Determination of earthquake source parameters based on data from a limited number of seismic stations

Authors

DOI:

https://doi.org/10.17721/1728-2713.109.08

Keywords:

seismic moment tensor, focal mechanism, matrix method, synthetic seismograms, correlation analysis

Abstract

Background. This paper presents a method for determining the seismic moment tensor using only direct P- and S-waves, which are less sensitive to modeling effects of wave propagation than reflected and refracted waves, significantly improving the accuracy and reliability of the method. The earthquake source is considered as a point source with a known location and origin time.

Methods. Wave propagation in a medium modeled as a set of horizontally homogeneous elastic layers is calculated using the matrix method, which allows isolating only direct waves. Based on the forward problem and the solution of the generalized inversion, an inversion algorithm for observed waveforms to determine the components of the seismic moment tensor M(t) is presented. The analysis is conducted based on records of the earthquake that occurred on February 22, 2024, in Eastern Slovakia, using data from only two seismic stations of the Slovak network: sk19 (49.25°N, 21.93°E) and sk20 (49.21°N, 21.61°E).

Results. To verify the reliability of the obtained earthquake source parameters, a comparative analysis was conducted between synthetic seismograms, calculated using the wavefield modeling methodology based on the matrix method, and observed records of direct P- and S-waves at station sk19. A correlation analysis of direct P- and S-waves for observed and synthetic seismograms was performed. The results of the analysis demonstrated a high reliability of the determined seismic moment tensor for the February 22, 2024 earthquake (Eastern Slovakia), obtained through inversion using only direct waves.

Conclusions. The use of a point source represented by a seismic moment tensor, placed within a horizontally stratified half-space, is an effective approach for determining earthquake focal mechanisms. The study results confirm the feasibility of using only direct P- and S-waves for determining the seismic moment tensor, which enhances computational accuracy and reduces the impact of modeling effects on wave propagation.

References

Aki, K., & Richards, P. G. (2002). Quantitative seismology. University Science Books.

Asano, K., Sekiguchi, H., & Iwata, T. (2024). Validation of Deep Velocity Structure Model in the Kyoto and Nara Basins Using Autocorrelation Functions of Strong Motion Records. Journal of Japan Association for Earthquake Engineering, 24(5), 45-57. https://doi.org/10.5610/jaee.24.5_45

Chen, Y.-C., Huang, H.-C., Iwata, T., & Asano, K. (2019). Strong Ground Motion Simulation of the 2016 ML 6.6 Meinong, Taiwan, Earthquake Using the Empirical Green's Function Method. Journal of Geophysical Research: Solid Earth, 124(12), 12905–12919. https://doi.org/10.1029/2019JB017661

Chiles, J.-P., & Delfiner, P. (2012). Geostatistics: Modeling spatial uncertainty (2nd ed.). Wiley-Interscience.

Dreger, D. S., & Helmberger, D. V. (1993). Determination of source parameters at regional distances with single station or sparse network data. Journal of Geophysical Research, 98(B1), 1162–1179.

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, 86(B4), 2825–2852.

Hallo, M., & Gallovič, F. (2016). Fast and cheap approximation of Green function uncertainty for waveform-based earthquake source inversions. Geophysical Journal International, 207(2), 1012–1029.

Kubo, H., Asano, K., Iwata, T., & Aoi, S. (2020). Along-dip variation in seismic radiation of the 2011 Ibaraki-oki, Japan, earthquake (Mw 7.9) inferred using a multiple-period-band source inversion approach. Journal of Geophysical Research: Solid Earth, 125(12), e2020JB019936. https://doi.org/10.1029/2020JB019936

Malek, J., Brokesova, J., & Novotny, O. (2023). New velocity structure of the Novy Kostel earthquake – swarm region, West Bohemia, determined by the isometric inversion. Pure and Applied Geophysics, 180, 2111–2134.

Malytskyy, D., & Asano, K. (2024). Seismic Moment Tensor and Focal Mechanism of the MW3.3 earthquake of May 11, 2021 in the Kyoto-Osaka Border Region Determined by Waweform Inversion. Baltic Journal of Modern Computing, 12(4), 434–442. https://doi.org/10.22364/bjmc.2024.12.4.05

Malytskyy, D., Fojtikova, L., Malek, J., Astashkina, O., Gnyp, A., Dobushovskyy, M., Pak, R., Melnyk, M., Nikulins, V., & Ignatyshyn, V. (2025). Seismic moment tensor and focal mechanism for earthquake of February 22, 2024 in Eastern Slovakia (12:54:15 UTC, 21.75°E, 49.03°N, depth 9 km, ML3.0). Геофізичний журнал (у друці).

Malytskyy, D. V. (2016). Mathematical modeling in seismology problems. Naukova Dumka [in Ukrainian].

Minson, S. E. (2024). Cross-fade sampling: extremely efficient Bayesian inversion for a variety of geophysical problems. Geophysical Journal International, 239(3), 1629–1649.

Pak, R. M. (2015). Modeling of a wave field perturbed by local sources in a vertically inhomogeneous half-space and calculation of synthetic seismograms. Geoinformatics, 4(56), 35–42 [in Ukrainian].

Schlomer, A., Hetenyi, G., Plomerova, J., Vecsey, L., Bielik, M., Bokelmann, G., Csicsay, K., Fojtikova, L., Friederich, W., Fuchs, F., Grad, M., Janik, T., Exnerova, H., K., Kolinsky, P., Malinowski, S., Meier, T., Mendecki, M., Papco, J., Szucs, E., Sule, B., Timko, M., Gyarmati, A., Weber, Z., Wesztergom, V., Zlebcikova, H., & AlpArray-PACASE Working Group. (2024). The Pannonian-Carpathian-Alpine seismic experiment (PACASE): network description and implementation. Acta Geodaetica et Geophysica, 59, 249–270. https://doi.org/10.1007/s40328-024-00439-w

Stiernström, V., Almquist, M., & Dunham, E. M. (2024). Adjoint-based inversion for stress and frictional parameters in earthquake modeling. Journal of Computational Physics, 519, 113447.

Thomson, W. T. (1950). Transmission of elastic waves through stratified solid medium. Journal of Applied Physics, 21(2), 89–93.

Vavryčuk, V., & Kuhn, D. (2012). Moment tensor inversion of waveforms: a two-step time-frequency approach. Geophysical Journal International, 190(3), 1761–1776. https://doi.org/10.1111/j.1365-246X.2012.05592.x

Published

2025-07-03

How to Cite

Malytskyy, D., Astashkina, O., Pak, R., Gnyp, A., & Dobushovskyy, M. (2025). Determination of earthquake source parameters based on data from a limited number of seismic stations. Visnyk of Taras Shevchenko National University of Kyiv. Geology, 2(109), 59-63. https://doi.org/10.17721/1728-2713.109.08