Within the framework of the basic model of migrating seismicity, the main geoinformation criteria for identifying quasi-linear chains of earthquakes in epicentral fields of complex geometry and variable density of shock distribution have been determined by numerical methods. The developed model is used to study the migrations of earthquake foci and identify zones of hidden seismically active faults: it provides statistical criteria for the presence of quasi-linear chains of seismicity migration and zones of hidden seismic faults in arrays of various volumes of seismological data as an excess at a given level of significance of the average numbers of chains of earthquakes, spatially temporal distribution of shocks. The established dependences of the average number of selected chains of random events on the sample size and site shape make it possible to reveal the presence of seismicity migration and zones of hidden faults under the given criteria of “significance”, “representativeness” and ISMA. The developed methods, implemented programs and patents lay the theoretical and practical basis for GIS technology for identifying hidden faults and studying the migrations of earthquake foci in the lithosphere of the Baikal rift system. Since the main laws governing the formation of the internal structure of continental fault zones and seismicity are determined by the fundamental properties of the progressive deformation of transgressive shearing realized within them and are uniform, the developed GIS technologies can be applied in other seismically active regions.

Anna A. Kakourova,JuniorResearcher, The Institute of the Earth’s crust SB RAS. 128, Lermontov street, Irkutsk, 664033, Russia anna2015@crust.irk.ru

Anatolii V. Klyuchevskii, Doctor of Geological and Mineralogical sciences, Chief Researcher, The Institute of the Earth’s crust SB RAS. 128, Lermontov street, Irkutsk, 664033, Russia. e-mail: akluchev@crust.irk.ru

Vladimir M. Dem’yanovich, Lead Engineer, The Institute of the Earth’s crust SB RAS. 128, Lermontov street, Irkutsk, 664033, Russia. e-mail: vmdem@mail.ru

Anna A. Klyuchevskaya, Lead Engineer, Institute of the Earth’s crust SB RAS. 128, Lermontov street, Irkutsk, 664033, Russia.
e-mail: kluchevskaya@mail.ru

1. Keilis-BorokV.I., MolchanG.M. (eds.) Analiz geodinamicheskikh i seismicheskikh protsessov [Analysis of geodynamic and seismic processes]. In: Computational Seismology. Iss. 35. Moscow: GEOS; 2004. 329 p. [In Russian].
2. Baikal’skii filial “Edinoi geofizicheskoi sluzhby Rossiiskoi Akademii nauk” [Baikal Branch of the Federal Research Center “Unified Geophysical Service of the Russian Academy of Sciences”]. 2017. Available at: http://www.seis-bykl.ru (accessed 27.11.2019). [In Russian].
3. Bykov V.G. Strain waves in the Earth: theory, field data, and models. Russian Geology and Geophysics. 2005;46(11):1176−1190. [In Russian].
4. Bykov V.G. Nonlinear waves and solitons in models of fault block geological media. Russian Geology and Geophysics. 2015;56(5):793−803. DOI: 10.15372/GiG20150510. [In Russian].
5. Vikulin A.V. The Physics of Wave Seismic Process. Petropavlovsk-Kamchatsky: KGPU; 2003. 150 p. [In Russian].
6. Vikulin A.V., Dolgaya A.A., Gerus A.I. O volnovom geodinamicheskom protsesse v ramkakh modeli blokovoi geosredy kory [On the wave geodynamic process within the framework of the model of the block geoenvironment of the crust]. In: Tektonofizika i aktual’nye voprosy nauk o Zemle. Moscow: Institute of Physics of the Earth RAS, 2016. V. 1. pp. 451–455. [In Russian].
7. Vilkovich E.V., Guberman Sh.A., Keilis-Borok V.I. Volny tektonicheskikh deformatsii na krupnykh razlomakh [Waves of tectonic deformation at major faults]. Transactions (Doklady) of the USSR Academy of Sciences. 1974;219(1):77–80. [In Russian].
8. Goldin S.V. Lithosphere destruction and physical mesomechanics. Physical Mesomechanics. 2002;5(5–6):5–20.
9. Guberman Sh.A. D-volny i zemletryaseniya. Teoriya i analiz seismicheskikh nablyudenii [D-waves and earthquakes. Theory and analysis of seismological observations]. Computational Seismology. 1979;12:158–188. [In Russian].
10. Demyanovich V.M., Demyanovich M.G., Klyuchevskii A.V. Osnovnye razlomy Baikal’skoi riftovoi zony i formiruemaya imi seismichnost’ [The main faults of the Baikal rift zone and the seismicity formed by them]. In: Problemy sovremennoi seismogeologii i geodinamiki Tsentral’noi i Vostochnoi Azii. Irkutsk: The Institute of the Earth’s crust SB RAS, 2007. V. 1. pp. 108–116.
11. Demyanovich V.M., Klyuchevskii A.V., Chernykh E.N. Lithospheric stress and strain and seismicity in the Belin-Busiingol fault zone, southern Baikal region. Journal of Volcanology and Seismology. 2008;2(1):40–54. DOI: 10.1007/s11711-008-1004-y.
12. Dzhurik V.I., Klyuchevsky A.V., Serebrennikov S.P., Demyanovich  V.M., Batsaykhan Ts., Bayaraa G. Seismichnost’ i raionirovanie seismicheskoi opasnosti territorii Mongolii [Seismicity and zoning of seismic hazard in the territory of Mongolia]. Irkutsk: Institute of the Earth’s Crust SB RAS; 2009. 420 p. [In Russian].
13. Emanov A.F, Emanov A.A., Filina A.G., Leskova E.V. Spatio-temporal features of seismicity of the Altai-Sayan folded area. Physical Mesomechanics. 2005;8(1):49–64. [In Russian].
14 Kakourova A.A., Klyuchevskii A.V. Simulation base model of migration seismicity: fault zone. Proceedings of Irkutsk State Technical University. 2017;21(6(125)):49–59. DOI: 10.21285/1814-3520-2017-6-49-59. [In Russian].
15. Kakourova A.A., Klyuchevskii A.V. Migrating Seismicity in the Lithosphere of the Baikal Rift Zone: Spatiotemporal and Energy Distribution of Earthquake Chains. Russian Geology and Geophysics. 2020;61(11):1298–1312. DOI: 10.15372/RGG2019164.
16. Kasahara K. Earthquake mechanics. Cambridge: Cambridge University Press; 1981. – 248 p.
17. Klyuchevskii A.V. Aftershocks kinematics and dynamics of the 1991 Busiyngol earthquake. Journal of volcanology and seismology. 2003;4:65–78. [In Russian].
18. Klyuchevskii A.V. Seismicity under conditions of the self-organization of the Baikal Rift System. Doklady Earth Sciences. 2005;403(5):785–788.
19. Klyuchevskii A.V. Kinematics and dynamics of shocks in the Angarakan and Amut earthquake sequences of the Baikal region. Izvestiya. Physics of the Solid Earth. 2005;41(1):1–16.
20. Klyuchevski A.V. Kinematics and dynamics of aftershocks following the South Yakutia earthquake. Journal of volcanology and seismology. 2005;4:63–78. [In Russian].
21. Klyuchevskii A.V. Stresses and seismicity at the present stage of evolution of the Baikal rift zone lithosphere. Izvestiya. Physics of the Solid Earth. 2007;43(12):992–1004. DOI:10.1134/S1069351307120026.
22. Klyuchevskii A.V., Dem’yanovich V.M. The 3D Seismotectonic Flow of Geological Masses in the Lithosphere of the Baikal Rift Zone. Journal of Volcanology and Seismology. 2015;9(1):48–64. DOI: 10.1134/S0742046315010042.
23. Klyuchevskii A.V., Dem’yanovich V.M., Bayar G. Large earthquakes in the Baikal region and Mongolia: Recurrence time and probability. Russian Geology and Geophysics. 2005;46(7):731−745.
24. Klyuchevskii A.V., Dem’yanovich V.M., Klyuchevskaya A.A. Energy structure of seismicity at the Southwestern flank of the Baikal Rift System. Doklady Earth Sciences. 2015;464(2):1069–1074. DOI: 10.1134/S1028334X15100141.
25. Klyuchevskii A.V., Dem’yanovich V.M., Klyuchevskaya A.A., Zuev F.L., Kakourova A.A., Chernykh E.N., Bryzhak E.V. Gruppiruyushchayasya seismichnost’ Pribaikal’ya  [Grouping Seismicity of the Baikal Region]. In: Aktual’nye problemy nauki Pribaikal’ya. Bychkov I.V., Kazakov A.L., eds. Irkutsk: Institute of Geography SB RAS; 2015. pp. 139–143. [In Russian].
26. Klyuchevski A.V., Zuev F.L. Structure of the epicenter field of earthquakes in the Baikal region. Doklady Earth Sciences. 2007;415(2):944–949. DOI: 10.1134/S1028334X07060268.
27. Klyuchevskii A.V., Kakourova A.A. Base simulation model of migrating seismicity. Proceedings of Irkutsk State Technical University. 2016;8(115);74–84. DOI: 10.21285/1814-3520-2016-8-74-84. [In Russian].
28. Klyuchevskii А.V., Kakourova A. A. Investigation of Migrating Seismicity in the Lithosphere of the Baikal Rift Zone. Doklady Earth Sciences. 2019;488(1):1128–1133. DOI: 10.1134/S1028334X19090265.
29. Klyuchevskii A.V., Kakourova A.A., Dem’yanovich V.M. Tsepochki migratsii zemletryasenii v litosfere Baikal’skogo regiona [Chains of earthquake migrations in the lithosphere of the Baikal region]. In: Geodinamicheskaya evolyutsiya litosfery Tsentral’no-Aziatskogo podvizhnogo poyasa (ot okeana k kontinentu). Irkutsk: Institute of the Earth’s Crust SB RAS; 2017. Issue 15. pp. 122–123. [In Russian].
30. Kuz’min Yu.O. Deformation Autowaves in Fault Zones. Izvestiya. Physics of the Solid Earth. 2012;48(1):1–16. DOI: 10.1134/S1069351312010089.
31. Levina E.A., Ruzhich V.V. The seismicity migration study based on space-time diagrams. Geodynamics & Tectonophysics. 2015;6(2):225–240. DOI: 10.5800/GT-2015-6-2-0178.
32. Logachev N.A. (ed.) Lithosphere of Central Asia. Novosibirsk :Nauka, Sibirskaya izdatel’skaya firma RAN; 1996. 240 p.
33. Logachev N.A. History and geodynamics of the Baikal rift. Russian Geology and Geophysics. 2003;44(5):391– 406.
34. Makarov P.V. Self-organized criticality of deformation and prospects for fracture prediction. Physical Mesomechanics. 2010;13(5–6):292–305.
35. Makarov P.V., Peryshkin A.Yu. Modeling of “slow movements” or inelastic deformation autowaves in ductile and brittle materials and media. Physical Mesomechanics. 2016;19(2):32–46. [In Russian].
36. Malamud A.S., Nikolaevsky V.N. Periodichnost’ Pamiro-Gindukushskikh zemletryasenii i tektonicheskie volny v subduktsirovannykh litosfernykh plitakh [Periodicity of the Pamir – HinduKush earthquakes and tectonic waves in subducted lithospheric plates]. Transactions (Doklady) of the USSR Academy of Sciences. 1983;269(6):1075–1078. [In Russian].
37. Mikhailov D.N., Nikolaevskii V.N. Rotational tectonic waves with emission of seismic signals. Izvestia. Physics of the Solid Earth. 2000;11:895–903.
38. Misharina L.A., Solonenko A.V. Vliyanie blokovoi delimosti zemnoi kory na raspredelenie seismichnosti v Baikal’skoi riftovoi zone [Influence of the block divisibility of the Earth’s crust on seismicity distribution in the Baikal Rift Zone]. In: Seismichnost’ Baikal’skogo rifta. Prognosticheskie aspekty. Novosibirsk: Nauka; 1990. pp. 70–78. [In Russian].
39. Myachkin V.I., Kostrov B.V., Sobolev G.A. Shamina O.G. Osnovy fiziki ochaga i predvestniki zemletryasenii [Fundamentals of source physics and earthquake precursors]. In: Fizika ochaga zemletryaseniya. Moscow: Nauka; 1975. pp. 6–29. [In Russian].
40. Nevskii M.V., Artamonov A.M., Riznichenko O.Yu. Volny deformatsii i energetika seismichnosti [Deformation waves and seismicity energetic]. Transactions (Doklady) of the USSR Academy of Sciences. 1991;318(2.):316–320. [In Russian].
41. Nikolaevskii V.N. Mathematical modeling of solitary deformation and seismic waves. Transactions (Doklady) of the Russian Academy of Sciences. 1995;341(3):403–405. [In Russian].
42. Zonenshain L.P., Kovalyov A.A. (eds.), Volkovitch K.E., Denisova G.I. (transl.) Novaya global’naya tektonika : sb. statei [New global tectonics : coll. of papers]. Moscow: Mir; 1974. 472 p. [In Russian].
43. Novopashina A.V. Technique of the Cis-Baikal seismic activity migration isolation by GIS. Geoinformatika. 2013;1:33–36. [In Russian].
44. Molchan G.M., Naimark B.M., Levshin A.L. (eds.) Problemy dinamiki litosfery i seismichnosti [Problems of the dynamics of the lithosphere and seismicity]. In: Computational seismology. Issue 32. Moscow: GEOS; 2001. 303 p. [In Russian].
45. Dem’yanovich V.M., Klyuchevskii A.V. Computer program “Azimut” Rus. Federation №2016662608. Declared 05.07.2016; published 16.11.2016.
46. Kakourova A.A., Klyuchevskii A.V. Computer program (RU) “Chain” Rus. Federation №2016661616. Declared 24.08.2016; published 14.10.2016.
47. Kakourova A.A., Klyuchevskii A.V. Computer program (RU) “Migrations_fault_y” Rus. Federation №201761912. Declared 04.07.2017; published 28.08.2017.
48. Klyuchevskii A.V., Kakourova A.A. Computer program “Migrations” Rus. Federation №2016661511. Declared 23.05.2016; published 12.10.2016.
49. Psakh’e S.G., Ruzhich V.V., Smekalin O.P., Shilko E.V. Response of the geological media to dynamic loading. Physical Mesomechanics. 2001;4(1):67–71. [In Russian].
50. Richter C.F. Elementary Seismology. San Francisco: W.H. Freeman and Company; London: Bailey Bros. & Swinfen Ltd; 1958. 768 p.
51. Sadovskii M.A., Bolkhovitinov L.G., Pisarenko V.F. Deformirovanie geofizicheskoi sredy i seismicheskii protsess [Deformation of the Geophysical Medium and the Seismic Process]. Moscow: Nauka; 1987. 101 p. [In Russian].
52. Medvedev S.V. (ed.) Seismicheskoe raionirovanie SSSR [Seismic zoning of the USSR]. Moscow: Nauka; 1968. 476 p. [In Russian].
53. Klyuchevski A.V., Kakourova A.A., Klyuchevskaya A.A., Dem’yanovich V.M., Chernykh E.N. Method for determining earthquake chains in an epicentral seismicity field: patent 2659334 Rus. Federation. № 2017131805. Declared 09.11.2017; published 29.06.2018, bul. № 19.
54. Ulomov V.I. Ochagovaya seismichnost’ i dolgosrochnyi prognoz zemletryasenii [Focal seismicity and long-term forecast of earthquakes]. In: Problemnye voprosy seismologii Srednei Azii. Tashkent: FAS; 1988. Pp. 32–87. [In Russian].
55. Ulomov V.I. Volny seismogeodinamicheskoi aktivizatsii i dolgosrochnyi prognoz zemletryasenii [Waves of seismogeodynamic activation and long-term prediction of earthquakes]. Izvestiya. Physics of the Solid Earth. 1993;4:43–53. [In Russian].
56. Sherman S.I. Deformation waves as a trigger mechanism of seismic activity in seismic zones of the continental lithosphere. Geodynamics& Tectonophysics. 2013;4(2):83–117. DOI: 10.5800/GT2013420093. [In Russian].
57. Sherman S.I. Izbrannye trudy. Tektonika razlomoobrazovaniya i soputstvuyushchikh protsessov v litosfere [Selected Works. Tectonics of fault formation and associated processes in the lithosphere]. Irkutsk: Institut of Earth’s crust SB RAS; 2017. 1476 p. [In Russian].
58. Sherman S.I., Gorbunova E.A. Wave origin of fault activation in Central Asia on the basis of seismic monitoring. Physical Mesomechanics. 2008;11(1):115–122. [In Russian].
59. Box G.E.P., Muller M.E. A Note on the Generation of Random Normal Deviates. The Annals of Mathematical Statistics. 1958;29(2):610–611.
60. Golenetsky S.I. Problems of seismicity of the Baikal rift zone. Journal of Geodynamics. 1990;11:293–307.
61. Isack B., Oliver J., Sykes L.R. Seismology and the new global tectonics. Journal of Geophysical Research. 1968;73:5855–5899.
62. Lee W.H.K., Kanamori H., Jennings P.C., Kisslinge C. (eds.) International handbook of earthquake and engineering seismology. Amsterdam; Boston; New York; Tokyo: Academic Press; 2002. Part A. 934 p.
63. Mogi K. Migration of seismic activity. Bulletin of the Earthquake Research Institute, Tokyo University. 1968;46:53–74.
64. Sherman S.I., Dem’yanovich V.M., Lysak S.V. Active faults, seismicity and fracturing in the lithosphere of the Baikal rift system. Tectonophysics. 2004;380(3–4):261–272. DOI: 10.1016/j.tecto.2003.09.023.