Inverse boundary value problem for ocean acoustics

Abstract

For an ocean with constant depth and rigid bottom which contains compactly supported inhomogeneity of the water sound velocity, we prove uniqueness for the identification of the inhomogeneity from the Dirichlet‐to‐Neumann (DtN) map on the surface of a bounded region containing the inhomogeneity. The DtN map is the map which maps the pressure applied on the boundary of this region to the corresponding flux (displacement). In an analogous geometric configuration and with similar boundary conditions, the uniqueness for the inverse electroconductivity problem from the DtN map (i.e. voltage‐to‐current map) can be proved in the same framework. Copyright © 2001 John Wiley & Sons, Ltd.

Inverse Boundary-Value Problem for Ocean Acoustics Using Point Sources

“…In Section 2 we will give the proof of Theorem 1.1. This is done by reduction to the uniqueness result for the inverse boundary value problem for ocean acoustics proved by Ikehata et al [8]. In Section 3 we will give the proof of Theorem 1.2 by reduction to Nachman's result [9].…”

Inverse Boundary-Value Problem for Ocean Acoustics Using Point Sources

“…In Section 2 we will give the proof of Theorem 1.1. This is done by reduction to the uniqueness result for the inverse boundary value problem for ocean acoustics proved by Ikehata et al [8]. In Section 3 we will give the proof of Theorem 1.2 by reduction to Nachman's result [9].…”

Inverse problem for the Schrödinger operator in an unbounded strip

“…Few results for inverse problems exist in a two-dimensional strip (see [7]). For the layer R n × [0, h] with n ≥ 2, several results exist for the stationnary inverse problems (see [2], [8], [9], [13], [17], ...). On the other hand, we can link our problem to the determination of the curvature function for a curved quantum guide (see [11], [6], [10], ...).…”

Inverse boundary value problems with partial data in unbounded domains

“…Also, the gauges on the boundary are different in these two cases. We would like to point out that the inverse problems with full boundary measurements for Schrödinger equations with Yang-Mills potentials in a bounded domain were studied by Eskin [9], and the inverse problems in a slab with various settings were also investigated in [2,3,8,13,16,17,27,31].…”

Inverse Boundary-Value Problem for Ocean Acoustics Using Point Sources

“…In Section 2 we will give the proof of Theorem 1.1. This is done by reduction to the uniqueness result for the inverse boundary value problem for ocean acoustics proved by Ikehata et al [8]. In Section 3 we will give the proof of Theorem 1.2 by reduction to Nachman's result [9].…”

Inverse problem for the Schrödinger operator in an unbounded strip

“…Few results for inverse problems exist in a two-dimensional strip (see [7]). For the layer R n × [0, h] with n ≥ 2, several results exist for the stationnary inverse problems (see [2], [8], [9], [13], [17], ...). On the other hand, we can link our problem to the determination of the curvature function for a curved quantum guide (see [11], [6], [10], ...).…”

Inverse boundary value problems with partial data in unbounded domains

“…Also, the gauges on the boundary are different in these two cases. We would like to point out that the inverse problems with full boundary measurements for Schrödinger equations with Yang-Mills potentials in a bounded domain were studied by Eskin [9], and the inverse problems in a slab with various settings were also investigated in [2,3,8,13,16,17,27,31].…”

Inverse Boundary-Value Problem for Ocean Acoustics Using Point Sources

“…In Section 2 we will give the proof of Theorem 1.1. This is done by reduction to the uniqueness result for the inverse boundary value problem for ocean acoustics proved by Ikehata et al [8]. In Section 3 we will give the proof of Theorem 1.2 by reduction to Nachman's result [9].…”

Inverse problem for the Schrödinger operator in an unbounded strip

“…Few results for inverse problems exist in a two-dimensional strip (see [7]). For the layer R n × [0, h] with n ≥ 2, several results exist for the stationnary inverse problems (see [2], [8], [9], [13], [17], ...). On the other hand, we can link our problem to the determination of the curvature function for a curved quantum guide (see [11], [6], [10], ...).…”

Inverse boundary value problems with partial data in unbounded domains

“…Also, the gauges on the boundary are different in these two cases. We would like to point out that the inverse problems with full boundary measurements for Schrödinger equations with Yang-Mills potentials in a bounded domain were studied by Eskin [9], and the inverse problems in a slab with various settings were also investigated in [2,3,8,13,16,17,27,31].…”