{"id":5192,"date":"2016-03-30T13:39:40","date_gmt":"2016-03-30T11:39:40","guid":{"rendered":"http:\/\/www.geology.com.ua\/?page_id=5192"},"modified":"2017-10-26T14:47:16","modified_gmt":"2017-10-26T12:47:16","slug":"geoinformatika-2016-157-66-78","status":"publish","type":"page","link":"http:\/\/www.geology.com.ua\/en\/geoinformatika-2016-157-66-78\/","title":{"rendered":"Geoinformatika 2016; 1(57) : 66-78"},"content":{"rendered":"

Geoinformatika 2016; 1(57) : 66-78 (in Ukrainian)<\/em><\/p>\n

FOCAL EARTHQUAKE MECHANISM: MODELING, PARAMETER IDENTIFICATION AND APPLICATION<\/span><\/strong><\/h4>\n
D.\u00a0Malytskyy, O. Muyla, A. Pavlova, O. Hrytsay, Yu. Koval, O. Obidina<\/span><\/em><\/h5>\n

Carpathian Branch of the Institute of Geophysics, NAS of Ukraine, 3B Naukova Str., Lviv 79060, Ukraine,
\n<\/span><\/em>e-mail: dmytro@cb-igph.lviv.ua, grycaj.oksana@gmail.com, orest-aro@rambler.ru, obidinaeriol@gmail.com, susyinet@gmail.com<\/span><\/em><\/p>\n

Purpose.<\/span><\/strong> The purpose of the article is to determine focal mechanisms using a graphical method and the method of inverse waveforms with a limited number of stations, and to construct a fault plane for distributed sources.
\n<\/span>Design\/methodology\/approach.<\/span><\/strong> A matrix method was used for modelling seismic waves in a heterogeneous medium, which is represented as a horizontal layered elastic structure. The obtained expression for the displacement fields on the free surface on the layered half-space was used to determine the seismic moment tensor as a function of time by providing only direct P<\/i>– and S<\/i>-waves. We determined the slip for distributed sources using the methodology for a point source. So, to determining the components of the moment tensor, a source time function and a slip numerical method based on direct problem solution were used for inversion signals.
\n<\/span>Findings.<\/span><\/strong> We present the solution of the inverse problem to determine the focal mechanism using inverse waveforms for a limited number of stations and with graphic methods, as well as to determine the fault plane. Focal mechanism was defined by a graphic method and signal inversion for the event that took place near village Uhlya (24.10.2012, 03:13:40.50, <\/span>j<\/span>0<\/span>\u00a0<\/span>=<\/span>\u00a0<\/span>48,1676\u00b0, <\/span>l<\/span>0<\/span>\u00a0<\/span>=<\/span>\u00a0<\/span>23,6525\u00b0, h<\/i><\/span>\u00a0<\/span>=<\/span>\u00a0<\/span>4,5 km, ML<\/i><\/span>\u00a0<\/span>=<\/span>\u00a0<\/span>2,43), and also for the events that took place at Alberta, Canada (09.08.2014. 15:28:51.00, <\/span>j<\/span>0<\/span>\u00a0<\/span>=<\/span>\u00a0<\/span>52,1646, <\/span>l<\/span>0<\/span>\u00a0<\/span>=<\/span>\u00a0<\/span>\u2013115,256, h<\/i><\/span>\u00a0<\/span>=<\/span>\u00a0<\/span>4,9, ML<\/i><\/span>\u00a0<\/span>=<\/span>\u00a0<\/span>3,8).
\n<\/span>Practical value\/implications.<\/span><\/strong> We propose to apply graphic method to determine the focal mechanisms for events in the Carpathian region. We describe the method of inverse waveforms for a limited number of stations to determine focal mechanisms. The method for determining the fault plane using data from one or more stations is presented. The obtained focal mechanisms of local earthquakes and the parameters for distributed sources can be used to study stressed strained state of the mountain ranges in the regions with low seismic activity, which is important for Transcarpathian region.<\/span><\/p>\n

Keywords:<\/span><\/strong> matrix method, graphic method, the focal mechanism, seismic waves propagation, moment tensor, source time function, fault plane.<\/span><\/p>\n

The full text of papers\u00a0<\/strong><\/em><\/span><\/a><\/p>\n

\u00a0<\/span>References:<\/span><\/strong><\/p>\n

    \n
  1. Alekseev A.S., Mikhailenko B.G. Calculation of non-stationary wave fields in heterogeneous environments. Moscow, Radio & Communication, 1981, pp. 6-21 (in Russian).<\/span><\/li>\n
  2. Malytskyy D. Fundamental principles of solving a dynamic problem of seismology based on the recurrent approach. Geofizicheskiy zhurnal<\/i>, 1998, no. 5, pp. 96-98 (in Ukrainian).<\/span><\/li>\n
  3. Malytskyy D., Pak R. Using the recurrent method for solving of problems of seismology. Geofizicheskiy zhurnal<\/i>, 2004, vol.<\/span>26, no 6, pp. 189-195 (in Ukrainian).<\/span><\/li>\n
  4. Malytskyy D. Analytic-numerical approaches to the calculation of seismic moment tensor as a function of time. Geoinformatika<\/i>, 2010, no.1, pp. 79-86 (in Ukrainian). <\/span><\/li>\n
  5. Molotkov L.A. The matrix method in the theory of wave propagation in layered elastic and liquid. Sankt Peterburg, Nauka,1984, p. 204 (in Russian).<\/span><\/li>\n
  6. Molotkov L.A. Study of wave propagation in the porous and fractured media based on effective models of bio and of the media. SanktPeterburg, Nauka, 2001, p. 348 (in Russian).<\/span><\/li>\n
  7. Aki K., Richards P.G. Quantitative Seismology. Sausalito, California: University Science books, 2002, 520 p.<\/span><\/li>\n
  8. Ben-Menahem A., Singh S.J. Seismic Waves and Sources. New York, Springer, 1981.<\/span><\/li>\n
  9. Bouchon M. A simple method to calculate Green’s functions for elastic layered media. Bull. Seismol. Soc. Am.<\/i>, 1981, vol. 71, pp. 959-971.<\/span><\/li>\n
  10. Chapman C.H. A new method for computing synthetic seismograms. Geophys. J. R. Astron. Soc.<\/i>, 2004, vol. 54, pp.<\/span>481-518.<\/span><\/li>\n
  11. Cormier V.P., Richards P.G. Full wave theory applied to a discontinuous velocity increase: The inner core boundary. J.<\/i><\/span><\/i>Geophys.<\/span><\/i>, 1977, vol. 43, pp. 3-31.<\/span><\/li>\n
  12. D\u2019Amico S. Source parameters related to a small earthquake swarm off-shore of Malta (Central Mediterranean). Development in Earth Science<\/i>, 2014, vol. 2, no. 1, pp. 8-13.<\/span><\/li>\n
  13. Dziewonski A.M., Chou T.A., Woodhouse J.H. Determination of earthquake source parameters from waveform data for studies of regional and global seismicity. J. Geophys. Res.<\/i>, 1981, vol. 86, pp. 2825-2852.<\/span><\/li>\n
  14. Godano M., Bardainne T., Regnier M., Deschamps A. Moment tensor determination by nonlinear inversion of amplitudes. Bull. Seism. Soc. Am.<\/i>, 2001, vol. 101, pp. 366-378.<\/span><\/li>\n
  15. Fuchs K., Muller G. Computation of synthetic seismograms with the reflectivity method and comparison with observations. Geophys. J.R. Astron. Soc.<\/i>, 1971, vol. 23, pp. 417-433.<\/span><\/li>\n
  16. Hardebeck J.L., Shearer P.M. Using S\/P amplitude ratios to constrain the focal mechanisms of small earthquakes. Bull. Seism. Soc. Am.<\/i>, 2003, vol. 93, no. 6, pp. 2432-2444.<\/span><\/li>\n
  17. Kennett B.L.N. Seismic waves in laterally inhomogeneous media. Geophys. J.R. Astron. Soc.<\/i>, 1972, vol. 27, no. 3, pp. 301-325.<\/span><\/li>\n
  18. Kennett B.L.N. The Seismic wavefield, 1, 2. Cambridge University Press, UK, 2002.<\/span><\/li>\n
  19. Kikuchi M., Kanamori H. Inversion of complex body waves-III. Bull. Seism. Soc. Am.<\/i>, 1991, vol. 81, pp. 2335-2350.<\/span><\/li>\n
  20. Malytskyy, D., Kozlovskyy, E. Seismic waves in layered media. J. of Earth Science and Engineering<\/i>, 2014, vol. 4, pp. 311-325.<\/span><\/li>\n
  21. Miller A.D., Julian B.R., Foulger G.R. Three- dimensional seismic structure and moment tensors of non-double-couple earthquakes at the Hengill-Grensdalur volcanic complex, Iceland. Geophys. J. Int.<\/i>, 1998, vol. 133, pp. 309-325.<\/span><\/li>\n
  22. Muller, G. The reflectivity method: A tutorial. J. Geophys.<\/i>, 1985, no. 58, pp. 153-174.<\/span><\/li>\n
  23. Sileny, J., Panza, G.F., Campus, P. Waveform inversion for point source moment tensor retrieval with variable hypocentral depth and structural model. Geophys. J. Int.<\/i>, 1992, vol. 109, pp. 259-274.<\/span><\/li>\n
  24. Sipkin, S.A. Estimation of earthquake source parameters by the inversion of waveform data: Global seismicity, 1981-1983. Bull. Seism. Soc. Am.<\/i>, 1986, vol. 76, pp. 1515-1541.<\/span><\/li>\n
  25. Vavrychuk, V., Kuhn, D. Moment tensor inversion of waveforms: a two- step time frequency approach. Geophys. J. Int.<\/i>, 2012, vol. 190, pp. 1761-1776.<\/span><\/li>\n
  26. Wiggins, R.A., Helmberger, D.V., 1974. Synthetic seismogram computation by expansion in generalized rays. Geophys. J.<\/i>, 1974, vol. 37, pp. 73-90.<\/span><\/li>\n<\/ol>\n

    <\/p>","protected":false},"excerpt":{"rendered":"

    Geoinformatika 2016; 1(57) : 66-78 (in Ukrainian) FOCAL EARTHQUAKE MECHANISM: MODELING, PARAMETER IDENTIFICATION AND APPLICATION D.\u00a0Malytskyy, O. Muyla, A. Pavlova, O. Hrytsay, Yu. Koval, O. Obidina Carpathian Branch of the Institute of Geophysics, NAS of Ukraine, 3B Naukova Str., Lviv 79060, Ukraine, e-mail: dmytro@cb-igph.lviv.ua, grycaj.oksana@gmail.com, orest-aro@rambler.ru, obidinaeriol@gmail.com, susyinet@gmail.com Purpose. The purpose of the article is to determine focal mechanisms using a graphical method and the method of inverse waveforms with a limited number of stations, and to construct a fault plane for distributed sources. Design\/methodology\/approach. A matrix method was used for modelling seismic waves in a heterogeneous medium, which is represented as a horizontal layered elastic structure. The obtained expression for the displacement fields on the free surface on the layered half-space was used to determine the seismic moment tensor as a function of time by providing only direct P– and S-waves. We determined the slip for distributed sources using the methodology for a point source. So, to determining the components of the moment tensor, a source time function and a slip numerical method based on direct problem solution were used for inversion signals. Findings. We present the solution of the inverse problem to determine the focal mechanism using inverse waveforms for a limited number of stations and with graphic methods, as well as to determine the fault plane. Focal mechanism was defined by a graphic method and signal inversion for the event that took place near village Uhlya (24.10.2012, 03:13:40.50, j0\u00a0=\u00a048,1676\u00b0, l0\u00a0=\u00a023,6525\u00b0, h\u00a0=\u00a04,5 km, ML\u00a0=\u00a02,43), and also for the events that took place at Alberta, Canada (09.08.2014. 15:28:51.00, j0\u00a0=\u00a052,1646, l0\u00a0=\u00a0\u2013115,256, h\u00a0=\u00a04,9, ML\u00a0=\u00a03,8). Practical value\/implications. We propose to apply graphic method to determine the focal mechanisms for events in the Carpathian region. We describe the method of inverse waveforms for a limited number of stations to determine focal mechanisms. The method for determining the fault plane using data from one or more stations is presented. The obtained focal mechanisms of local earthquakes and the parameters for distributed sources can be used to study stressed strained state of the mountain ranges in the regions with low seismic activity, which is important for Transcarpathian region. Keywords: matrix method, graphic method, the focal mechanism, seismic waves propagation, moment tensor, source time function, fault plane. The full text of papers\u00a0 \u00a0References: Alekseev A.S., Mikhailenko B.G. Calculation of non-stationary wave fields in heterogeneous environments. Moscow, Radio & Communication, 1981, pp. 6-21 (in Russian). Malytskyy D. Fundamental principles of solving a dynamic problem of seismology based on the recurrent approach. Geofizicheskiy zhurnal, 1998, no. 5, pp. 96-98 (in Ukrainian). Malytskyy D., Pak R. Using the recurrent method for solving of problems of seismology. Geofizicheskiy zhurnal, 2004, vol.26, no 6, pp. 189-195 (in Ukrainian). Malytskyy D. Analytic-numerical approaches to the calculation of seismic moment tensor as a function of time. Geoinformatika, 2010, no.1, pp. 79-86 (in Ukrainian). Molotkov L.A. The matrix method in the theory of wave propagation in layered elastic and liquid. Sankt Peterburg, Nauka,1984, p. 204 (in Russian). Molotkov L.A. Study of wave propagation in the porous and fractured media based on effective models of bio and of the media. SanktPeterburg, Nauka, 2001, p. 348 (in Russian). Aki K., Richards P.G. Quantitative Seismology. Sausalito, California: University Science books, 2002, 520 p. Ben-Menahem A., Singh S.J. Seismic Waves and Sources. New York, Springer, 1981. Bouchon M. A simple method to calculate Green’s functions for elastic layered media. Bull. Seismol. Soc. Am., 1981, vol. 71, pp. 959-971. Chapman C.H. A new method for computing synthetic seismograms. Geophys. J. R. Astron. Soc., 2004, vol. 54, pp.481-518. Cormier V.P., Richards P.G. Full wave theory applied to a discontinuous velocity increase: The inner core boundary. J.Geophys., 1977, vol. 43, pp. 3-31. D\u2019Amico S. Source parameters related to a small earthquake swarm off-shore of Malta (Central Mediterranean). Development in Earth Science, 2014, vol. 2, no. 1, pp. 8-13. Dziewonski A.M., Chou T.A., Woodhouse J.H. Determination of earthquake source parameters from waveform data for studies of regional and global seismicity. J. Geophys. Res., 1981, vol. 86, pp. 2825-2852. Godano M., Bardainne T., Regnier M., Deschamps A. Moment tensor determination by nonlinear inversion of amplitudes. Bull. Seism. Soc. Am., 2001, vol. 101, pp. 366-378. Fuchs K., Muller G. Computation of synthetic seismograms with the reflectivity method and comparison with observations. Geophys. J.R. Astron. Soc., 1971, vol. 23, pp. 417-433. Hardebeck J.L., Shearer P.M. Using S\/P amplitude ratios to constrain the focal mechanisms of small earthquakes. Bull. Seism. Soc. Am., 2003, vol. 93, no. 6, pp. 2432-2444. Kennett B.L.N. Seismic waves in laterally inhomogeneous media. Geophys. J.R. Astron. Soc., 1972, vol. 27, no. 3, pp. 301-325. Kennett B.L.N. The Seismic wavefield, 1, 2. Cambridge University Press, UK, 2002. Kikuchi M., Kanamori H. Inversion of complex body waves-III. Bull. Seism. Soc. Am., 1991, vol. 81, pp. 2335-2350. Malytskyy, D., Kozlovskyy, E. Seismic waves in layered media. J. of Earth Science and Engineering, 2014, vol. 4, pp. 311-325. Miller A.D., Julian B.R., Foulger G.R. Three- dimensional seismic structure and moment tensors of non-double-couple earthquakes at the Hengill-Grensdalur volcanic complex, Iceland. Geophys. J. Int., 1998, vol. 133, pp. 309-325. Muller, G. The reflectivity method: A tutorial. J. Geophys., 1985, no. 58, pp. 153-174. Sileny, J., Panza, G.F., Campus, P. Waveform inversion for point source moment tensor retrieval with variable hypocentral depth and structural model. Geophys. J. Int., 1992, vol. 109, pp. 259-274. Sipkin, S.A. Estimation of earthquake source parameters by the inversion of waveform data: Global seismicity, 1981-1983. Bull. Seism. Soc. Am., 1986, vol. 76, pp. 1515-1541. Vavrychuk, V., Kuhn, D. Moment tensor inversion of waveforms: a two- step time frequency approach. Geophys. J. Int., 2012, vol. 190, pp. 1761-1776. Wiggins, R.A., Helmberger, D.V., 1974. Synthetic seismogram computation by expansion in generalized rays. Geophys. J., 1974, vol. 37, pp. 73-90.<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5192","page","type-page","status-publish","hentry"],"yoast_head":"\nGeoinformatika 2016; 1(57) : 66-78 - \u0421\u0430\u0439\u0442 \u0436\u0443\u0440\u043d\u0430\u043b\u0443 \u00ab\u0413\u0435\u043e\u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u00bb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/www.geology.com.ua\/en\/geoinformatika-2016-157-66-78\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Geoinformatika 2016; 1(57) : 66-78 - \u0421\u0430\u0439\u0442 \u0436\u0443\u0440\u043d\u0430\u043b\u0443 \u00ab\u0413\u0435\u043e\u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u00bb\" \/>\n<meta property=\"og:description\" content=\"Geoinformatika 2016; 1(57) : 66-78 (in Ukrainian) FOCAL EARTHQUAKE MECHANISM: MODELING, PARAMETER IDENTIFICATION AND APPLICATION D.\u00a0Malytskyy, O. Muyla, A. Pavlova, O. Hrytsay, Yu. Koval, O. Obidina Carpathian Branch of the Institute of Geophysics, NAS of Ukraine, 3B Naukova Str., Lviv 79060, Ukraine, e-mail: dmytro@cb-igph.lviv.ua, grycaj.oksana@gmail.com, orest-aro@rambler.ru, obidinaeriol@gmail.com, susyinet@gmail.com Purpose. The purpose of the article is to determine focal mechanisms using a graphical method and the method of inverse waveforms with a limited number of stations, and to construct a fault plane for distributed sources. Design\/methodology\/approach. A matrix method was used for modelling seismic waves in a heterogeneous medium, which is represented as a horizontal layered elastic structure. The obtained expression for the displacement fields on the free surface on the layered half-space was used to determine the seismic moment tensor as a function of time by providing only direct P– and S-waves. We determined the slip for distributed sources using the methodology for a point source. So, to determining the components of the moment tensor, a source time function and a slip numerical method based on direct problem solution were used for inversion signals. Findings. We present the solution of the inverse problem to determine the focal mechanism using inverse waveforms for a limited number of stations and with graphic methods, as well as to determine the fault plane. Focal mechanism was defined by a graphic method and signal inversion for the event that took place near village Uhlya (24.10.2012, 03:13:40.50, j0\u00a0=\u00a048,1676\u00b0, l0\u00a0=\u00a023,6525\u00b0, h\u00a0=\u00a04,5 km, ML\u00a0=\u00a02,43), and also for the events that took place at Alberta, Canada (09.08.2014. 15:28:51.00, j0\u00a0=\u00a052,1646, l0\u00a0=\u00a0\u2013115,256, h\u00a0=\u00a04,9, ML\u00a0=\u00a03,8). Practical value\/implications. We propose to apply graphic method to determine the focal mechanisms for events in the Carpathian region. We describe the method of inverse waveforms for a limited number of stations to determine focal mechanisms. The method for determining the fault plane using data from one or more stations is presented. The obtained focal mechanisms of local earthquakes and the parameters for distributed sources can be used to study stressed strained state of the mountain ranges in the regions with low seismic activity, which is important for Transcarpathian region. Keywords: matrix method, graphic method, the focal mechanism, seismic waves propagation, moment tensor, source time function, fault plane. The full text of papers\u00a0 \u00a0References: Alekseev A.S., Mikhailenko B.G. Calculation of non-stationary wave fields in heterogeneous environments. Moscow, Radio & Communication, 1981, pp. 6-21 (in Russian). Malytskyy D. Fundamental principles of solving a dynamic problem of seismology based on the recurrent approach. Geofizicheskiy zhurnal, 1998, no. 5, pp. 96-98 (in Ukrainian). Malytskyy D., Pak R. Using the recurrent method for solving of problems of seismology. Geofizicheskiy zhurnal, 2004, vol.26, no 6, pp. 189-195 (in Ukrainian). Malytskyy D. Analytic-numerical approaches to the calculation of seismic moment tensor as a function of time. Geoinformatika, 2010, no.1, pp. 79-86 (in Ukrainian). Molotkov L.A. The matrix method in the theory of wave propagation in layered elastic and liquid. Sankt Peterburg, Nauka,1984, p. 204 (in Russian). Molotkov L.A. Study of wave propagation in the porous and fractured media based on effective models of bio and of the media. SanktPeterburg, Nauka, 2001, p. 348 (in Russian). Aki K., Richards P.G. Quantitative Seismology. Sausalito, California: University Science books, 2002, 520 p. Ben-Menahem A., Singh S.J. Seismic Waves and Sources. New York, Springer, 1981. Bouchon M. A simple method to calculate Green’s functions for elastic layered media. Bull. Seismol. Soc. Am., 1981, vol. 71, pp. 959-971. Chapman C.H. A new method for computing synthetic seismograms. Geophys. J. R. Astron. Soc., 2004, vol. 54, pp.481-518. Cormier V.P., Richards P.G. Full wave theory applied to a discontinuous velocity increase: The inner core boundary. J.Geophys., 1977, vol. 43, pp. 3-31. D\u2019Amico S. Source parameters related to a small earthquake swarm off-shore of Malta (Central Mediterranean). Development in Earth Science, 2014, vol. 2, no. 1, pp. 8-13. Dziewonski A.M., Chou T.A., Woodhouse J.H. Determination of earthquake source parameters from waveform data for studies of regional and global seismicity. J. Geophys. Res., 1981, vol. 86, pp. 2825-2852. Godano M., Bardainne T., Regnier M., Deschamps A. Moment tensor determination by nonlinear inversion of amplitudes. Bull. Seism. Soc. Am., 2001, vol. 101, pp. 366-378. Fuchs K., Muller G. Computation of synthetic seismograms with the reflectivity method and comparison with observations. Geophys. J.R. Astron. Soc., 1971, vol. 23, pp. 417-433. Hardebeck J.L., Shearer P.M. Using S\/P amplitude ratios to constrain the focal mechanisms of small earthquakes. Bull. Seism. Soc. Am., 2003, vol. 93, no. 6, pp. 2432-2444. Kennett B.L.N. Seismic waves in laterally inhomogeneous media. Geophys. J.R. Astron. Soc., 1972, vol. 27, no. 3, pp. 301-325. Kennett B.L.N. The Seismic wavefield, 1, 2. Cambridge University Press, UK, 2002. Kikuchi M., Kanamori H. Inversion of complex body waves-III. Bull. Seism. Soc. Am., 1991, vol. 81, pp. 2335-2350. Malytskyy, D., Kozlovskyy, E. Seismic waves in layered media. J. of Earth Science and Engineering, 2014, vol. 4, pp. 311-325. Miller A.D., Julian B.R., Foulger G.R. Three- dimensional seismic structure and moment tensors of non-double-couple earthquakes at the Hengill-Grensdalur volcanic complex, Iceland. Geophys. J. Int., 1998, vol. 133, pp. 309-325. Muller, G. The reflectivity method: A tutorial. J. Geophys., 1985, no. 58, pp. 153-174. Sileny, J., Panza, G.F., Campus, P. Waveform inversion for point source moment tensor retrieval with variable hypocentral depth and structural model. Geophys. J. Int., 1992, vol. 109, pp. 259-274. Sipkin, S.A. Estimation of earthquake source parameters by the inversion of waveform data: Global seismicity, 1981-1983. Bull. Seism. Soc. Am., 1986, vol. 76, pp. 1515-1541. Vavrychuk, V., Kuhn, D. Moment tensor inversion of waveforms: a two- step time frequency approach. Geophys. J. Int., 2012, vol. 190, pp. 1761-1776. Wiggins, R.A., Helmberger, D.V., 1974. Synthetic seismogram computation by expansion in generalized rays. Geophys. J., 1974, vol. 37, pp. 73-90.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/www.geology.com.ua\/en\/geoinformatika-2016-157-66-78\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0421\u0430\u0439\u0442 \u0436\u0443\u0440\u043d\u0430\u043b\u0443 \u00ab\u0413\u0435\u043e\u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u00bb\" \/>\n<meta property=\"article:modified_time\" content=\"2017-10-26T12:47:16+00:00\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"http:\\\/\\\/www.geology.com.ua\\\/en\\\/geoinformatika-2016-157-66-78\\\/\",\"url\":\"http:\\\/\\\/www.geology.com.ua\\\/en\\\/geoinformatika-2016-157-66-78\\\/\",\"name\":\"Geoinformatika 2016; 1(57) : 66-78 - \u0421\u0430\u0439\u0442 \u0436\u0443\u0440\u043d\u0430\u043b\u0443 \u00ab\u0413\u0435\u043e\u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u00bb\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/www.geology.com.ua\\\/en\\\/#website\"},\"datePublished\":\"2016-03-30T11:39:40+00:00\",\"dateModified\":\"2017-10-26T12:47:16+00:00\",\"breadcrumb\":{\"@id\":\"http:\\\/\\\/www.geology.com.ua\\\/en\\\/geoinformatika-2016-157-66-78\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[[\"http:\\\/\\\/www.geology.com.ua\\\/en\\\/geoinformatika-2016-157-66-78\\\/\"]]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\\\/\\\/www.geology.com.ua\\\/en\\\/geoinformatika-2016-157-66-78\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"http:\\\/\\\/www.geology.com.ua\\\/en\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Geoinformatika 2016; 1(57) : 66-78\"}]},{\"@type\":\"WebSite\",\"@id\":\"http:\\\/\\\/www.geology.com.ua\\\/en\\\/#website\",\"url\":\"http:\\\/\\\/www.geology.com.ua\\\/en\\\/\",\"name\":\"\u0421\u0430\u0439\u0442 \u0436\u0443\u0440\u043d\u0430\u043b\u0443 \u00ab\u0413\u0435\u043e\u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u00bb\",\"description\":\"\u0426\u0435\u043d\u0442\u0440 \u043c\u0435\u043d\u0435\u0434\u0436\u043c\u0435\u043d\u0442\u0443 \u0442\u0430 \u043c\u0430\u0440\u043a\u0435\u0442\u0438\u043d\u0433\u0443 \u0432 \u0433\u0430\u043b\u0443\u0437\u0456 \u043d\u0430\u0443\u043a \u043f\u0440\u043e \u0417\u0435\u043c\u043b\u044e\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"http:\\\/\\\/www.geology.com.ua\\\/en\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Geoinformatika 2016; 1(57) : 66-78 - \u0421\u0430\u0439\u0442 \u0436\u0443\u0440\u043d\u0430\u043b\u0443 \u00ab\u0413\u0435\u043e\u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u00bb","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"http:\/\/www.geology.com.ua\/en\/geoinformatika-2016-157-66-78\/","og_locale":"en_US","og_type":"article","og_title":"Geoinformatika 2016; 1(57) : 66-78 - \u0421\u0430\u0439\u0442 \u0436\u0443\u0440\u043d\u0430\u043b\u0443 \u00ab\u0413\u0435\u043e\u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u00bb","og_description":"Geoinformatika 2016; 1(57) : 66-78 (in Ukrainian) FOCAL EARTHQUAKE MECHANISM: MODELING, PARAMETER IDENTIFICATION AND APPLICATION D.\u00a0Malytskyy, O. Muyla, A. Pavlova, O. Hrytsay, Yu. Koval, O. Obidina Carpathian Branch of the Institute of Geophysics, NAS of Ukraine, 3B Naukova Str., Lviv 79060, Ukraine, e-mail: dmytro@cb-igph.lviv.ua, grycaj.oksana@gmail.com, orest-aro@rambler.ru, obidinaeriol@gmail.com, susyinet@gmail.com Purpose. The purpose of the article is to determine focal mechanisms using a graphical method and the method of inverse waveforms with a limited number of stations, and to construct a fault plane for distributed sources. Design\/methodology\/approach. A matrix method was used for modelling seismic waves in a heterogeneous medium, which is represented as a horizontal layered elastic structure. The obtained expression for the displacement fields on the free surface on the layered half-space was used to determine the seismic moment tensor as a function of time by providing only direct P– and S-waves. We determined the slip for distributed sources using the methodology for a point source. So, to determining the components of the moment tensor, a source time function and a slip numerical method based on direct problem solution were used for inversion signals. Findings. We present the solution of the inverse problem to determine the focal mechanism using inverse waveforms for a limited number of stations and with graphic methods, as well as to determine the fault plane. Focal mechanism was defined by a graphic method and signal inversion for the event that took place near village Uhlya (24.10.2012, 03:13:40.50, j0\u00a0=\u00a048,1676\u00b0, l0\u00a0=\u00a023,6525\u00b0, h\u00a0=\u00a04,5 km, ML\u00a0=\u00a02,43), and also for the events that took place at Alberta, Canada (09.08.2014. 15:28:51.00, j0\u00a0=\u00a052,1646, l0\u00a0=\u00a0\u2013115,256, h\u00a0=\u00a04,9, ML\u00a0=\u00a03,8). Practical value\/implications. We propose to apply graphic method to determine the focal mechanisms for events in the Carpathian region. We describe the method of inverse waveforms for a limited number of stations to determine focal mechanisms. The method for determining the fault plane using data from one or more stations is presented. The obtained focal mechanisms of local earthquakes and the parameters for distributed sources can be used to study stressed strained state of the mountain ranges in the regions with low seismic activity, which is important for Transcarpathian region. Keywords: matrix method, graphic method, the focal mechanism, seismic waves propagation, moment tensor, source time function, fault plane. The full text of papers\u00a0 \u00a0References: Alekseev A.S., Mikhailenko B.G. Calculation of non-stationary wave fields in heterogeneous environments. Moscow, Radio & Communication, 1981, pp. 6-21 (in Russian). Malytskyy D. Fundamental principles of solving a dynamic problem of seismology based on the recurrent approach. Geofizicheskiy zhurnal, 1998, no. 5, pp. 96-98 (in Ukrainian). Malytskyy D., Pak R. Using the recurrent method for solving of problems of seismology. Geofizicheskiy zhurnal, 2004, vol.26, no 6, pp. 189-195 (in Ukrainian). Malytskyy D. Analytic-numerical approaches to the calculation of seismic moment tensor as a function of time. Geoinformatika, 2010, no.1, pp. 79-86 (in Ukrainian). Molotkov L.A. The matrix method in the theory of wave propagation in layered elastic and liquid. Sankt Peterburg, Nauka,1984, p. 204 (in Russian). Molotkov L.A. Study of wave propagation in the porous and fractured media based on effective models of bio and of the media. SanktPeterburg, Nauka, 2001, p. 348 (in Russian). Aki K., Richards P.G. Quantitative Seismology. Sausalito, California: University Science books, 2002, 520 p. Ben-Menahem A., Singh S.J. Seismic Waves and Sources. New York, Springer, 1981. Bouchon M. A simple method to calculate Green’s functions for elastic layered media. Bull. Seismol. Soc. Am., 1981, vol. 71, pp. 959-971. Chapman C.H. A new method for computing synthetic seismograms. Geophys. J. R. Astron. Soc., 2004, vol. 54, pp.481-518. Cormier V.P., Richards P.G. Full wave theory applied to a discontinuous velocity increase: The inner core boundary. J.Geophys., 1977, vol. 43, pp. 3-31. D\u2019Amico S. Source parameters related to a small earthquake swarm off-shore of Malta (Central Mediterranean). Development in Earth Science, 2014, vol. 2, no. 1, pp. 8-13. Dziewonski A.M., Chou T.A., Woodhouse J.H. Determination of earthquake source parameters from waveform data for studies of regional and global seismicity. J. Geophys. Res., 1981, vol. 86, pp. 2825-2852. Godano M., Bardainne T., Regnier M., Deschamps A. Moment tensor determination by nonlinear inversion of amplitudes. Bull. Seism. Soc. Am., 2001, vol. 101, pp. 366-378. Fuchs K., Muller G. Computation of synthetic seismograms with the reflectivity method and comparison with observations. Geophys. J.R. Astron. Soc., 1971, vol. 23, pp. 417-433. Hardebeck J.L., Shearer P.M. Using S\/P amplitude ratios to constrain the focal mechanisms of small earthquakes. Bull. Seism. Soc. Am., 2003, vol. 93, no. 6, pp. 2432-2444. Kennett B.L.N. Seismic waves in laterally inhomogeneous media. Geophys. J.R. Astron. Soc., 1972, vol. 27, no. 3, pp. 301-325. Kennett B.L.N. The Seismic wavefield, 1, 2. Cambridge University Press, UK, 2002. Kikuchi M., Kanamori H. Inversion of complex body waves-III. Bull. Seism. Soc. Am., 1991, vol. 81, pp. 2335-2350. Malytskyy, D., Kozlovskyy, E. Seismic waves in layered media. J. of Earth Science and Engineering, 2014, vol. 4, pp. 311-325. Miller A.D., Julian B.R., Foulger G.R. Three- dimensional seismic structure and moment tensors of non-double-couple earthquakes at the Hengill-Grensdalur volcanic complex, Iceland. Geophys. J. Int., 1998, vol. 133, pp. 309-325. Muller, G. The reflectivity method: A tutorial. J. Geophys., 1985, no. 58, pp. 153-174. Sileny, J., Panza, G.F., Campus, P. Waveform inversion for point source moment tensor retrieval with variable hypocentral depth and structural model. Geophys. J. Int., 1992, vol. 109, pp. 259-274. Sipkin, S.A. Estimation of earthquake source parameters by the inversion of waveform data: Global seismicity, 1981-1983. Bull. Seism. Soc. Am., 1986, vol. 76, pp. 1515-1541. Vavrychuk, V., Kuhn, D. Moment tensor inversion of waveforms: a two- step time frequency approach. Geophys. J. Int., 2012, vol. 190, pp. 1761-1776. Wiggins, R.A., Helmberger, D.V., 1974. Synthetic seismogram computation by expansion in generalized rays. Geophys. J., 1974, vol. 37, pp. 73-90.","og_url":"http:\/\/www.geology.com.ua\/en\/geoinformatika-2016-157-66-78\/","og_site_name":"\u0421\u0430\u0439\u0442 \u0436\u0443\u0440\u043d\u0430\u043b\u0443 \u00ab\u0413\u0435\u043e\u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u00bb","article_modified_time":"2017-10-26T12:47:16+00:00","twitter_misc":{"Est. reading time":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"http:\/\/www.geology.com.ua\/en\/geoinformatika-2016-157-66-78\/","url":"http:\/\/www.geology.com.ua\/en\/geoinformatika-2016-157-66-78\/","name":"Geoinformatika 2016; 1(57) : 66-78 - \u0421\u0430\u0439\u0442 \u0436\u0443\u0440\u043d\u0430\u043b\u0443 \u00ab\u0413\u0435\u043e\u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u00bb","isPartOf":{"@id":"http:\/\/www.geology.com.ua\/en\/#website"},"datePublished":"2016-03-30T11:39:40+00:00","dateModified":"2017-10-26T12:47:16+00:00","breadcrumb":{"@id":"http:\/\/www.geology.com.ua\/en\/geoinformatika-2016-157-66-78\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":[["http:\/\/www.geology.com.ua\/en\/geoinformatika-2016-157-66-78\/"]]}]},{"@type":"BreadcrumbList","@id":"http:\/\/www.geology.com.ua\/en\/geoinformatika-2016-157-66-78\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"http:\/\/www.geology.com.ua\/en\/"},{"@type":"ListItem","position":2,"name":"Geoinformatika 2016; 1(57) : 66-78"}]},{"@type":"WebSite","@id":"http:\/\/www.geology.com.ua\/en\/#website","url":"http:\/\/www.geology.com.ua\/en\/","name":"\u0421\u0430\u0439\u0442 \u0436\u0443\u0440\u043d\u0430\u043b\u0443 \u00ab\u0413\u0435\u043e\u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u00bb","description":"\u0426\u0435\u043d\u0442\u0440 \u043c\u0435\u043d\u0435\u0434\u0436\u043c\u0435\u043d\u0442\u0443 \u0442\u0430 \u043c\u0430\u0440\u043a\u0435\u0442\u0438\u043d\u0433\u0443 \u0432 \u0433\u0430\u043b\u0443\u0437\u0456 \u043d\u0430\u0443\u043a \u043f\u0440\u043e \u0417\u0435\u043c\u043b\u044e","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"http:\/\/www.geology.com.ua\/en\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"http:\/\/www.geology.com.ua\/en\/wp-json\/wp\/v2\/pages\/5192","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.geology.com.ua\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.geology.com.ua\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.geology.com.ua\/en\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/www.geology.com.ua\/en\/wp-json\/wp\/v2\/comments?post=5192"}],"version-history":[{"count":6,"href":"http:\/\/www.geology.com.ua\/en\/wp-json\/wp\/v2\/pages\/5192\/revisions"}],"predecessor-version":[{"id":6981,"href":"http:\/\/www.geology.com.ua\/en\/wp-json\/wp\/v2\/pages\/5192\/revisions\/6981"}],"wp:attachment":[{"href":"http:\/\/www.geology.com.ua\/en\/wp-json\/wp\/v2\/media?parent=5192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}