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Impedance profile inversion via the first transport equation. (English) Zbl 0529.73029

MSC:
74J20Wave scattering (solid mechanics)
74J25Inverse problems (waves in solid mechanics)
74J15Surface waves (solid mechanics)
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Full Text: DOI
References:
[1] Gerver, M.: Geophys J. Roy. astronom. Soc.. 21, 337-357 (1970)
[2] Ware, J.; Aki, K.: Continuous and discrete inverse-scattering problems in a stratified elastic medium: I, plane waves at normal incidence. J. acoust. Soc. amer. 45, 911-921 (1969) · Zbl 0197.23102
[3] Berryman, J.: Inverse methods for elastic waves in stratified media. Bell labs preprint (1979)
[4] Carroll, R.; Santosa, F.: Scattering techniques for a one-dimensional inverse problem in geophysics. Math. meth. Appl. sci. (1980) · Zbl 0456.73087
[5] Bamberger, A.; Chavent, G.; Lailly, P.: About the stability of the inverse problem in 1-D wave equations--application to the interpretation of seismic profiles. Appl. math. Optim. 5, 1-47 (1979) · Zbl 0407.35073
[6] Symes, W.: Stable solution of the inverse reflection problem for a smoothly stratified elastic medium. SIAM J. Math. anal. 12, No. 3 (1981) · Zbl 0482.73025
[7] Symes, W.: Inverse boundary value problems and a theorem of Gelfand and levitan. J. math. Anal. appl. 71, No. 1, 379-402 (1979) · Zbl 0425.35092
[8] W. Symes, Numerical stability in an inverse scattering problem, SIAM J. Numer. Anal. 17 (5) 707--732. · Zbl 0463.65064
[9] Symes, W.: Invertibility of the trace operator and local energy decay for the string with BV coefficient. (1980)
[10] Symes, W.: Linearization stability of 2-D and 3-D acoustic imaging problems. (1983)
[11] Symes, W.; Driessel, K.: Fast and accurate algorithms for 1-D impedance profile reconstruction. (1981)
[12] Courant, R.; Hilbert, D.: Methods of mathematical physics. (1962) · Zbl 0099.29504
[13] Hadamard, J.: Le problème de Cauchy et LES équations aux derivées partielles linéaires hyperboliques. (1952)
[14] Gel’fand, I. M.; Levitan, B. M.: On the determination of a differential equation from its spectral function. Trans. amer. Math. soc. 1, No. 2, 253-304 (1955) · Zbl 0066.33603