an:04052956
Zbl 0645.65087
Lamm, Patricia K.; Murphy, Katherine A.
Estimation of discontinuous coefficients and boundary parameters for hyperbolic systems
EN
Q. Appl. Math. 46, No. 1, 1-22 (1988).
00168002
1988
j
65Z05 35R30 35L05 65J10 86A15 65N30 93B30 93C20
boundary parameters; hyperbolic systems; inverse problems; parameter identification; identification of the wave equation; (acoustic) seismic problems; discontinuous coefficients; numerical examples; convergence
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 \textit{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.
V.Pereyra
Zbl 0613.93018; Zbl 0612.93014