Factorization of the wave equation in a nonplanar stratified medium. (English) Zbl 0646.73012
The method of wave splitting is a powerful technique for solving one- dimensional time-dependent direct and inverse problems. The author considers the wave equation for a stratified medium where the stratifications are in the form of a family of nested \(C^ 2\) surfaces along which the velocity c is constant and, using potential type integral operators (single and double layer potential type) he gives the expression of incoming and outgoing wave conditions for surfaces where c is constant. Then the scalar wave equation is split into a vector system involving the components u \(+\) (outgoing wave) and u - (incoming wave). As pointed out in the paper this system is decoupled in a region where c is constant.
Reviewer: Ding Hua
MSC:
74J25 | Inverse problems for waves in solid mechanics |
35L99 | Hyperbolic equations and hyperbolic systems |
35R30 | Inverse problems for PDEs |
31A25 | Boundary value and inverse problems for harmonic functions in two dimensions |
Keywords:
family of nested C(sup 2)-surfaces; wave splitting; inverse scattering problem; time-dependent single and double layer potential type; decomposition; one-dimensional time-dependent direct and inverse problems; stratifications; potential type integral operators; incoming and outgoing wave conditions; scalar wave equationReferences:
[1] | DOI: 10.1002/sapm19624111 · Zbl 0104.43605 · doi:10.1002/sapm19624111 |
[2] | DOI: 10.1016/0022-247X(83)90115-4 · Zbl 0542.35058 · doi:10.1016/0022-247X(83)90115-4 |
[3] | DOI: 10.1121/1.390166 · Zbl 0525.73028 · doi:10.1121/1.390166 |
[4] | DOI: 10.1063/1.525978 · Zbl 0548.35027 · doi:10.1063/1.525978 |
[5] | DOI: 10.1063/1.526149 · Zbl 0551.76069 · doi:10.1063/1.526149 |
[6] | DOI: 10.1063/1.527086 · Zbl 0594.45011 · doi:10.1063/1.527086 |
[7] | DOI: 10.1063/1.527547 · Zbl 0636.35044 · doi:10.1063/1.527547 |
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