Spatiotemporal variations in the Gutenberg–Richter (GR) b-value and in the minimum magnitude of a predicted earthquake (MPE) are studied in detail depending on the depth and lateral position of the selected sample of earthquakes in the Garm region, Tajikistan. The time variations in b-value estimated from the data on the earthquakes in the different depth intervals indicate that most of the “strong” events with M ≥ MPE were preceded by the significant time anomalies localized in the vicinity of the source depths of these earthquakes. The maximum amplitudes of these anomalies gravitate to the vicinity of the hypocenters of the strong earthquakes and decay with distance from the hypocenter. The observed time anomalies in the b-value, which have a shape of a positive bay, are not accidental, which is demonstrated by their sufficient statistical representativeness (18 events). It is concluded that based on the used approach it will be possible to estimate the source depth of a future strong earthquake. The estimate of earthquake prediction quality based on 38 “strong” earthquakes with M ≥ MPE that occurred in seven local regions during a 23-year observation period shows that in 84% of cases, the emergence of b-value anomalies is accompanied by the successful forecasts. At the same time, the overall probability estimate of a medium-term forecast of the “strong” earthquakes with false alarms and missed events taken into account is 71%. Meanwhile, the forecasting quality of the strong earthquakes substantially increases if the b-value time variations are monitored separately in the different depth intervals of the Earth’s crust. It is shown that the parameter of the minimum MPE estimated from the rightmost part of the linear segment of GR relationship is a characteristic of the structural blocks of the Earth’s crust and varies both across the area and along the depth. It is hypothesized that the front of the deformation waves emerging on certain time intervals in a number of the local regions of the sample has probably been detected. The supposed deformation waves propagate with the velocities of 40–50 km/yr with their front moving NE to SE.The results of the study can be used for medium-term forecasting of the earthquakes with M ≥ MPE, for estimating the depth of the expected earthquake, and for overall seismic hazard assessment in the seismically active regions.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Aki, K., Maximum likelihood estimate of b in the formula log N = a – bM and its confidence limits, Bull. Earthquake Res. Inst., Univ. Tokyo, 1965, vol. 43, pp. 237–239.
Amitrano, D., Brittle_ductile transition and associated seismicity: Experimental and numerical studies and relationship with the b value, J. Geophys. Res., 2003, vol. 108, no. B1, p. 2044. https://doi.org/10.1029/2001JB000680
Baskoutas, I. and Popandopoulos, G., Qualitative precursory pattern before several strong earthquakes in Greece, Res. Geophys., 2014, vol. 4, pp.7–11. https://doi.org/10.4081/rg.2014.4899
Bath, M., Spectral Analysis in Geophysics, Amsterdam: Elsevier, 1974.
Bykov, V.G., Strain waves in the Earth: theory, field data, and models, Russ. Geol. Geophys., 2005, no. 11, pp. 1158–1170.
Daub, E.G., Shelly, D.R., Guyer, R.A., and Johnson, P.A., Brittle and ductile friction and the physics of tectonic tremor, Geophys. Res. Lett., 2011, vol. 38, Paper ID L10301. https://doi.org/10.1029/2011GL046866
Dinkelman, M.G., Granath, J., Bird, D., Helwig, J., Kumar, N., and Emmet, P., Predicting the Brittle_Ductile (B_D) Transition in Continental Crust Through Deep, Long Offset, Prestack Depth Migrated (PSDM), 2D Seismic Data, Search Discovery Artic., 2010, no. 40511.
Dobrovol’skii, I.P., Earthquake preparation. Deformations and the size of the zone of manifestation of the precursors, in Eksperimental’naya seismologiya (Experimental Seismology), Moscow: Nauka, 1983, pp. 17–25.
Dobrovol’skii, I.P., Teoriya podgotovki tektonicheskogo zemletryaseniya (Theory of Preparation of a Tectonic Earthquake), Moscow: IFZ AN SSSR, 1991.
Doglioni, C., Barba, S., Carminati, E., and Riguzzi, F., Role of the brittle–ductile transition on fault activation, Phys. Earth Planet. Inter., 2010, vol. 184, nos. 3–4, pp. 160–171.
Dragoni, M., The brittle-ductile transition in tectonic boundary zones, Ann. Geofis., 1993, vol. 36, no. 2, pp. 37–44.
Gerstenberger, M.C., Wiemer, S., Giardini, D., Hauksson, E., and Jones, L.M., Time-dependent hazard assessment for California in near real-time, Seismol. Res. Lett., 2001b, vol. 72, p. 273.
Gomberg, J., Seismicity and detection/location threshold in the southern Great Basin seismic network, J. Geophys. Res., 1991, vol. 96, no. B10, pp.16,401–16,414.
Gueydan, F., Leroy, Y.M., and Jolivet, L., Mechanics of low_angle extensional shear zones at the brittle–ductile transition, J. Geophys. Res., 2004, vol. 109, Paper ID B12407. https://doi.org/10.1029/2003JB002806
Gutenberg, B. and Richter, Ch.F., Frequency of earthquakes in California, Bull. Seismol. Soc. Am., 1944, vol. 34, pp. 185–188.
Hamburger, M.W., Sarewitz, D.E., Pavlis, G.L., and Popandopulos, G.A., Structural and seismic evidance for intracontinental subduction in the Peter the First Range, Soviet Central Asia, Geol. Soc. Am. Bull., 1992, vol. 104, pp. 397–408.
Ishimoto, M. and Iida, K., Observations of earthquakes registered with the microseismograph constructed recently, Bull. Earthquake Res. Inst., Univ. Tokyo, 1939, vol. 17, pp. 443–478.
Jin, A., Aki, K., Liu, Z., and Keilis-Borok, V.I., Seismological evidence for the brittle ductile interaction hypothesis on earthquake loading, Earth Planets Space, 2004, vol. 56, pp. 823–830.
Kasahara, K., Earthguake Mechanics, Cambriage: Cambriage Univ. Prress, 1981.
Kijko, A. and Sellevoll, M.A., Estimation of Earthquake Hazard Parameters from Incomplete Data Files. 2. Incorporation of Magnitude Heterogeneity, Bull. Seismol. Soc. Am., 1992. vol. 82, no. 1, pp. 120–134.
Kostrov, B.V. and Das, S., Principles of Earthquake Source Mechanics, Cambridge: Cambridge Univ. Press, 1988.
Lukk, A.A. and Popandopoulos, G.A., Reliability of determining the parameters of Gutenberg–Richter distribution for weak earthquakes in Garm, Tajikistan, Izv.,Phys. Solid Earth, 2012, vol. 48, nos. 9–10, pp. 698–720.
Lukk, A.A. and Shevchenko, V.I., Structure of seismic field and fault tectonics of the Garm region in Tajikistan, Izv. Akad. Nauk SSSR,Fiz. Zemli, 1990, no. 1, pp. 5–20.
Main, I.G., Meredith, P.G., and Sammonds, P.R., Temporal variations in seismic event rate and b-values from stress corrosion constitutive laws, Tectonophysics, 1992, vol. 211, pp. 233–246.
Marzocchi, W. and Sandri, L., A review and new insights on the estimation of the b-value and its uncertainty, Ann. Geophys., 2003, vol.46, no. 6, pp. 1271–1282.
Mignan, A. and Woessner, J. Completeness magnitude in earthquake catalogs. Community Online Resource for Statistical Seismicity Analysis. 2012. https://doi.org/10.5078/corssa-00180805
Mogi, K., Study of the elastic shocks caused by the fracture of heterogeneous materials and its relation to earthquake phenomena, Bull. Earthquake Res. Inst., Univ. Tokyo, 1962, vol. 40, pp. 125–173.
Mori, J. and Abercrombie, R.E., Depth dependence of earthquake frequency-magnitude distributions in California: implications for the rupture initiation, J. Geophys. Res., 1997, vol. 102, pp. 15081–15090.
Myachkin, V.I., Kostrov, B.V., Sobolev, G.A., and Shamina, O.G., Basic physics of the source and earthquake precursors, in Fizika ochaga zemletryaseniya (Physics of an Earthquake Source), Moscow: Nauka, 1975, pp. 6–29.
Nersesov, I.L. and Popandopoulos, G.A., Spatial heterogeneity of temporal variations in the velocity parameters in the Earth’s crust of the Garm region, Izv. Akad. Nauk SSSR,Fiz. Zemli, 1988, no. 8, pp. 13–24.
Nikolaevskiy, V.N., Geomechanics and Fluid Dynamics, Dordecht: Kluwer, 1996.
Popandopoulos, G.A., Determining the coordinates of the hypocenters of local earthquakes at the Garm Geophysical Test Site, in Zemletryaseniya i protsessy ikh podgotovki (Earthquakes and the Processes of Their Preparation), Moscow: Nauka, 1991, pp. 5–23.
Popandopoulos, G.A., Detailed study of time variations in the Gutenberg–Richter b-value based on highly accurate seismic observations at the Garm prognostic site, Tajikistan, Izv.,Phys. Solid Earth, 2018, vol. 54, no. 4, pp. 612–631.
Papadopoulos, G.A. and Baskoutas, I.G., New tool for the temporal variation analysis of seismic parameters, Nat. Hazards Earth Syst. Sci., 2009, vol. 9, pp. 859–864. www.nat-hazards-earth-syst-sci.net/9/859/2009.
Popandopoulos, G.A. and Baskoutas, I., Regularities in the time variations of seismic parameters and their implications for prediction of strong earthquakes in Greece, Izv.,Phys. Solid Earth, 2011, vol. 47, no. 11, pp. 974–994.
Popandopoulos, G.A. and Chatziioannou, E., Gutenberg-Richter Law Parameters Analysis Using the Hellenic Unified Seismic Network Data Through FastBee Technique, Earth Sci., 2014, vol. 3, no. 5, pp. 122–131. https://doi.org/10.11648/jearth.20140305.12
Popandopoulos, G.A. and Lukk, A.A., The depth variations in the b-value of frequency–magnitude distribution of the earthquakes in the Garm region of Tajikistan, Izv.,Phys. Solid Earth, 2014, vol. 50, no. 2, pp. 273–288.
Popandopoulos, G.A. and Nersesov, I.L., Some results of the analysis of 30-year time series of valocity parameters at the Garm geodynamical testing site, in Zemletryaseniya i protsessy ikh podgotovki (Earthquakes and the Processes of Their Preparation), Moscow: Nauka, 1991, pp. 139–152.
Popandopoulos, G.A., Baskoutas, I., and Chatziioannou, E., The spatiotemporal analysis of the minimum magnitude of completeness Mc and the Gutenberg–Richter b-value using the earthquake catalog of Greece, Izv.,Phys. Solid Earth, 2016, vol. 52, no. 2, pp. 195–209.
Ruff, L., Asperity distributions and large earthquake occurrence in subduction zones, Tectonophysics, 1992, vol. 211, pp. 61–83.
Rydelek, P.A. and Sacks, I.S., Testing the completeness of earthquake catalogs and the hypothesis of self-similarity, Nature, 1989, vol. 337, pp. 251–253.
Sadovskii, M.A. and Pisarenko, V.F., Seismicheskii protsess v blokovoi srede (Seismic Process in a Block Medium), Moscow: Nauka, 1991.
Sandri, L. and Marzocchi, W., A technical note on the bias in the estimation of the b-value and its uncertainty through the Least Squares technique, Ann. Geophys., 2007, vol. 50, no. 3. pp. 329–339.
Scholz, C.H., The frequency-magnitude relation of microfracturing in rock and its relation to earthquakes, Bull. Seismol. Soc. Am., 1968, vol. 58, pp. 399–415.
Scholz, C.H., On the stress dependence of the earthquake b value, Geophys. Res. Lett., 2015, vol. 42, pp.1399–1402. https://doi.org/10.1002/2014GL062863
Schorlemmer, D., Wiemer, S., and Wyss, M., Earthquake statistics at Park field: 1. Stationarity of b-values, J. Geophys. Res., 2004a, vol. B12307. https://doi.org/10.1029/2004JB003234
Schorlemmer, D., Wiemer, S., Wyss, M., and Jackson, D.D., Earthquake statistics at Park field: 2. Probabilistic forecasting and testing, J. Geophys. Res., 2004b, vol. B12307. https://doi.org/10.1029/2004JB003234
Schorlemmer, D., Wiemer, S., and Wyss, M., Variations in earthquake-size distribution across different stress regimes, Nature, 2005, vol. 437, pp. 539–542. https://doi.org/10.1038/nature04094
Sherman, S.I., Deformation waves as a trigger mechanism of seismic activity in seismic zones of the continental lithosphere, Geodinam.Tektonofiz., 2018, vol. 4, no. 2, pp. 83–117.
Shi, Y. and Bolt, B.A., The standard error of the Magnitude-frequency b value, Bull. Seismol. Soc. Am., 1982, vol. 72, pp. 1677–1687.
Smirnov, V.B., Earthquake catalogs: evaluation of data completeness, Volcanol. Seismol., 1998, vol. 19, pp. 497–510.
Sobolev, G.A., Osnovy prognoza zemletryasenii (Basics of Earthquake Prediction), Moscow: Nauka, 1993.
Spada, M., Tormann, T., Wiemer, S., and Enescu, B., Generic dependence of the frequency-size distribution of earthquakes on depth and its relation to the strength profile of the crust, Geophys. Res. Lett., 2013, vol. 40, pp. 709–714. https://doi.org/10.1029/2012GL054198
Turcotte, D.L. and Schubert, G., Geodynamics, New York: Wiley, 1982.
Wiemer, S., A software package to analyze seismicity: ZMAP, Seismol. Res. Lett., 2001, vol. 72, no. 3, pp. 373–382.
Wiemer, S. and Wyss, M., Mapping the frequency-magnitude distribution in asperities: An improved technique to calculate recurrence times?, J. Geophys. Res., 1997, vol. 102, pp. 15,115–15,128.
Wiemer, S. and Wyss, M., Minimum magnitude of completeness in earthquake catalogs: Examples from Alaska, the western United States and Japan, Bull. Seismol. Soc. Am., 2000, vol. 90, no. 4, pp. 859–869.
Wiemer, S. and Wyss, M., Mapping spatial variability of the frequency—magnitude distribution of earthquakes, Adv. Geophys., 2002, vol. 5, pp. 259–302.
Woessner, J. and Wiemer, S., Assessing the quality of earthquake catalogues: Estimating the magnitude of completeness and its uncertainty, Bull. Seismol. Soc. Am., 2005, vol. 95, pp. 684–698.
Wyss, M. and Stefansson, R., Nucleation points of recent main shocks in southern Iceland mapped by b-values, Bull. Seismol. Soc. Am., 2006, vol. 96, pp. 599–608.
Wyss, M., Hasegawa, A., and Nakajima, J., Source and path of magma for volcanoes in the subduction of northeastern Japan, Geophys. Res. Lett., 2001a, vol. 28, pp.1819–1822.
Wyss, M., Pacchiani, F., Deschamps, A., and Patau, G., Mean magnitude variations of earthquakes as a function of depth: different crustal stress distribution depending on tectonic setting, Geophys. Res. Lett., 2008, vol. 35, Paper ID L01307. https://doi.org/10.1029/2007GL031057
Zheng, B., Hamburger, M.W., and Popandopulos, G.A., Precursory seismicity changes preceding moderate and large earthquakes in the Garm region, Central Asia, Bull. Seismol. Soc. Am., 1995, vol. 85, pp. 571–589.
Zhu, A., Xu, X., Hu, P., Zhou, Y., Chen, G., and Gan, W., Variation of b value with hypocentral depth in Beijing area: Implications for earthquake nucleation, Chin. Sci. Bull., 2005, vol. 50, no. 7, pp.691–695.
Translated by M. Nazarenko
About this article
Cite this article
Popandopoulos, G.A. Spatiotemporal Variations in Gutenberg–Richter b-Value Depending on the Depth and Lateral Position in the Earth’s Crust of the Garm Region, Tajikistan. Izv., Phys. Solid Earth 56, 337–356 (2020). https://doi.org/10.1134/S1069351320020081
- Gutenberg–Richter law
- positive bay-like anomalies
- detection of a front of deformation waves