Estimation of the parameters of seismic waves
DOI:
https://doi.org/10.15407/dopovidi2014.02.118Keywords:
estimation, parameters, seismic wavesAbstract
We consider a problem of estimation of the parameters of a seismic signal based on real observed data. For this purpose, we propose a new mathematical model that reduces the task to a nonlinear, nonsmooth, nonconvex minimization problem. Using a special structure of the signal, we also propose a numerical algorithm of finding the solution of the optimization problem. Our method is based on the combination of the Levenberg–Marquardt algorithm and a simulated annealing type approach. We show the convergence of the algorithm and discuss the practical implications, which lie in a good compatibility with real seismic data, and the applicability to experiments.
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References
Bertsekas D. P. Nonlinear programming. Belmont, MA: Athena Sci., 1999.
Berzon I. S., Epinat’eva A. M., Pariiskaya G. N., Starodubrovskaya S. P. Dynamical characteristics of seismic waves in real media. Moscow: Izd. AN SSSR, 1962. (in Russian).
Bliss G. A. Lectures on the calculus of variations. Chicago: Univ. of Chicago, 1947.
Evans L. C. Partial differential equations. Providence, RI: Amer. Math. Soc., 1997.
Fleming W. R., Rieshel R.W. Deterministic and stochastic optimal control. New York: Springer, 1975. https://doi.org/10.1007/978-1-4612-6380-7
Kirkpatrick S., Gelatt C., Vecchi M. Science, 1983, 220: 671–680. https://doi.org/10.1126/science.220.4598.671
Levenberg K. Quart. Appl. Math., 1944, 2: 164–168. https://doi.org/10.1090/qam/10666
Marquardt D.W. J. Soc. Indust. Appl. Math., 1963, 2, No. 2: 431–441. https://doi.org/10.1137/0111030
Metropolis N., Rosenbluth A., Teller A., Teller E. J. Chem. Phys., 1953, 21, No. 6: 1087–1092. https://doi.org/10.1063/1.1699114
Mostovyi S. V., Mostovoy V. S. Dopov. Nac. akad. nauk Ukr., 2008, No. 8: 113–116 (in Russian).
Mostovyi S. V., Starostenko V. I. Izv. AN USSR. Fiz. Zem, 1987, No. 5: 31–40 (in Russian).
Mostovoy V. S. Models of systems of monitoring of geophysical fields (Unpublished Doctoral thesis). Taras Shevchenko National university of Kyiv. Kyiv, Ukraine, 2013 (in Russian).
Pujol J. Geophys., 2007, 72, No. 4: W1-W16.
Ricker N. Geophys., 1953, 18: 10–40. https://doi.org/10.1190/1.1437843
Robinson E. Geophys., 1967, 32, No. 3: 418–484. https://doi.org/10.1190/1.1439873
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