slope equation, and analyze the topographic…

We investigate the propagation of Love waves in an isotropic half-space modelled as a linear {elastic isotropic} Cosserat material. To this aim, we show that a method commonly used to study Rayleigh wave propagation is also applicable to…

We consider an inverse problem for the elastic wave of simultaneously reconstructing the impedance and the geometric information of the bounded body that is occupied by a homogeneous and isotropic elastic medium from the measured Cauchy…

Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…

In this work, we are concerned with the inverse scattering by interfaces for the linearized and isotropic elastic model at a fixed frequency. First, we derive complex geometrical optic solutions with linear or spherical phases having a…

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,…

We deal with the problem of the linearized and isotropic elastic inverse scattering by interfaces. We prove that the scattered $P$-parts or $S$-parts of the far field pattern, corresponding to all the incident plane waves of pressure or…

Love waves are antiplane elastic waves which propagate along the surface of a heterogeneous medium. Under time-harmonic regime, they are governed by a scalar equation of the Helmholtz type. We exploit the invariance of this governing…

An inverse problem of wave propagation into a weakly laterally inhomogeneous medium occupying a half-space is considered in the acoustic approximation. The half-space consists of an upper layer and a semi-infinite bottom separated with an…

We show that an inverse scattering problem for a semilinear wave equation can be solved on a manifold having an asymptotically Minkowskian infinity, that is, scattering functionals determine the topology, differentiable structure, and the…

We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…