Estimation of the parameters of seismic waves

TitleEstimation of the parameters of seismic waves
Publication TypeJournal Article
Year of Publication2014
AuthorsMostovoy, VS, Mostovyi, SV
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2014.02.118
Issue2
SectionGeosciences
Pagination118-123
Date Published2/2014
LanguageEnglish
Abstract

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.

Keywordsestimation, parameters, seismic waves
References: 

1. Bertsekas D. P. Nonlinear programming. Belmont, MA: Athena Sci., 1999.
2. 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).
3. Bliss G. A. Lectures on the calculus of variations. Chicago: Univ. of Chicago, 1947.
4. Evans L. C. Partial differential equations. Providence, RI: Amer. Math. Soc., 1997.
5. 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
6. Kirkpatrick S., Gelatt C., Vecchi M. Science, 1983, 220: 671–680. https://doi.org/10.1126/science.220.4598.671
7. Levenberg K. Quart. Appl. Math., 1944, 2: 164–168. https://doi.org/10.1090/qam/10666
8. Marquardt D.W. J. Soc. Indust. Appl. Math., 1963, 2, No. 2: 431–441. https://doi.org/10.1137/0111030
9. Metropolis N., Rosenbluth A., Teller A., Teller E. J. Chem. Phys., 1953, 21, No. 6: 1087–1092. https://doi.org/10.1063/1.1699114
10. Mostovyi S. V., Mostovoy V. S. Dopov. Nac. akad. nauk Ukr., 2008, No. 8: 113–116 (in Russian).
11. Mostovyi S. V., Starostenko V. I. Izv. AN USSR. Fiz. Zem, 1987, No. 5: 31–40 (in Russian).
12. Mostovoy V. S. Models of systems of monitoring of geophysical fields (Unpublished Doctoral thesis).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).
13. Pujol J. Geophys., 2007, 72, No. 4: W1-W16.
14. Ricker N. Geophys., 1953, 18: 10–40. https://doi.org/10.1190/1.1437843
15. Robinson E. Geophys., 1967, 32, No. 3: 418–484. https://doi.org/10.1190/1.1439873