Skip to main content
SpringerLink
Log in

Cluster Analysis for the Study of Stress Patterns in the Vrancea-Zone (SE-Carpathians)

  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

Abstract

The goal of this paper is to describe cluster analyses of the focal mechanism solutions estimated from local and teleseismic measurements and stress inversions to support the recent and previously published studies in the investigated region, that is the Vrancea seismic zone. We have applied different established clustering methods—e.g. hierarchical density-based clustering for applications with noise (HDBSCAN) and agglomerative hierarchical analysis—to the geographical coordinates, focal depths and parameters of the focal mechanism solutions of the gathered seismic events. We have attempted to develop a fully automated algorithm for the classification of earthquakes and to support the further investigation of stress inversions. This algorithm does not call for the setting of hyper-parameters by the users, thus the contribution from any bias of the user can be reduced significantly and the time required to carry out the clustering can also be decreased. In most cases, the resulting stress tensors are in close agreement with those we found in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data Availability

Internet sources: moment tensor solutions of EMSC-CSEM: https://www.emsc-csem.org/Earthquake/tensors.php. Isola-Gui: http://mt.infp.ro/. National Institute for Research and Development for Earth Physics (NIEP, http://atlas2.infp.ro/~rt/fms/). SRTM Data: http://srtm.csi.cgiar.org/srtmdata/.

Notes

  1. https://docs.python.org/3/library/random.html.

  2. http://atlas2.infp.ro/~rt/fms/.

  3. https://www.emsc-csem.org/Earthquake/tensors.php.

  4. https://en.wikipedia.org/wiki/Outlier#Tukey's_fences.

  5. https://en.wikipedia.org/wiki/Freedman%E2%80%93Diaconis_rule.

References

  • Álvarez-Gómez, J. A. (2019). FMC—earthquake focal mechanisms data management, cluster and classification. SoftwareX, 9, 299–307.

    Article  Google Scholar 

  • Bălă, A., Radulian, M., Popescu, E., & Toma-Danilă, D. (2018). Catalogue of earthquake mechanism and correlation with the most active seismic zones in south-eastern part of Romania. In R. Vacareanu & C. Ionescu (Eds.), Seismic hazard and risk assessment (pp. 23–37). Cham: Springer Natural Hazards. https://doi.org/10.1007/978-3-319-74724-8_2

    Chapter  Google Scholar 

  • Baron, J., & Morelli, A. (2017). Full-waveform seismic tomography of the Vrancea, Romania, subduction region. Physics of the Earth and Planetary Interiors, 273, 36–49.

    Article  Google Scholar 

  • Bokelmann, G., & Rodler, F. A. (2014). Nature of the Vrancea seismic zone (Eastern Carpathians)–New constraints from dispersion of first-arriving P-waves. Earth and Planetary Science Letters, 390, 59–68.

    Article  Google Scholar 

  • Bott, M. H. (1959). The mechanics of oblique slip faulting. Geological Magazine, 96, 109–117.

    Article  Google Scholar 

  • Byerlee, J. (eds) (1978). Friction of rocks. In: Rock friction and earthquake prediction Birkhäuser, Basel, pp. 615–626.

  • Campello, R. J., Moulavi, D., and Sander, J. (2013). Density-based clustering based on hierarchical density estimates. In: Pei, J., Tseng, V.S., Cao, L., Motoda, H., Xu, G. (eds) Advances in knowledge discovery and data mining. PAKDD 2013. Lecture Notes in Computer Science (Vol 7819). From: Pacific-Asia conference on knowledge discovery and data mining, Springer, Berlin, pp. 160–172

  • Carbunar, O. F., & Radulian, M. (2011). Geometrical constraints for the configuration of the Vrancea (Romania) intermediate-depth seismicity nest. Journal of Seismology, 15(4), 579.

    Article  Google Scholar 

  • Cesca, S., Rohr, A., & Dahm, T. (2013). Discrimination of induced seismicity by full moment tensor inversion and decomposition. Journal of Seismology, 17(1), 147–163.

    Article  Google Scholar 

  • Cesca, S., Şen, A. T., & Dahm, T. (2014). Seismicity monitoring by cluster analysis of moment tensors. Geophysical Journal International, 196(3), 1813–1826.

    Article  Google Scholar 

  • Chang, M., Zhou, Y., Zhou, C., et al. (2021). Coseismic landslides induced by the 2018 Mw 6.6 Iburi, Japan, Earthquake: Spatial distribution, key factors weight, and susceptibility regionalization. Landslides, 18, 755–772. https://doi.org/10.1007/s10346-020-01522-3

    Article  Google Scholar 

  • Chen, X., Wang, R., Huang, W., Jiang, Y., & Yin, C. (2018). Clustering-based stress inversion from focal mechanisms in microseismic monitoring of hydrofracturing. Geophysical Journal International, 215(3), 1887–1899.

    Article  Google Scholar 

  • Cronin, V. (2010). A primer on focal mechanism solutions for geologists. Science Education Resource Center, Carleton College, p. 14.

  • Custódio, S., Lima, V., Vales, D., Cesca, S., & Carrilho, F. (2016). Imaging active faulting in a region of distributed deformation from the joint clustering of focal mechanisms and hypocentres: Application to the Azores–western Mediterranean region. Tectonophysics, 676, 70–89.

    Article  Google Scholar 

  • Czirok, L. (2016). Analysis of stress relations using focal mechanism solutions in the Pannonian Basin. Geosciences and Engineering, 5(8), 65–84.

    Google Scholar 

  • Czirok, L., & Kuslits, L. (2018). Effects of earthquake data clustering on the results of stress inversions. Geosciences and Engineering, 6(9), 127–141.

    Google Scholar 

  • Erden, T., & Karaman, H. (2012). Analysis of earthquake parameters to generate hazard maps by integrating AHP and GIS for Küçükçekmece region. Natural Hazards and Earth Systems Sciences, 12, 475–483. https://doi.org/10.5194/nhess-12-475-2012

    Article  Google Scholar 

  • Freedman, D., & Diaconis, P. (1981a). On the histogram as a density estimator: L 2 theory. Zeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete, 57(4), 453–476.

    Article  Google Scholar 

  • Freedman, D., & Diaconis, P. (1981b). On the maximum deviation between the histogram and the underlying density. Zeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete, 58(2), 139–167.

    Article  Google Scholar 

  • Gephart, J. W., & Forsyth, D. W. (1984). An improved method for determining the regional stress tensor using earthquake focal mechanism data: Application to the San Fernando earthquake sequence. Journal of Geophysical Research: Solid Earth, 89(B11), 9305–9320.

    Article  Google Scholar 

  • Goualard, F. (2020). Generating random floating-point numbers by dividing integers: A case study. In: Krzhizhanovskaya V. V. et al. (eds) Computational Science—ICCS 2020, Lecture Notes in Computer Science, (Vol 12138). 20th International Conference on Computational Science, Springer, Cham, pp. 15–28. https://doi.org/10.1007/978-3-030-50417-5_2

  • Harangi, S., Novák, A., Kiss, B., Seghedi, I., Lukács, R., Szarka, L., Wesztergom, V., Metwaly, M., & Gribovszki, K. (2015). Combined magnetotelluric and petrologic constrains for the nature of the magma storage system beneath the Late Pleistocene Ciomadul volcano (SE Carpathians). Journal of Volcanology and Geothermal Research, 290, 82–96.

    Article  Google Scholar 

  • Hardebeck, J. L., & Michael, A. J. (2006). Damped regional-scale stress inversions: Methodology and examples for southern California and the Coalinga aftershock sequence. Journal of Geophysical Research, 111(B11), 310–321.

    Article  Google Scholar 

  • Heidbach, O., Ledermann, P., Kurfeß, D., Peters, G., Buchmann, T., Matenco, L., Negut, M., Sperner, B., Müller, B., Nuckelt, A., and Schmitt, G. (2007). Attached or not attached: Slab dynamics beneath Vrancea, Romania. In Proceedings of the International Symposium On Strong Vrancea Earthquakes and Risk Mitigation, pp. 4–20.

  • Ioane, D., & Stanciu, I. M. (2018). Extensional tectonics in Vrancea zone (Romania) interpreted on recent seismicity, geophysical and GPS data. Proceeding SGEM, 2018(18), 939–946.

    Google Scholar 

  • Ismail-Zadeh, A., Matenco, L., Radulian, M., Cloetingh, S., & Panza, G. (2012). Geodynamics and intermediate-depth seismicity in Vrancea (the south-eastern Carpathians): Current state-of-the art. Tectonophysics, 530, 50–79.

    Article  Google Scholar 

  • Kassaras, I. G., Kapetanidis, V. (2018). Resolving the tectonic stress by the inversion of earthquake focal mechanisms. Application in the region of Greece. A tutorial. Moment Tensor Solutions. Springer, Cham, pp. 405–452. https://doi.org/10.1007/978-3-319-77359-9_19

  • Koulakov, I., Zaharia, B., Enescu, B., Radulian, M., Popa, M., Parolai, S., & Zschau, J. (2010). Delamination or slab detachment beneath Vrancea? New arguments from local earthquake tomography. Geochemistry Geophysics Geosystems. https://doi.org/10.1029/2009GC002811

    Article  Google Scholar 

  • Lentas, K. (2018). Towards routine determination of focal mechanisms obtained from first motion P-wave arrivals. Geophysical Journal International, 212(3), 1665–1686. https://doi.org/10.1093/gji/ggx503

    Article  Google Scholar 

  • Lentas, K., Di Giacomo, D., Harris, J., & Storchak, D. A. (2019). The ISC Bulletin as a comprehensive source of earthquake source mechanisms. Earth System Science Data, 11, 565–578. https://doi.org/10.5194/essd-11-565-2019

    Article  Google Scholar 

  • Lizurek, G., Wiszniowski, J., Van Giang, N., Plesiewicz, B., & Van, D. Q. (2017). Clustering and Stress Inversion in the Song Tranh 2 Reservoir, VietnamClustering and Stress Inversion in the Song Tranh 2 Reservoir, Vietnam. Bulletin of the Seismological Society of America, 107(6), 2636–2648.

    Article  Google Scholar 

  • Lund, B., & Slunga, R. (1999). Stress tensor inversion using detailed microearthquake information and stability constraints: Application to Ölfus in southwest Iceland. Journal of Geophysical Research, 104(B7), 14947–14964.

    Article  Google Scholar 

  • Martínez-Garzón, P., Ben-Zion, Y., Abolfathian, N., Kwiatek, G., & Bohnhoff, M. (2016). A refined methodology for stress inversions of earthquake focal mechanisms. Journal of Geophysical Research, 121, 8666–8687. https://doi.org/10.1002/2016JB013493

    Article  Google Scholar 

  • Matenco, L., & Radivojević, D. (2012). On the formation and evolution of the Pannonian Basin: Constraints derived from the structure of the junction area between the Carpathians and Dinarides. Tectonics, 31, TC6007. https://doi.org/10.1029/2012TC003206

    Article  Google Scholar 

  • Maury, J., Cornet, F. H., & Dorbath, L. (2013). A review of methods for determining stress fields from earthquakes focal mechanisms; Application to the Sierentz 1980 seismic crisis (Upper Rhine graben). Bulletin De La Societe Geologique De France, 184(4–5), 319–334.

    Article  Google Scholar 

  • McInnes, L., Healy, J., & Astels, S. (2017). hdbscan: Hierarchical density based clustering. Journal of Open Source Software, 2(11), 205.

    Article  Google Scholar 

  • Meželovskij, N.V., Conseil d'assistance économique mutuelle (1987): Kosmotektoničeskaâ karta evropejskih stran-členov SÈV i SFRO / Sovet Èkonomičeskoj vzaimopomoŝi / glavnyj redaktor N.V. Meželovskij = Space tectonic of map european countries - the CMEA members and SFRY/Council for Mutual Economic Assistance, Echelle 1:1 000 000 (E 8°--E 30° /N 54°--N 42° ), [Moskva] : Mingeo, Fédération de Russie.

  • Michael, A. J. (1984). Determination of stress from slip data: Faults and folds. Journal of Geophysical Research: Solid Earth, 89(B13), 11517–11526.

    Article  Google Scholar 

  • Onescu, M. C., & Bonjer, K. P. (1997). A note on the depth recurrence and strain release of large intermediate Vrancea earthquakes. Tectonophysics, 272, 291–302.

    Article  Google Scholar 

  • Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., & Duchesnay, É. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12, 2825–2830.

    Google Scholar 

  • Petrescu, L., Borleanu, F., Radulian, M., Ismail-Zadeh, A., & Maţenco, L. (2021). Tectonic regimes and stress patterns in the Vrancea Seismic Zone: Insights into intermediate-depth earthquake nests in locked collisional settings. Tectonophysics, 799, 228688.

    Article  Google Scholar 

  • Popa, M., Radulian, M., Szakács, A., Seghedi, I., & Zaharia, B. (2012). New seismic and tomography data in the southern part of the Harghita Mountains (Romania, Southeastern Carpathians): Connection with recent volcanic activity. Pure and Applied Geophysics, 169(9), 1557–1573.

    Article  Google Scholar 

  • Popescu, E., Radulian, M., Bala, A., & Toma-Danila, D. (2018). Earthquake mechanism in the Vrancea subcrustal source and in the adjacent crustal seismogenic zones of the south-eastern Romania. Romanian Reports in Physics, 70, 704.

    Google Scholar 

  • Radulian, M., Bala, A., Ardeleanu, L., Toma-Danila, D., Petrescu, L., & Popescu, E. (2019). Revised catalogue of earthquake mechanisms for the events occurred in Romania until the end of twentieth century: REFMC. Acta Geodaetica Et Geophysica, 54(1), 3–18.

    Article  Google Scholar 

  • Radulian, M., Bala, A., Popescu, E., & Toma-Danila, D. (2018). Earthquake mechanism and characterization of seismogenic zones in south-eastern part of Romania. Annals of Geophysics, 61(1), 108.

    Article  Google Scholar 

  • Radulian, M., Bala, A., & Toma-Danila, D. (2020). REFMC 1929–2012 (Romanian Earthquake Focal Mechanism Catalogue). Mendeley Data. https://doi.org/10.17632/mykkx4gygy.3

    Article  Google Scholar 

  • Radulian, M., Mandrescu, N., Panza, G. F., Popescu, E., & Utale, A. (2000). Characterization of seismogenic zones of Romania. Pure and Applied Geophysics, 157, 57–77.

    Article  Google Scholar 

  • Schmitt, G., Nuckelt, A., Knöpfler, A., and Marcu, C. (2007). Three dimensional plate kinematics in Romania. In Proceedings of the International Symposium on Strong Vrancea Earthquakes and Risk Mitigation (pp. 34–45). Romania, Bucharest.

  • Seghedi, I., & Downes, H. (2011). Geochemistry and tectonic development of Cenozoic magmatism in the Carpathian-Pannonian region. Gondwana Research, 20(4), 655–672.

    Article  Google Scholar 

  • Sturges, H. A. (1926). The Choice of a Class Interval. Journal of the American Statistical Association, 21(153), 65–66. https://doi.org/10.1080/01621459.1926.10502161

    Article  Google Scholar 

  • Szűcs, E., Bozsó, I., Kovács, I. J., Bányai, L., Gál, Á., Szakács, S., & Wesztergom, V. (2018). Probing tectonic processes with space geodesy in the south Carpathians: Insights from archive SAR data. Acta Geodaetica Et Geophysica, 53, 331–345.

    Article  Google Scholar 

  • Tukey, J. W. (1977). Exploratory data analysis. Addison-Wesley Series in Behavioral Science, 2, 131–160.

    Google Scholar 

  • Van Der Hoeven, A. G. A., Mocanu, V., Spakman, W., Nutto, M., Nuckelt, A., Matenco, L., Munteanu, L., Marcu, C., & Ambrosius, B. A. C. (2005). Observation of present-day tectonic motions in the Southeastern Carpathians: Results of the ISES/CRC-461 GPS measurements. Earth and Planetary Science Letters, 239, 177–184.

    Article  Google Scholar 

  • Vavryčuk, V. (2007). On the retrieval of moment tensors from borehole data. Geophysical Prospecting, 55(3), 381–391.

    Article  Google Scholar 

  • Vavryčuk, V. (2014). Iterative joint inversion for stress and fault orientations from focal mechanisms. Geophysical Journal International, 199, 69–77.

    Article  Google Scholar 

  • Vavryčuk, V. (2015). Earthquake mechanisms and stress field. In M. Beer, I. Kougioumtzoglou, E. Patelli, & I. K. Au (Eds.), Encyclopedia of earthquake engineering (pp. 728–746). Berlin: Springer. https://doi.org/10.1007/978-3-642-36197-5_295-1

    Chapter  Google Scholar 

  • Vavryčuk, V., Bouchaala, F., & Fischer, T. (2013). High-resolution fault image from accurate locations and focal mechanisms of the 2008 swarm earthquakes in West Bohemia, Czech Republic. Tectonophysics, 590, 189–195.

    Article  Google Scholar 

  • Wallace, R. E. (1951). Geometry of shearing stress and relation to faulting. The Journal of Geology, 59(2), 118–130.

    Article  Google Scholar 

  • Wessel, P., Luis, J. F., Uieda, L., Scharroo, R., Wobbe, F., Smith, W. H. F., & Tian, D. (2019). The generic mapping tools version 6. Geochemistry, Geophysics, Geosystems, 20, 5556–5564. https://doi.org/10.1029/2019GC008515

    Article  Google Scholar 

  • Wiemer, S. (2001). A software package to analyze seismicity: ZMAP. Seismological Research Letters, 72(3), 373–382.

    Article  Google Scholar 

  • Willemann, R. J. (1993). Cluster analysis of seismic moment tensor orientations. Geophysical Journal International, 115(3), 617–634.

    Article  Google Scholar 

  • Zoback, M. L. (1992). First-and second-order patterns of stress in the lithosphere: The world stress map project. Journal of Geophysical Research, 97(B8), 11703–11728.

    Article  Google Scholar 

Download references

Acknowledgements

This work could have not been established without the funding of the ÚNKP-18-3-I New National Excellence Program of the Ministry of Human Capacities in Hungary. Furthermore, we would like to say thanks to the Romanian Institute for Earth Physics for the availability of the seismological data and the co-workers of the Hungarian Geological and Geophysical Library who have given us the tectonic maps for our investigations. We are really grateful to the ES1401—Time Dependent Seismology (TIDES) Action of the European Cooperation in Science and Technology (COST), the International Union of Geodesy and Geophysics, the Association of the Hungarian Geophysicist and the Hungarian Geological Society for supporting our associated conference and training course participations. We owe special thanks to István János Kovács, senior research fellow of the Institute of Earth Physics and Space Science, ELKH and Norbert Péter Szabó, the head of the Department of Geophysics and Geoinformatics of the University of Miskolc who have provided a continuous support.

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. Roth Gyula Forestry and Wildlife Management Sciences Doctoral School, University of Sopron, Sopron, Hungary

    Lili Czirok

  2. Department of Geology and Meteorology, Faculty of Sciences, Institute of Geography and Earth Sciences, University of Pécs, Pécs, Hungary

    Lili Czirok

  3. ELKH Institute of Earth Physics and Space Science, Sopron, Hungary

    Lili Czirok, Lukács Kuslits, István Bozsó & Katalin Gribovszki

  4. National Institute for Earth Physics, Magurele, Ilfov, Romania

    Mircea Radulian

  5. Academy of Romanian Scientists, Bucharest, Romania

    Mircea Radulian

  6. Romanian Academy, Bucharest, Romania

    Mircea Radulian

Authors
  1. Lili Czirok
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lukács Kuslits
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. István Bozsó
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mircea Radulian
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Katalin Gribovszki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lili Czirok.

Ethics declarations

Conflict of interest

The authors have no conflict of interest to declare that are relevant to the content of this article. No current funding was received for conducting this manuscript.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

See Figs. 12, 13.

Fig. 12
figure 12

Silhouette characteristics of each clustering algorithm with varying hyper-parameters (Hdbscan_min_cluster_size, Hier_n_clusters, CluStress_k), in the LAS zone of the study area. The 3D cases were computed using only the geographic coordinates, the 4D cases used both geographic coordinates and rake values

Full size image

12,

Fig. 13
figure 13

Silhouette characteristics of each clustering algorithm with varying hyper-parameters, similarly to Fig. 12, in the UASZ zone

Full size image

13.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Czirok, L., Kuslits, L., Bozsó, I. et al. Cluster Analysis for the Study of Stress Patterns in the Vrancea-Zone (SE-Carpathians). Pure Appl. Geophys. 179, 3693–3712 (2022). https://doi.org/10.1007/s00024-022-03159-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-022-03159-w

Keywords

Search

Navigation