Modeling of earthquake source parameters on December 12, 2018 (08:49:56,16; 36,4478° N; 140,5788° E; H = 62,0 km; Mw = 4,3, Japan)


  • R.M. Pak Carpathian Branch of S.I. Subbotin Institute of Geophysics of the National Academy of Sciences of Ukraine; Hetman Petro Sahaidachny National Army Academy, Ukraine
  • O.D. Hrytsai Carpathian Branch of S.I. Subbotin Institute of Geophysics of the National Academy of Sciences of Ukraine; «Lviv Polytechnic» National University, Ukraine



Modeling of earthquake source parameters, such as the orientation of the fault plane and the direction of the fault slip, is important for understanding the physics of earthquake source processes, determining the stress-strain state of the geological medium and seismic hazard estimation. For modeling source parameters of the earthquake on December 12, 2018 at 08:49:56,16 (UTC) in Japan (36,4478° N, 140,5788° E, Northern Ibaraki Pref region) at a depth of 62 km with a magnitude of Mw = 4.3, the waveforms inversion was used to determine seismic moment tensor and representation it through a focal mechanism. The earthquake source is considered as a point source of seismic waves which propagate in a medium represented by a set of horizontally homogeneous elastic layers. An algorithm for determining seismic tensor components based on the forward problem solved by the matrix method, and using the generalized inverse solution, selecting only direct waves is applied. The input data for determining seismic moment components are data of only direct P waves selected from the observed records at six seismic stations of the Japanese local network NIED F-net: TSK, YMZ, ASI, ONS, SBT, KSK. The seismic moment tensor components were determined through waveform inversion using the matrix method. The obtained results, presented through a focal mechanism, are compared to the results obtained by the National Research Institute of Earth Sciences and Resistance to Natural Disasters (NIED CMT solutions). As a result of focal mechanisms comparison, it is concluded that the proposed algorithm for determining seismic moment tensor components can be used if it is impossible to use another method, or requires some refinement for another method. This approach is especially relevant for regions with low seismicity and insufficient number of stations. In addition, this method reduces the effects of an inaccurate medium model, because direct waves are much less distorted than reflected and converted, and that increases the accuracy and reliability of the method.


Malytskyy, D. (2010). Analytic-Numerical Approaches to the Calculation of Seismic Moment Tensor as a Function of Time. Geoinformatik, (1), 79—85 (in Ukrainian).

Malytskyy, D. (2016). Mathematical Modeling in the Problems of Seismology. Kyiv: Naukova Dumka, 241 p. (in Ukrainian).

Malytskyi, D., Hnyp, A., Hrytsai, O., Murovska, A., Kravets, S., Kozlovskyi, E., & Mykyta, A. (2018). Source mechanism and tectonic setting of 29.09.2017 earthquake near Stebnyk Geodynamics, (1), 100—110. (in Ukrainian).

Molotkov, L.A. (1984). Matrix method in the theory of wave propagation in layered, elastic and

liquid media. Leningrad: Nauka, 201 p. (in Russian).

Pak, R.M. (2017). Modeling of wave field, which has been excited of deep or superficial source in horizontally layered half-space. Geodynamics, (1), 114—124. (in Russian).

Roganov, Yu., & Pak, R. (2013). Representation of potentials from point sources for a homogeneous isotropic medium in the form of Bessel—Mellin integrals. Geofizicheskiy Zhurnal, 35(2), 163—167. (in Ukrainian).

Aki, K., & Richards, P.G. (2002). Quantitative seismology. Theory and methods. Sausalito, California: University Science Books.

Cronin, V. (2004). A Draft Primer on Focal Mechanism Solutions for Geologists. Baylor University.

D’Amico, S. (2014). Source parameters related to a small earthquake swarm off-shore of Malta (central Mediterranean). Development in Earth Science, 2, 8—13.

Dreger, D.S., & Helmberger, D.V. (1993). Determination of source parameters at regional distances with three-component sparse network data. Journal of Geophysical Research: Solid Earth, 98(B5), 8107—8125.

Dreger, D.S. (2003) TDMT_INV: Time domain seismic moment tensor inversion. International Geophysics, 81.

Dziewonski, A.M., Chou, T.A., & Woodhouse, J.H. (1981). Determination of earthquake source parameters from waveform data for studies of regional and global seismicity. Journal of Geophysical Research: Solid Earth, 86(B4), 2825—2852.

F-net Broadband Seismograph Network. (2018). Retrieved from

Godano, M., Bardainne, T., Regnier, M., & Deschamps, A. (2011). Moment tensor determination by nonlinear inversion of amplitudes. Bulletin of the Seismological Society of America, 101(1), 366—378.

Hardebeck, J.L., & Shearer, P.M. (2003). Using S/P amplitude ratios to constrain the focal mechanisms of small earthquakes. Bulletin of the Seismological Society of America, 93(6), 2432—2444.

Herrmann, R.B. (2008). Toward automated focal mechanism and moment determination for the continental U.S. — an ANSS product. Final Technical Report USGS Grant 05HQGR0047.

Herrmann, R.B., Withers, M. & Benz, H. (2008). The April 18, 2008 Illinois earthquake: an ANSS monitoring success. Seismological Research Letters, 79(6), 830—843.

Kikuchi, M., & Kanamori, H. (1991). Inversion of complex body waves — III. Bulletin of the Seismological Society of America, 6(81), 2335—2350.

Kozlovskyy, E., Maksymchuk, V., Malytskyy, D., Tymoschuk, V., Hrytsai, O., & Pyrizhok, N. (2020). Structural-tectonic and seismic characteristics relationships in the Central part of the Transcarpathian internal depression. Geodynamics, 1(28), 62—70.

Malytskyy, D., & D’Amico, S. (2015). Moment tensor solutions through waveforms inversion. Published by Mistral Service S.a.S., 25 p.

Malytskyi, D., Muyla, O., Pavlova A., & Hrytsai, O. (2013). Determining the focal mechanism of an earthquake in the Transcarpathian region of Ukraine. Visnyk Kyyivs’koho natsional’noho universytetu imeni Tarasa Shevchenka. Heolohiya, 4(63), 38—44.

Miller, A.D., Julian, B.R., & Foulger, G.R. (1998). Three-dimensiona1l seismic structure and moment tensors of non-double-couple earthquakes at the Hengill-Grensdalur volcanic complex, Iceland. Geophysical Journal International, 133(2), 309—325.

Pavlova, A., Hrytsai, O., & Malytskyy, D. (2014). Determining the focal mechanisms of the events in the Carpathian region of Ukraine. Geoscientific Instrumentation, Methods and Data Systems, 3, 229—239.

Šílený, J., Panza, G.F., & Campus, P. (1992). Waveform inversion for point source moment tensor retrieval with variable hypocentral depth and structural model. Geophysical Journal International, 109(2), 259-274.

Sipkin, S.A. (1986). Estimation of earthquake so-urce parameters by the inversion of waveform data: Global seismicity, 1981—1983. Bulletin of the Seismological Society of America, 76, 1515—1541.

Vavryčhuk, V., & Kühn, D. (2012). Moment tensor inversion of waveforms: a two-step time frequency approach. Geophysical Journal International, 190(3), 1761-1776.

Wéber, Z. (2006). Probabilistic local waveform inversion for moment tensor and hypocentral location, Geophysical Journal International, 165(2), 607—621.

Wéber, Z. (2016). Probabilistic waveform inversion for 22 earthquake moment tensors in Hungary: new constraints on the tectonic stress pattern inside the Pannonian basin. Geophysical Journal International, 204(1), 236-249.

Zhu, L., Akyol, N., Mitchell, B., & Sozbiliz, H. (2006). Seismotectonics of western Turkey from high resolution earthquake relocations and moment tensor determinations. Geophysical Research Letters, 33(7), L07316.



How to Cite

Pak, R. ., & Hrytsai, O. . (2021). Modeling of earthquake source parameters on December 12, 2018 (08:49:56,16; 36,4478° N; 140,5788° E; H = 62,0 km; Mw = 4,3, Japan). Geofizicheskiy Zhurnal, 43(4), 105–118.