Abstract
An algorithm for the recovery of the parameter field of elastic waves by the method diffraction tomography is suggested. A priori information is taken into account in probabilistic form. Under different assumptions on the statistical correlations of the parameter field, different modifications of the algorithm are considered. The notion of the information sensitivity of the measurement field with respect to a fixed linear parameter field is introduced. It is shown that the greater the energy of the useful signal that has passed through the medium with a nonhomogeneity, the higher the information sensitivity of a given system of tomographic functionals.
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References
V. N. Troyan and G. A. Ryzhikov, “Diffraction tomography: construction and interpretation of tomographic functionals,”Zap. Nauchn. Semin. POMI,218, 176–196 (1994).
F. M. Golzman,Statistical Models of Interpretation [in Russian], Moscow (1971).
V. N. Troyan, “Estimation of seismic signal parameters by the correct method of moments,”Vopr. Dinam. Tear. Rasprostr. Seismich. Voln, Vol.24, 238–254 (1984).
V. N. Troyan, “A method of local estimation of parameters of seismic waves,”Vestn. Leningr. Univ.,11, 24–35 (1985).
C. R. Rao,Linear Statistical Interference and Its Applications, Wiley, New York (1965).
A. N. Tikhonov and V. Ya. Arsenin,Methods of Solving Ill-Posed Problems [in Russian], Moscow (1968).
V. F. Turchin, V. P. Kozlov, and N. S. Malkevich, “The use of methods of mathematical statistics for the solution of ill-posed problems,”Usp. Fiz. Nauk,102, No. 3, 13–48 (1970).
A. Tarantola,Inverse Problem Theory, Amsterdam (1987).
G. Backus and F. Gilbert, “Numerical applications of a formalism for geophysical inverse problems,”Geophys. J. R. Astr. Soc.,13, 136–152 (1967).
G. Backus and F. Gilbert, “The resolving power of gross Earth data,”Geophys. J. R. Astr. Soc.,16, 213–234 (1968).
V. N. Troyan, “The application of spline-functions for approximating geophysical information,”Vopr. Dinam. Teor. Rasprostr. Seismich. Voln, Vol.20, 184–197 (1981).
V. N. Troyan, “Solutions of interpretational seismic problems by the finite-element method,”Vestn. Leningr. Univ.,16, 25–37 (1983).
V. A. Morozov,Regular Methods for Solving Ill-Posed Problems [in Russian], Moscow (1987).
A. B. Bakushinskii and A. V. Goncharskii, “Ill-posed problems,” in:Numerical Methods and Applications [in Russian], Moscow (1989), pp. 123–178.
V. N. Troyan and Yu. M. Sokolov,Methods for Approximation of Geophysical Data on Computers [in Russian], Leningrad (1987).
V. N. Troyan,Statistical Methods for Processing Seismic Information in the Investigation of Complex Media [in Russian], Moscow (1982).
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 225–235.
This work was supported in part by the Russian Foundation for Basic Research (Grant No. 96-05-65904).
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Troyan, V.N., Ryzhikov, G.A. Construction of algorithms of reconstruction tomography. J Math Sci 96, 3423–3429 (1999). https://doi.org/10.1007/BF02172821
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DOI: https://doi.org/10.1007/BF02172821