Uniqueness result for inverse problem of geophysics II

Uniqueness Result for Inverse Problem of Geophysics II

It is proved that an analytic in a bounded region inhomogeneity can be uniquely recovered from the surface measurements of the acoustic field for a fixed position of the source and all frequencies. Introduction. Let evu := [v* + k* + k*V(Z)] U(Z!,k) = -6(Z) in R3, I = (~i,~&ts) (1) U satisfies the radiation condition, k = const > 0, (2) u = 0 outside V, a bounded domain with a C” boundary, V C ...

Uniqueness result for inverse problem of geophysics : I

A uniqueness result is proved for the 3D inverse scattering problem of geophysics with a fixed position of the source and surface data given for all frequencies.

Uniqueness Result for Inverse Problem of Geophysics: I

A Uniqueness Result for the Inverse Transmission Problem

The problem of inverse scattering of a plane acoustic wave by a penetrable scatterer with the transmission boundary condition is studied. It is proved that, if the constant exterior wavenumber is known, then the shape of the obstacle and the constant transmission parameter and the constant interior wavenumber are uniquely determined by the scattering amplitude known at the constant exterior wav...

Non-uniqueness result for a hybrid inverse problem

Hybrid inverse problems aim to combine two imaging modalities, one that displays large contrast and one that gives high resolution. Mathematically, quantitative reconstructions in such hybrid problems involve reconstructing coefficients in a partial differential equation (PDE) from point-wise functionals of the coefficients and the PDE solution. There are many settings in which such inverse pro...