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He, Sailing; Weston, Vaughan H.

Inverse problem for the dissipative wave equation in a stratified half- space and linearization of the imbedding equations. (English) Zbl 0748.35056

Inverse Probl. 8, No. 3, 435-455 (1992).
Summary: The invariant imbedding procedure with a modified planar wave-splitting process is applied to the dissipative wave equation for a smooth stratified medium. The imbedding equations for \(R_ 0\) and \(R_ 2\), respectively the zeroth and second moments of the kernel of the reflection operator, are obtained. A linearization of the nonlinear imbedding equation for \(R_ 0\) is given, which greatly simplifies the numerical procedure and improves the speed one order in the direct and inverse problems. Numerical results are given for the direct problem, and for the inverse problem where the zeroth and second transverse moments of the reflection data are given on one side.

Cited in 9 Documents

MSC:

35R30 Inverse problems for PDEs
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
35L05 Wave equation
78A45 Diffraction, scattering

Keywords:

reconstruction of the phase velocity and the dissipation coefficient; one-sided reflection data; moment method; invariant imbedding procedure; modified planar wave-splitting process; smooth stratified medium; zeroth and second moments; kernel of the reflection operator
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References:

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