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Numerical scheme for the inversion of acoustical impedance profile based on the Gelfand-Levitan method. (English) Zbl 0539.73019

The author considers the propagation of plane waves in a smoothly stratified elastic half-space, with direction of propagation perpendicular to the free surface, and the material properties of the medium assumed to be depth-dependent. The inverse problem is the reconstruction of the elastic parameters from the reflected waves, due to an impulsive source at the surface. The method is due to R. Carroll and F. Santosa [Math. Methods Appl. Sci. 3, 145-171 (1981; Zbl 0456.73086)] and is mainly a spectral approach, requiring only continuous differentiability of the spectral densities. It is further refined to give it time-domain meaning, and a numerical scheme for solving the resulting integral equation is proposed and discussed.
Reviewer: W.Wreszinski

MSC:

74J25 Inverse problems for waves in solid mechanics
35R30 Inverse problems for PDEs
65L20 Stability and convergence of numerical methods for ordinary differential equations
74S99 Numerical and other methods in solid mechanics

Citations:

Zbl 0456.73086
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