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Modeling the earthquake occurrence with time-dependent processes: a brief review

  • Review Article - Solid Earth Sciences
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Abstract

The complexity of seismogenesis tantalizes the scientific community for understanding the earthquake process and its underlying mechanisms and consequently, precise earthquake forecasting, although a realistic target, is yet far from being a practice. Therefore, seismic hazard assessment studies are focused on estimating the probabilities of earthquake occurrence. For a more precise representation of seismicity-regarding time, space and magnitude stochastic modeling is engaged. The candidate models deal with either a single fault or fault segment, or a broader area, leading to fault-based or seismicity-based models, respectively. One important factor in stochastic model development is the time scale, depending upon the target earthquakes. In the case of strong earthquakes, the interevent times between successive events are relatively large, whereas, if we are interested in triggering and the probability of an event to occur in a small time increment then a family of short-term models is available. The basic time-dependent models that can be applied toward earthquake forecasting are briefly described in this review paper.

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References

  • Abaimov SG, Turcotte DL, Shcherbakov R, Runlde JB, Yakovlev G, Goltz C, Newman WI (2008) Earthquakes: recurrence and interoccurrence times. Pure appl Geophys 165:777–795. https://doi.org/10.1007/s00024-008-0331-y

    Google Scholar 

  • Bakun WH, Aagaard B, Dost B, Ellsworth WL, Hardebeck JL, Harris RA, Ji C, Johnston MJS, Langbein J, Lienkaemper JJ, Michael AJ, Murray JR, Nadeau RM, Reasenberg PA, Reichle MS, Roeloffs EA, Shakal A, Simpson RW, Waldhausen F (2005) Implications for prediction and hazard assessment from the 2004 Parkfield earthquake. Nature 437:969–974

    Google Scholar 

  • Bebbington M, Harte D (2001) On the statistics of the linked stress release process. J Appl Probab 38:176–187

    Google Scholar 

  • Bebbington M, Harte D (2003) The linked stress release model for spatio-temporal seismicity: formulations, procedures and applications. Geophys J Int 154:925–946

    Google Scholar 

  • Bountzis P, Papadimitriou E, Tsaklidis G (2018) Estimating the earthquake occurrence rates in Corinth Gulf (Greece) through Markovian arrival process modeling. J Appl Stat. https://doi.org/10.1080/02664763.2018.1531977

    Google Scholar 

  • Bowman DD, Ouillon G, Sammis CG, Sornette A, Sornette D (1998) An observational test of the critical earthquake concept. J Geophys Res 103:24359–24372

    Google Scholar 

  • Bufe CG, Varnes DJ (1993) Predictive modeling of the seismic cycle of the greater San Francisco Bay region. J Geophys Res 98:9871–9883

    Google Scholar 

  • Chingtham P, Yavad RBS, Chopra S, Yavad AK, Gupta AK, Roy PNS (2015) Time-dependent seisimicity analysis in the Northwest Himalaya and its adjoining regions. Nat Hazards 80:1783–1800. https://doi.org/10.1007/s11069-015-2031-0

    Google Scholar 

  • Console R, Murru M (2001) A simple and testable model for earthquake clustering. J Geophys Res 106:8699–8711

    Google Scholar 

  • Console R, Murru M, Lombardi AM (2003) Refining earthquake clustering models. J Geophys Res 108:2468

    Google Scholar 

  • Console R, Murru M, Catalli F (2006a) Physical and stochastic models of earthquake clustering. Tectonophysics 417:141–153

    Google Scholar 

  • Console R, Rhoades DA, Murru M, Evison FF, Papadimitriou EE, Karakostas VG (2006b) Comparative performance of time-invariant, long range and short-range forecasting models on the earthquake catalogue of Greece. J Geophys Res 111:B09304. https://doi.org/10.1029/2005JB004113

    Google Scholar 

  • Console R, Murru M, Catalli F, Falcone G (2007) Real time forecasts through an earthquake clustering model constrained by the rate-and-state constitutive law: comparison with a purely stochastic ETAS model. Seismol Res Let 78:49–56

    Google Scholar 

  • Console R, Murru M, Falcone G, Catalli F (2008) Stress interaction effect on the occurrence probabilities of characteristic earthquakes in Central Apennines. J Geophys Res 113:B08313. https://doi.org/10.1029/2007JB0005418

    Google Scholar 

  • Console R, Falcone G, Karakostas V, Murru M, Papadimitriou E, Rhoades D (2013) Renewal models and coseismic stress transfer in the Corinth Gulf, Greece, fault system. J Geophys Res Solid Earth 118:3655–3673. https://doi.org/10.1002/jgrb.50277

    Google Scholar 

  • Convertito V, Faenza L (2014) Earthquake Recurrence. In: Beer M, Kougioumtzoglou IA, Patelli E, Siu-Kui Au I (eds) Encyclopedia of earthquake engineering. Springer, Berlin, pp 1–22. https://doi.org/10.1007/978-3-642-36197-5-236-1

    Google Scholar 

  • Daley D, Vere-Jones D (2003) An introduction to the theory of point processes, 2nd edn. Springer, New York, pp 211–287

    Google Scholar 

  • Di Giovambattista R, Tyupkin YS (2000) Spatial and temporal distribution of the seismicity before the Umbria-Marche September 26, 1997 earthquakes. J Seismol 4:589–598

    Google Scholar 

  • Dieterich J (1994) A constitutive law for rate of earthquake production and its application to earthquake clustering. J Geophys Res 99:2601–2618

    Google Scholar 

  • Dreger D, Savage B (1999) Aftershocks of the 1952 Kern County, California, earthquake sequence. Bull Seismol Soc Am 89:1094–1108

    Google Scholar 

  • Ellsworth WL, Matthews MV, Nadeau RM, Nishenko SP, Reasenberg PA (1999) A physically based recurrence model for estimation of long-term earthquake probabilities. US Geol Surv Rept 99:522

    Google Scholar 

  • Evison FF, Rhoades DA (2004) Demarcation and scaling of long-term seismogenesis. Pure appl Geophys 161:21–45

    Google Scholar 

  • Field EH (2015) Computing elastic—rebound—motivated earthquake probabilities in unsegment fault models: a new methodology supported by physics—based simulators. Bull Seismol Soc Am 105:544–559. https://doi.org/10.1785/0120140094

    Google Scholar 

  • Field EH, Dawson TE, Felzer KR, Frankel AD, Gupta V, Jordan TH, Parsons T, Petersen MD, Stein RS, Weldon RJ II, Wills CJ (2009) Uniform California rupture forecast, version 2 (UCERF 2). Bull Seismol Soc Am 99:2053–2107. https://doi.org/10.1785/0120080049

    Google Scholar 

  • Field EH, Biasi GP, Bird P, Dawson TE, Felzer KR, Jackson DD, Johnson KM, Jordan TH, Madden C, Michael AJ, Milner KR, Page MT, Parsons T, Powers PM, Shaw BE, Thatcher WR, Weldon RJ II, Zeng Y (2015) Long-term time-dependent probabilities for the third uniform California earthquake rupture forecast (UCERF3). Bull Seismol Soc Am 105:511–543. https://doi.org/10.1785/0120140093

    Google Scholar 

  • Frankel AM (1995) Mapping seismic hazard in the central and eastern United States. Seismol Res Let 60:8–21

    Google Scholar 

  • Gerstenberger MC, Rhoades DA (2010) New Zealand earthquake forecast testing centre. Pure appl Geophys 167:877–892. https://doi.org/10.1007/s00024-010-0082-4

    Google Scholar 

  • Gomberg M, Belardinelli ME, Cocco M, Reasenberg P (2005) Time-dependent earthquake probabilitied. J Geophys Res 110:B05S04. https://doi.org/10.1019/2004jb003405

    Google Scholar 

  • Gutenberg B, Richter C (1949) Seismicity of the earth and associated phenomena, 2nd edn. University Press, Princeton

    Google Scholar 

  • Hagiwara Y (1974) Probability of earthquake occurrence as obtained from a Weibull distribution analysis of crustal strain. Tectonophysics 23:313–318

    Google Scholar 

  • Hainzl S, Ogata Y (2005) Detecting fluid signals in seismicity data through statistical earthquake modeling. J Geophys Res 110:B05S07

    Google Scholar 

  • Hardebeck JL (2004) Stress triggering and earthquake probability estimated. J Geophys Res 109:B04310. https://doi.org/10.1029/2003JB002437

    Google Scholar 

  • Hawkes AG, Oakes D (1974) A cluster process representation of a self-exciting process. J Appl Prob 11:493–503

    Google Scholar 

  • Helmstetter A, Sornette D (2002) Sub-critical and supercritical regimes in epidemic models of earthquake aftershocks. J Geophys Res 107:2237

    Google Scholar 

  • Iervolino I, Giorgio M, Polidoro B (2014) Sequence-based probabilistic seismic hazard analysis. Bull Seismol Soc Am 104(2):1006–1012. https://doi.org/10.1785/0120130207

    Google Scholar 

  • Imoto M, Hurukawa N (2006) Assessing potential seismic activity in Vrancea, Romania, using a stress-release model. Earth Planets Space 58:1511–1514

    Google Scholar 

  • Jackson DD, Kagan YY (1999) Testable earthquake forecasts for 1999. Seismol Res Lett 70:393–403

    Google Scholar 

  • Jackson DD, Aki K, Cornell CA, Dieterich JH, Henyey TL, Mahdyiar M, Schwartz D, Ward SN (1995) Seismic hazard in Southern California: Probable earthquakes, 1994 to 2024. Bull Seism Soc Am 85:379–439

    Google Scholar 

  • Jaume SC, Sykes LR (1999) Evolving towards a critical point: a review of accelerating seismic moment/energy release prior to large and great earthquakes. Pure appl Geophys 155:279–306

    Google Scholar 

  • Jiang C, Wu Z (2006) Benioff strain release before earthquakes in China: accelerating or not? Pure appl Geophys 163:965–976

    Google Scholar 

  • Jones LM, Molnar P (1979) Some characteristics of foreshocks and their possible relationship to earthquake prediction and premonitory slip on faults. J Geophys Res 84(B7):3596–3608

    Google Scholar 

  • Kagan YY, Jackson DD (1991) Long-term earthquake clustering. Geophys J Int 104:117–133

    Google Scholar 

  • Kagan YY, Jackson DD (1998) Spatial aftershock distribution: effect of normal stress. J Geophys Res 103:24453–24467

    Google Scholar 

  • Kagan YY, Knopoff L (1987) Random stress and earthquake statistics: time dependence. Geoplys JR Astron Soc 88:723–731

    Google Scholar 

  • Karakaisis GF (1993) Long term earthquake prediction in the New Guinea-Bismarck Sea region based on the time and magnitude predictable model. J Phys Earth 41:365–389

    Google Scholar 

  • Karakaisis GF (1994a) Long-term earthquake prediction along the North and East Anatolian Fault Zones based on the time and magnitude predictable model. Geophys J Int 116:198–204

    Google Scholar 

  • Karakaisis GF (1994b) Long term earthquake prediction in Iran based on the time and magnitude predictable model. Phys Earth Planet Inter 83:129–145

    Google Scholar 

  • Kourouklas C, Papadimitriou E, Tsaklidis G, Karakostas V (2018) Earthquake recurrence models and occurrence probabilities of strong earthquakes in North Aegean Trough (Greece). J Seismol 22:1225–1246. https://doi.org/10.1007/s10950-018-9763-8

    Google Scholar 

  • Kuehn NM, Hainzl S, Scherbaum F (2008) Non-Poissonian earthquake occurrence in coupled stress release models and its effect on seismic hazard. Geophys J Int 174:649–658

    Google Scholar 

  • Liu J, Vere-Jones D, Ma L, Shi Y, Zhuang JC (1998) The principal of coupled stress release model and its application. Acta Seismol Sin 11:273–281

    Google Scholar 

  • Liu C, Chen Y, Shi Y, Vere-Jones D (1999) Coupled stress release model for timedependent seismicity. Pure appl Geophys 155:649–667

    Google Scholar 

  • Lombardi AM, Cocco M, Marzocchi W (2010) On the increase of background seismicity rate during the 1997–1998 Umbria-Marche, central Italy, sequence: apparent variation or fluid-driven triggering? Bull Seismol Soc Am 100:1138–1152

    Google Scholar 

  • Lu C, Vere-Jones D (2000) Application of linked stress release model to historical earthquake data: comparison between two kinds of tectonic seismicity. Pure appl Geophys 157:2351–2364

    Google Scholar 

  • Lu C, Harte D, Bebbington M (1999) A linked stress release model for historical Japanese earthquakes: coupling among major seismic regions. Earth Planets Space 51:907–916

    Google Scholar 

  • Mangira O, Vasiliadis G, Papadimitriou E (2017) Application of a linked stress release model in Corinth gulf and Central Ionian Islands (Greece). Acta Geophys. https://doi.org/10.1007/s11600-017-0031-z

    Google Scholar 

  • Mangira O, Console R, Papadimitriou E, Vasiliadis G (2018) A restricted linked stress release model (LSRM) for the Corinth gulf (Greece). Tectonophysics 723:162–171

    Google Scholar 

  • Marzocchi W, Lombardi AM (2008) A double branching model for earthquake occurrence. J Geophys Res 113:317

    Google Scholar 

  • Marzocchi W, Murru M, Lombardi AM, Falcone G, Console R (2012) Daily earthquake forecasts during the May-June 2012 Emilia earthquake sequence (northern Italy). Ann Geophys 55(4):561–567

    Google Scholar 

  • Matthews VM, Ellsworth WL, Reasenberg PA (2002) A Brownian model for recurrent earthquakes. Bull Seism Soc Am 92:2233–2250

    Google Scholar 

  • Michael AJ, Werner MJ (2018) Preface to the focus section on the collaboratory for the study of earthquake predictability (CSEP): new results and future directions. Seismol Res Lett 89(4):1226–1228. https://doi.org/10.1785/0220180161

    Google Scholar 

  • Mignan A (2008) The non-critical precursory accelerating sesmicity theory (NC PAST) and limits of the power-law fit methodology. Tectonophysics. https://doi.org/10.1016/j.tecto.2008.02.010

    Google Scholar 

  • Murru M, Zhuang Z, Console R, Falcone G (2014) Short-term earthquake forecasting experiment before and during the L’Aquila (central Italy) seismic sequence of April 2009. Ann Geophys 57(6):S0649. https://doi.org/10.4401/ag-6583

    Google Scholar 

  • Murru M, Akinci A, Falcone G, Pucci S, Console R, Parsons T (2016) M ≥ 7.0 earthquake rupture forecast and time-dependent probability for the Sea of Marmara region, Turkey. J Geophys Res Solid Earth 1:121. https://doi.org/10.1002/2015jb012595

    Google Scholar 

  • Musson RMW, Tsapanos T, Nakas CT (2002) A power-law function for earthquake interarrival time and magnitude. Bull Seismol Soc Am 92:1783–1794

    Google Scholar 

  • Nishenko SP, Bulland R (1987) A generic recurrence interval distribution for earthquake forecasting. Bull Seism Soc Am 77:1382–1399

    Google Scholar 

  • Ogata Y (1988) Statistical models for earthquake occurrences and residual analysis for point processes. J Am Stat Assoc 83:9–27

    Google Scholar 

  • Ogata Y (1998) Space-time point-process models for earthquake occurrences. Ann Inst Stat Math 50:379–402

    Google Scholar 

  • Ogata Y (2002) Slip-size-dependent renewal processes and Bayesian inferences for uncertainties. J Geophys Res 107:2268. https://doi.org/10.1029/2001JB000668

    Google Scholar 

  • Ogata Y (2005) Detection of anomalous seismicity as a stress change sensor. J Geophys Res 110:B05S06

    Google Scholar 

  • Ogata Y, Zhuang J (2006) Space–time ETAS models and an improved extension. Tectonophysics 413:13–23

    Google Scholar 

  • Omori F (1894) On the aftershocks of earthquakes. J Coll Sci Imp Univ Tokyo 7:111–200

    Google Scholar 

  • Panagiotopoulos DG (1994) Long term earthquake prediction along the seismic zone of Solomon Islands and New Hebrides based on the time and magnitude predictable model. Nat Hazards 11:17–43

    Google Scholar 

  • Panagiotopoulos DG (1995) Long term earthquake prediction in central America and Caribbean Sea based on the time and magnitude predictable model. Bull Seismol Soc Am 85:1190–1201

    Google Scholar 

  • Papadimitriou EE (1993) Long-term earthquake prediction along the Western Coast of South and Central America based on a Time Predictable Model. Pure appl Geophys 140:301–316

    Google Scholar 

  • Papadimitriou EE (1994a) Long term prediction in North Pacific seismic zone based on the time and magnitude predictable model. Nat Hazards 9:303–321

    Google Scholar 

  • Papadimitriou EE (1994b) Long term prediction of large shallow mainshocks along the Tonga-Kermadec-New Zealand seismic zone based on a time and magnitude predictable model. Tectonophysics 235:347–360

    Google Scholar 

  • Papazachos BC (1989) A time-predictable model for earthquake generation in Greece. Bull Seismol Soc Am 79:77–84

    Google Scholar 

  • Papazachos BC (1992) A time and magnitude predictable model for generation of shallow earthquakes in the Aegean area. Pure appl Geophys 138:287–308

    Google Scholar 

  • Papazachos BC, Papaioannou CA (1993) Long-term earthquake prediction in the Aegean area based on a time and magnitude predictable model. Pure appl Geophys 140:593–612

    Google Scholar 

  • Papazachos BC, Papadimitriou EE, Karakaisis GF, Tsapanos TM (1994) An application of the time and magnitude predictable model for the long term prediction of strong shallow earthquakes in Japan area. Bull Seismol Soc Am 84:426–437

    Google Scholar 

  • Papazachos BC, Papadimitriou EE, Karakaisis GF, Panagiotopoulos DG (1997a) Long-term Earthquake Prediction in the Circum-Pacific Convergent Belt. Pure appl Geophys 149:173–217

    Google Scholar 

  • Papazachos BC, Karakaisis GF, Papadimitriou EE, Papaioannou CA (1997b) The regional time and magnitude predictable model and its application to the Alpine-Himalayan belt. Tectonophysics 271:295–323

    Google Scholar 

  • Papazachos BC, Karakaisis GF, Scordilis EM, Papazachos CB (2006) New observational information on the precursory accelerating and decelerating strain energy release. Tectonophysics 423:83–96. https://doi.org/10.1016/j.tecto.2006.03.004

    Google Scholar 

  • Papazachos BC, Karakaisis GF, Papazachos CB, Scordilis EM (2007) Evaluation of the results for an intermediate-term prediction of the 8 January 2006 M w 6.9 Cythera Earthquake in Southwestern Aegean. Bull Seismol Soc Am 97:347–352. https://doi.org/10.1785/0120060075

    Google Scholar 

  • Papazachos BC, Papaioannou CA, Scordilis EM, Papazachos CB, Karakaisis GF (2008) A forward test of the Decelerating–Accelerating Seismic Strain model to western, south and central America. Tectonophysics 454:36–43. https://doi.org/10.1016/j.tecto.2008.03.012

    Google Scholar 

  • Paradisopoulou PM, Papadimitriou EE, Karakostas VG, Taymaz T, Kilias A, Yolsal S (2010) Seismic hazard evaluation in Western Turkey as revealed by stress transfer and time-dependent probability calculations. Pure appl Geophys 167:1013–1048. https://doi.org/10.1007/s00024-010-0085-1

    Google Scholar 

  • Parsons T (2004) Recalculated probability of M ≥ 7.0 earthquakes beneath the Sea of Marmara, Turkey. J Geophys Res 109:B05304. https://doi.org/10.1029/2003jb002667

    Google Scholar 

  • Parsons T (2008) Earthquake recurrence on the south Hayward fault is more consistent with a time dependent, renewal process. Geophys Res Lett 35:L21301. https://doi.org/10.1029/2008GL035887

    Google Scholar 

  • Parsons T, Console R, Falcone G, Murru M, Yamashina K (2012) Comparison of characteristic and Guterberg–Richter models for time-dependent M ≥ 7.9 earthquake probability in the Naknai-Tokai subduction zone, Japan. Geophys J Int 190:1673–1688. https://doi.org/10.1111/j.1365-246X.2012.05595.x

    Google Scholar 

  • Pertsinidou C, Tsaklidis G, Papadimitriou E, Limnios N (2016) Application of hidden semi-Markov models for the seismic hazard assessment of the North and South Aegean Sea, Greece. J Appl Stat 44:1064–1085

    Google Scholar 

  • Polidoro B, Iervolino I, Chioccarelli E, Giorgio M (2013) In: Proceedings of 11th conference on structural safety and reliability ICOSSAR 13, New York, June 16–20

  • Rhoades DA (2007) Application of the EEPAS model to forecasting earthquakes of moderate magnitude in southern California. Seismol Res Lett 78(1):110–115

    Google Scholar 

  • Rhoades DA, Evison FF (2004) Long-range earthquake forecasting with every earthquake a precursor according to scale. Pure appl Geophys 161:47–72

    Google Scholar 

  • Rhoades DA, Evison FF (2005) Test of the EEPAS forecasting model on the Japan earthquake catalogue. Pure appl Geophys 162(6/7):1271–1290

    Google Scholar 

  • Rhoades DA, Evison FF (2006) The EEPAS forecasting model and the probability of moderate-to-large earthquakes in central Japan. Tectonophysics 417(1/2):119–130

    Google Scholar 

  • Rhoades DA, Stirling MW (2012) An earthquake likelihood model based on proximity to mapped faults and cataloged earthquakes. Bull Seismol Soc Am 102(4):1593–1599

    Google Scholar 

  • Rhoades DA, Robinson R, Gerstenberger MC (2011) Long-range predictability in physics-based synthetic earthquake catalogues. Geophys J Int 185:1037–1048

    Google Scholar 

  • Rhoades DA, Christophersen A, Gerstenberger MC, Liukis M, Silva F, Marzocchi W, Werner MJ, Jordan TH (2018) Highlights from the first ten years of the New Zealand earthquake forecast testing center. Seismol Res Lett 89(4):1229–1237. https://doi.org/10.1785/02201800322

    Google Scholar 

  • Rikitake T (1974) Probability of earthquake occurrence as estimated from crustal strain. Tectonophysics 23:299–312

    Google Scholar 

  • Rikitake T (1976) Recurrence of great earthquakes at subduction zones. Tectonophysics 35:335–362

    Google Scholar 

  • Rotondi R, Varini E (2006) Bayesian analysis of marked stress release models for timedependent hazard assessment in the western Gulf of Corinth. Tectonophysics 423:107–113

    Google Scholar 

  • Schneider M, Clements R, Rhoades DA, Schorlemmer D (2014) Likelihood- and residual-based evaluation of medium-term earthquake forecast models for California. Geophys J Int 198(3):1307–1318. https://doi.org/10.1093/gji/ggu178

    Google Scholar 

  • Schorlemmer D, Werner MJ, Marzocchi W, Jordan TH, Ogata Y, Jackson DD, Mak S, Rhoades DA, Gerstenberger MC, Hirata N, Liukis M, Maechling PJ, Strader A, Taroni M, Wiemer S, Zechar JD, Zhuang J (2018) The collaboratory for the study of earthquake predictability: achievements and priorities. Seismol Res Lett 89(4):1305–1313. https://doi.org/10.1785/0220180053

    Google Scholar 

  • Schwartz DP, Coppersmith KJ (1984) Fault behavior and characteristic earthquakes: examples from Wasatch and San Andreas fault zones. J Geophys Res 89:5681–5698

    Google Scholar 

  • Shanker D, Papadimitriou EE (2004) Regional time-predictable modeling in the Hindukush-Pamir-Himalayas region. Tectonophysics 390:129–140

    Google Scholar 

  • Shimazaki K, Nakata T (1980) Time-predictable recurrence model for large earthquakes. Geophys Res Lett 7:279–282

    Google Scholar 

  • Stein RS, Barka AA, Dieterich JH (1997) Progressive failure on the North Anatolian fault since 1939 by earthquake stress triggering. Geophys J Int 128:594–604

    Google Scholar 

  • Sykes LR, Jaume SC (1990) Seismic activity on neighbouring faults as a long-term precursor to large earthquakes in San Francisco Bay area. Nature 348:595–599

    Google Scholar 

  • Utsu T (1961) A statistical study on the occurrence of aftershocks. Geophysics 30:521–605

    Google Scholar 

  • Utsu T, Ogata Y, Matsu’ura S (1995) The centenary of the Omori Formula for a decay law of aftershock activity. J Phys Earth 43:1–33

    Google Scholar 

  • Varini E, Rotondi R (2015) Probability distribution of the waiting time in the stress release model: the Gompertz distribution. Environ Ecol Stat 22:493–511

    Google Scholar 

  • Varini E, Rotondi R, Basili R, Barba S (2016) Stress release models and proxy measures of earthquake size. Application to Italian seismogenic sources. Tectonophysics 682:147–168

    Google Scholar 

  • Vere-Jones D (1978) Earthquake prediction—a statistician’s view. J Phys Earth 26:129–146

    Google Scholar 

  • Vere-Jones D, Deng YL (1988) A point process analysis of historical earthquakes from North China. Earthq Res China 2:165–181

    Google Scholar 

  • Votsi I, Tsaklidis G, Papadimitriou E (2011) Seismic hazard assessment in Central Ionian Islands area based on stress release models. Acta Geophys 59:701–727

    Google Scholar 

  • Votsi I, Limnios N, Tsaklidis G, Papadimitriou E (2013) Hidden markov models revealing the stress field underlying the earthquake generation. Phys A 392:2868–2885

    Google Scholar 

  • Votsi I, Limnios N, Tsaklidis G, Papadimitriou E (2014) Hidden semi-Markov modeling for the estimation of earthquake occurrence rates. Commun Stat Theory Methods 43:1484–1502

    Google Scholar 

  • Zhuang J, Ogata Y, Vere-Jones D (2002) Stochastic declustering of space-time earthquake occurrences. J Am Stat Assoc 97:369–380

    Google Scholar 

  • Zhuang J, Ogata Y, Vere-Jones D (2004) Analyzing earthquake clustering features by using stochastic reconstruction. J Geophys Res B5:301

    Google Scholar 

  • Zhuang J, Chang CP, Ogata Y, Chen YI (2005) A study on the background and clustering seismicity in the Taiwan region by using a point process model. J Geophys Res 110:B05S13

    Google Scholar 

  • Zoller G, Hainzl S, Holschneider M (2008) Recurrent large earthquakes in a fault region: what can be inferred from small and intermediate events? Bull Seismol Soc Am 98:2641–2651. https://doi.org/10.1785/0120080146

    Google Scholar 

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Acknowledgments

The constructive comments of two reviewers are acknowledged for their contribution to the improvement of the paper. Gratitude is also extended to Prof. Zuniga for his editorial assistance and constructive suggestions. The financial support by the European Union and Greece (Partnership Agreement for the Development Framework 2014–2020) for the Project “Development and application of time-dependent stochastic models in selected regions of Greece for assessing the seismic hazard” is gratefully acknowledged, MIS5004504. Geophysics Department Contribution 922.

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Mangira, O., Kourouklas, C., Chorozoglou, D. et al. Modeling the earthquake occurrence with time-dependent processes: a brief review. Acta Geophys. 67, 739–752 (2019). https://doi.org/10.1007/s11600-019-00284-4

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