Correction of velocity profile by the method of imitation of annealing
Keywords:method of imitation of annealing, “eikonal” equation, finite-difference valuation, minimization of function of losses, combinatorial optimization, arrivals of longitudinal waves, solution of direct problem, DSS, function of the losses value, iteration, hodograph
Reversal of hodograph in 2D formulation, obtained by finite-difference solution of eikonal has been put into practice by the method of imitation of “annealing” in the problem of combinatorial optimization for uneven and interrupted functions. Hodographs of seismic studies of DSS of the territory of Ukraine (profile DOBRE-5) have been used as a target function. Velocity function of the medium was restored by two-dimensional published models of P-waves velocities. Refinements of optimal functioning of the algorithm of “annealing” imitation and of regime of initial function filtration during the process of minimization of the function of losses value are presented in details.
Babich V. M., Buldyrev V. S., 1972. Asymptotic methods in problems of diffraction of short waves. Moscow: Nauka, 455 p. (in Russian).
Bazarov I. P., Gevorkyan E. V., Nikolaev P. N., 1986. Thermodynamics and Statistical Mechanics. The theory of equilibrium systems. Moscow: Publ. MSU, 312 p. (in Russian).
Nolet G., 1990. Seismic tomography. Moscow: Mir, 415 p. (in Russian).
Papadimitru Kh., Stayglits K., 1985. Combinatorial Optimization: Algorithms and complexity. Moscow: Mir, 512 p. (in Russian).
Hutton L., Uerdipton M., Makin J., 1986. Processing of the seismic data. Moscow: Nauka, 285 p. (in Russian).
Ammon C. J., Vidalе J. E., 1993. Tomography without Rays. Bull. Seysmol. Soc. Am. 83(2), 509—528.
Alford R. M., Kelly K. R., Booret D. M., 1974. Accuracy of finite-difference modeling of the acoustic wave equations. Geophysics 39(6), 834—842.
Cao S., Greenhalgh S., 1994. Finite-difference solution of the eiconal equation using an efficient, first arrival, wavefront tracking scheme. Geophysics 59(4), 632—643.
Černý V., 1985. Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm. J. Optim. Theor. Appl. 45, 41—51.
Goffe W. L., Farrier G. D., Rogers J., 1994. Global optimization of statistical functions with simulated annealing. J. of Econometrics 60, 65—99.
Guerra V., Tapia R. A., 1974. A local procedure for error detection and data smoothing. MRC Technical Summary Report 1452, Mathematics Research Center, University of Wisconsin, Madison.
Kim S. D., 1992. Eiconal solvtrs: first-arrival traveltimes. Geophysics 57(4), 632—643.
Kirkpatrik S., Gelatt C. D., Vecchi M. P., 1983. Optimization by simulated annealing. Science 220, 671—680.
Levievre P. G., Farquharson C. G. Hurich C. A., 2011. Inverision of first-arrival seismic traveltimes without rays, implemented on unstructured grids. Geophys J. Int. 185, 749—763. doi: 10.1111/j.1365-246X.2011.04964.x.
Metropolis N., Rosenbluth F., Rosenbluth V., Teller A., Teller E., 1953. Equation of State Calculation by Fast Computing Machines. J. Chem. Phys. 21, 1087—1092.
Mo L.-W., Harris J. M., 2002. Finite-difference calculations of direct arrival travel times and amplitudes. Geophisics 59(5), 167—176.
Nowack R. L., 1992. Wave fronts and solutions of the eikonal equation. Geophys. J. Int. 110, 55—62. doi: 10.1111/gji.1992.
Podvin P., Lecomte I., 1991. Finite difference computation of traveltime in very contrasted velocity models: a massively parallel approach and its associated tools. Geophys. J. Int. 105, 271—284.
Qian J., Symes W. W., 2002. An adaptive finite-difference method for traveltimes and amplitudes. Geophysics 67(1), 167—176.
Qin F., Luo Y., Olsen K. B., Cai W., Schuster G. T., 2002. Finite-difference solution of the eikonal equation along expanding wavefronts. Geophysics 67(4), 1225—1231.
Starostenko V., Janik T., Yegorova T., Farfuliak L., Czuba W., Środa P., Thybo H., Artemieva I., Sosson M., Volfman Y., Kolomiyets K., Lysynchuk D., Omelchenko V., Gryn D., Guterch A., Komminaho K., Legostaeva O., Tiira T., Tolkunov A., 2015. Seismic model of the crust and upper mantle in the Scythian Platform: the DOBRE-5 profile across the north western Black Sea and the Crimean Peninsula. Geophys. J. Int. 201(1), 406—428.
van Trier J., Symes W. W., 1991. Upwind finite-difference calculation of traveltimes. Geophysics 56(6), 812—821.
Vidale J., 1988, Finite-difference calculation of travel times. Bull. Seysmol. Soc. Am. 78(6), 2062—2076.
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).