Two approaches to the problem of ray seismic tomography
Keywords:geotomography, nonlinearity, geometrical seismics, Lavrentyev—Romanov linearization, the Taylor approximation
Approximation of nonlinear geophysical medium as a linear one substantiates a transition to geometrical seismics based on geometric optics. Conditions, necessary and sufficient for application of geometrical optics bring possibility of linearization the eikonal equation and produce two approaches in the problems of seismic tomography: a classical Lavrentyev— Romanov linearization and the Taylor approximation.
Bullen L. E., 1966. Introduction to theoretical seismology. Moscow: Mir, 460 p. (in Russian).
Geyko V. S., 1997. Teylor’s approximation of the wave equation and the eikonal equation in inverse seismic problems. Geofizicheskiy zhurnal 19(3), 48—68 (in Russian).
Gel'fand I. M., Graev M. I., Vilenkin N. Ya., 1962. Integral geometry and representation theory. Ser. Of generalized functions. Moscow: Fizmatgiz, is. 5. 656 p. (in Russian).
Goldin S. V., 2005. Introduction to geometric seismic. Novosibirsk: NSU Publ., 265 p. (in Russian).
Goldin S. V., 1997. Inverse problems of radiation of seismic tomography. Geologiya i geofizika 38(5), 981—998 (in Russian).
Jeffries G., 1960. Earth, its origin, history, and structure. Moscow: Izd-vo inostr. lit., 485 p. (in Russian).
Kravtsov Yu. A., Orlov Yu. I., 1980 a. Geometrical optics of inhomogeneous media. Moscow: Nauka, 305 p. (in Russian).
Kravtsov Yu. A., Orlov Yu. I., 1980 b. Limits of applicability of the method of geometric optics and related matters. Uspehi fizicheskih nauk 133(is.3), 475—496 (in Russian).
Lavrentiev M. M., Romanov V. G., 1966. On three linearized inverse problems for hyperbolic equations. Doklady AN SSSR 171, 1279—1281 (in Russian).
Lavrentev M. M., Romanov V. G., Shishatskiy S. P., 1980. Some problems of mathematical physics and analysis. Moscow: Nauka, 286 p. (in Russian).
Mukhametov R. G., 1977. Task of handling two-dimensional Riemannian metric integral geometry. Doklady AN SSSR 232, 32—45 (in Russian).
Nikolaev A. V., 1997. Problems geotomography. In: Issues geotomography. Moscow: Nauka, P. 4—38 (in Russian).
Geotomography problems, 1997. Ed. A. V. Nikolaev. Moscow: Nauka, 336 p. (in Russian).
Rudenko O. V., 2006. Giant nonlinearities in structurally inhomogeneous media and the fundamentals of nonlinear acoustic diagnostics. Uspehi fizicheskih nauk 176(1), 77—95 (in Russian).
Rudenko O. V., 2007. Nonlinear waves: some biomedical applications. Uspehi fizicheskih nauk 177(4), 374—383 (in Russian).
Rytov S. M., 1940. Modulated Waves. Proceedings of the Lebedev Physics Institute 2(1), P. 3 (in Russian).
Rytov S. M., 1938. On the transition from wave to geometrical optics. Doklady AN SSSR 18(2), 263—266 (in Russian).
Sadowskiy M. A., 2004. Selected works. Geophysics and physics of the explosion. Moscow: Nauka, 440 p. (in Russian).
Seismic tomography, 1990. Ed. G. Nolett. Moscow: Mir, 416 p. (in Russian).
Tichotskiy S. A., Fokin I. V., Shur D. Yu., 2011. Active radiation seismic tomography using adaptive wavelet parameterization of the system functions. Fizika Zemli (4), 67—86 (in Russian).
Yakovlev A. B., Bushmina N. A., Kulakov I. Yu, Dobretsov N. L., 2012. Structure of the upper mantle of the Arctic region according to regional seismic tomography. Geologiya i geofizika (10), 1261—1272 (in Russian).
Yanovska T. B., 2012. Methodology three-dimensional ray tomography based on the assumption of smoothness of lateral velocity variations. Fizika Zemli (5), 3—15 (in Russian).
Yanovska T. B., 1997. Problems seismic tomography. In: Issues geotomography. Moscow: Nauka, P. 86—98 (in Russian).
Aki K., Christofersson A., Husebye E. S., 1977. Determination of the three — dimensional seismic structure of the lithosphere. J. Geophys. Res. 82, 277—296.
Anderson D. L., 2002. Plate tectonics as far-from-equilibrium self-organized system. Plate boundary zones. Geodynamic series. Mon. 30. Amer. Geophys. Union. 411—425.
Geyko V. S., 2004. А general theory of the seismic travel-time tomography. Geofizicheskiy zhurnal 26(2), 3—32.
Gerver M., Markushevich V., 1966. Determination of a seismic wave velocity from the travel-time curve. Geophys. J. Roy. Astron. Soc. 11, 165—173.
Goldin S. V., 2011. Ray reflection tomography: review and comments. In: A theory of interpretation in seismic and seismology. Novosibirsk: IPGG SB RAS, P. 247—265.
Foulger G. R., Panza G. F, Artemieva I. M, Bastow I. D., Cammarano F., Evans R., Hamilton W. B, Julian B. R., Lustrino M., Thybo H., Yanovskaya T. B., 2013. Caveats on tomographic images. Terra Nova 25(4), 259—281.
Kulakov I., Kaban M. K., Tesouro M., Cloetingh S., 2009. P- and S-velocity anomalies in the upper mantle beneath Europe from tomographic inversion of the ISC-data. Geophys. J. Int. 179, 345—366.
Liu Q., Gu Y. J., 2012. Seismic imaging: From classical to adjoint tomography. Tectonophysics 566-567, 31—66.
Tikhotsky S., Achauer U., 2008. Inversion of controlled-source seismic tomography and gravity data with the self-adaptive wavelet parameterization of velocities and interface. Geophys. J. Int. 172, 619—630.
How to Cite
Copyright (c) 2020 Geofizicheskiy Zhurnal
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).