Estimation of discontinuous coefficients and boundary parameters for hyperbolic systems.

*(English)*Zbl 0645.65087This 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.

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

##### MSC:

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 |