Santosa, Fadil Numerical scheme for the inversion of acoustical impedance profile based on the Gelfand-Levitan method. (English) Zbl 0539.73019 Geophys. J. R. Astron. Soc. 70, 229-243 (1982). 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 Cited in 1 ReviewCited in 4 Documents 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 Keywords:Gelfand-Levitan technique; plane waves; smoothly stratified elastic half- space; propagation perpendicular to the free surface; material properties; depth-dependent; reconstruction of the elastic parameters; reflected waves; impulsive source at the surface; continuous differentiability of the spectral densities; time-domain meaning; numerical scheme; integral equation Citations:Zbl 0456.73086 PDFBibTeX XMLCite \textit{F. Santosa}, Geophys. J. R. Astron. Soc. 70, 229--243 (1982; Zbl 0539.73019)