Numerical recovery of the layered medium from the surface data. (English) Zbl 0673.65091
The purpose of the paper is to give the numerical solution of an inverse problem of practical interest (for example, in geophysics) and to report on the numerical results. The problem consists of finding the refraction coefficient of the medium, given the surface data. The method is based on the analytic solution of the inverse problem, found by a certain Fourier transform. The assumption of a layered medium (i.e. that the refraction coefficient is piecewise constant), making the problem less ill-posed, leads to a system of nonlinear algebraic equations. It can be solved by an optimization method.
Here a modified Newton method is used to minimize the target function (modified by a little change of the search direction to overcome the difficulties from ill-conditioned matrices). An outline of the algorithm and practical recommendations are given. Some (six) examples compare the assumed and recovered parameters. They show that the method can handle also the cases with noisy data when the noise level is within a certain level.
Here a modified Newton method is used to minimize the target function (modified by a little change of the search direction to overcome the difficulties from ill-conditioned matrices). An outline of the algorithm and practical recommendations are given. Some (six) examples compare the assumed and recovered parameters. They show that the method can handle also the cases with noisy data when the noise level is within a certain level.
Reviewer: E.Lanckau
MSC:
| 65Z05 | Applications to the sciences |
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
| 35R30 | Inverse problems for PDEs |
| 86A20 | Potentials, prospecting |
References:
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