Numerical solution of some inverse scattering problems of geophysics. (English) Zbl 0718.65092
The authors consider the inverse acoustic problem of finding a velocity inhomogeneity of unknown extension in a three-dimensional half space, given measurements of acoustic pressure on the free surface. By using theoretical results of the second author, they manage to reduce the problem to the solution of a linear integral equation of the first kind. They set to solve this equation numerically recognizing that it leads to a very ill-conditioned problem. By using quadratures, a regularization approach, and a trial and error method to determine the extent of the anomaly, they show in several examples the viability of the method.
Reviewer: V.Pereyra (Los Altos)
MSC:
| 65Z05 | Applications to the sciences |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 35R30 | Inverse problems for PDEs |
| 76Q05 | Hydro- and aero-acoustics |
| 86A22 | Inverse problems in geophysics |
Keywords:
inverse scattering; geophysics; inverse acoustic problem; linear integral equation of the first kind; ill-conditioned problem; regularization; trial and error methodReferences:
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