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Estimation of discontinuous coefficients and boundary parameters for hyperbolic systems. (English) Zbl 0645.65087
This paper deals with the problem of identifying various distributed parameters of interest in (acoustic) seismic problems for piecewise smooth, one-dimensional (i.e. horizontally stratified) media. It extends the ideas of H. T. Banks and the second author [SIAM J. Control Optimization 24, 926-950 (1986; Zbl 0613.93018)] to the case of discontinuous coefficients, including the determination of the location of the discontinuities. The method employed requires the knowledge a priori of the number of discontinuities, although the first author [ibid. 25, 18-37 (1987; Zbl 0612.93014)] has shown in examples that this assumption is not too restrictive.
Some numerical examples are included that show the viability of the method, as well as some indication on the practical aspects of its implementation, which are not apparent in the theoretical treatment of convergence which occupies the main bulk of the paper. A good grasp of previous development and of functional analysis is necessary to go through those theoretical results.
Reviewer: V.Pereyra

65Z05 Applications to the sciences
35R30 Inverse problems for PDEs
35L05 Wave equation
65J10 Numerical solutions to equations with linear operators (do not use 65Fxx)
86A15 Seismology (including tsunami modeling), earthquakes
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
93B30 System identification
93C20 Control/observation systems governed by partial differential equations
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