地震孕育非线性动力学过程研究的“扩展概率法”
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摘要
本文认为，小破裂可以扩展成大破裂，“扩展”行为是随机发生的，任何一个大破裂都可以视为小破裂随机“扩展”的一次“实现”．研究小地震破裂“扩展”成大地震破裂的概率特征，是合理研究地震孕育动力学过程的一个有效方法．对于理想的分形介质，给定任何一组成等比数列增大的破裂尺度Ｓ０，Ｓ１，…，Ｓｎ，存在一个不变的“扩展”概率Ｐ，使得破裂由Ｓｉ“扩展”为Ｓｉ＋１的概率为常数．如果假设地壳介质是理想分形介质，则可以通过小震统计，以“扩展”概率为“桥梁”，预测大震发生的概率．如果假设地壳介质不是理想分形介质，则研究Ｐ值随时间、空间、震级等情况的变化规律，有助于对地震孕育的非线性动力学过程产生更本质的认识．总之，复杂的地震孕育动力学过程可以简化为“扩展”概率Ｐ的特征和变化规律的研究．
It is believed in this paper that the small ruptures can be extended to large ruptures. The extensions occur stochasticaly. Any large ruptures can be treated as the realization of the extension occurrences from small ruptures. It is assumed that,a small earthquake is a small rupture of the crust,and a large earthquake is a large rupture of the crust,any large ruptures are the further extension of small ruptures. The condition probability from a smaller rupture with the magnitude of M to a larger rupture with the magnitude of M+ΔM is defined to be the “the extending probability from M to M+ΔM”, which is noted by P(M+ΔM|M).P(M+ΔM|M) has nothing to do with M only if the crust is ideal fractal medium in three dimensions. Because the real crust is not “ideal fractal medium in three dimensions”,the value of P(M+ΔM|M) changes with the next factors,which include: M (the magnitude),the distribution of faults,the environment stress distribution,and the characteristics of the crust. The relationships between the small earthquakes and the large earthquakes can be indicated by ∏ni=1 P(M+iΔM+ΔM|M+iΔM). This is helpful for the prediction of large earthquakes by means of small earthquakes. In the end,we propose two earthquake prediction methods,which are the linear method and the nonlinear method. The two methods are also used to predict the earthquake risk in the region of Xian Shui River Fault Zone.
It is believed in this paper that the small ruptures can be extended to large ruptures. The extensions occur stochasticaly. Any large ruptures can be treated as the realization of the extension occurrences from small ruptures. It is assumed that,a small earthquake is a small rupture of the crust,and a large earthquake is a large rupture of the crust,any large ruptures are the further extension of small ruptures. The condition probability from a smaller rupture with the magnitude of M to a larger rupture with the magnitude of M+ΔM is defined to be the “the extending probability from M to M+ΔM”, which is noted by P(M+ΔM|M).P(M+ΔM|M) has nothing to do with M only if the crust is ideal fractal medium in three dimensions. Because the real crust is not “ideal fractal medium in three dimensions”,the value of P(M+ΔM|M) changes with the next factors,which include: M (the magnitude),the distribution of faults,the environment stress distribution,and the characteristics of the crust. The relationships between the small earthquakes and the large earthquakes can be indicated by ∏ni=1 P(M+iΔM+ΔM|M+iΔM). This is helpful for the prediction of large earthquakes by means of small earthquakes. In the end,we propose two earthquake prediction methods,which are the linear method and the nonlinear method. The two methods are also used to predict the earthquake risk in the region of Xian Shui River Fault Zone.
引文
〔1〕Gabrielov，A．M．，Keilis－Borok，V．I．，Levshina，T．A．andShaposhnikov，V．A．，1986，Blockmodelfordynamicsofthelithosphere．Comput．Seismol．，No20：168－178．〔2〕Shnirman，M．G．，1987．Dynamichierarchicalmodelofdefectdevelopment．In：ComputationModelingandAnalysisofGeophysicalProceses．Comput．Seismol．，No20：87－95（inRusian）．〔3〕S．A．Molchanov，V．F．Pisarenko，andA．Ya．Reznikova，1986，Onpercolationapproachinfailuretheroy．In：R．V．Gamkrelidze（Editor），ItogiNaukiITechniki，ser．Teorijaverojtanostei，Mat．Statistica．Teor．KibemeticsVINITI．Moscow，pp53－130．〔4〕G．Costa，G．F．PaznaandI．M．Rotwain，Stabilityofpremonitoryseismicitypaternandintermediate－termearthquakepredictionincentralItaly，PAGEOPH＞Vol145，No2（1995）．〔5〕O．V．Novikova，I．A．Vorobieva，D．Enescu，M．Radulian，I．KuznetzovandG．F．Panza，PredictionofthestrongearthquakesinVrancea，RomaniausingtheCNalgorithm，PAGEOPH，Vol147，No1（1996）．〔6〕GiovanniCosta，IvankaOrozova－Stanishkova，GiulianoFrancescoPanzaandIrinaM．Rotwain，SeismotectonicmodelsandCNalgorithm：thecaseofItaly．〔7〕Keilis－Borok，Intermediate－termEarthquakesPrediction：Models，Algorithms，WorldwideTests，SecondWorkshoponNon－linearDynamicsandEarthquakePrediction，TranslatedbyChenYun，SeismologialPres，Beijing，China，inChinese，1991．〔8〕Keilis－Borok，Chaosandself－organizationinthelithosphereandearthquakeprediction，19thWorkshoponIUGG（1987），translatesbyChenYuan，SeismologicalPres，Beijing，China，inChinese，1989．〔9〕A．M．Garbrielor，V．I．Keilis－Borok，T．A．Levshina，V．A．Shaphosbikov，Blockmodelofdynamicofthelithosphere，WorkshopGlobalGeophysicalInformaticsApplicationstoResearchinEarthquakePredictionsandReducationofSeismicRisk，1988，TranslatedbyZhuLiYuan，SeismologicalPres，Beijing，China，inChinese，1989．〔10〕PerBakandChaoTang，Earthquakeasaself－organizedCriticalPhynomenon，JournalofGeophysicalResearch，Vol34，No．Bil，pp15，635－637，1989．〔11〕KeisukeITOandMitsuhiroMatsuzaki，Earthquakesasself－organizedcriticalphenomena，JournalofGeophysicalResearch，5，No．B5，pp6853－6860，May，10，1990．〔12〕KanChenandPerBak，Self－OrganizedCriticalityinaCrack－Propagationmodelofearthquakes，PhysicalReviewA，Third143，No2，15JAN．，1991．〔13〕J．M．CarlsonandJ．S．Langer，Mechanicalmodelofanearthquakefault，PhysicalReview．40，No11，Dec．，1989．〔14〕A．SometoireandD．Sornete，Self－organizedcriticalityandearthquakes，Europhys．Let．，9（3），pp197－202，1989．〔15〕Huang，J．andD．L．Turcote，1990a，Areearthquakesanexampleofdeterministic？Geophys．Res．Let，17，223－226．〔16〕Rundle，J．B．，1988（a），AphysicalModelforearthquakes，1，FluctuationandInteraction，J．Geophys，Res．，93，6237－6254．〔17〕Rundle，J．B．，1988（b），Aphysicalmodelforearthquakes，2，ApplicationtoSouthernCalifornia，J．Geophys．Res．，93，6255－6254．〔18〕Rundle，J．B．，1989，AphysicalModelforearthquakes，3，ThermodynamicalApproachanditsrelationtonondassicaltheoriesofnucleation，J．Geophys．Res．，94，2839－2855．〔19〕Ito，K．，Periodicityandchaosingreatearthquake，Geophys．Res．，85，B3，1399－1408，1980．〔20〕Julian，B．R．，AreearthquakesChaotic？，Nature，345，481－482，1990．〔21〕Andrews，D．J．，Astochasticfaultmodel，1．Staticcase，J．G．R．，1980，85（B7）．〔22〕HuangJie＆Turcote，D．L．，EvidenceforchaoticfaultinteractionsintheseismicityoftheSaenAndreasfaultandNankaiFrough，Nature，348（6298），1990b．〔23〕Keilis－Borok，V．I．，Kuznetsov，I．V．，Panza，G．F．，Rotwain，I．M．，andCosta，G．（1990b），Onintermaediate－termearthquakepredictioninCentralItaly，PureAppl．Geophys．134，79－92．〔24〕DelaVedova，B．，Marson，I．，Panza，G．F．，andSuhadolc，P．（1991），UppermantlepropertoesoftheTuscan－Tyrhenianarea：AkeyforunderstandingtheresenttectonicevolutionoftheItalianregion，Tectonophys．195，311－318．〔25〕Keilis－Borok，V．I．，andRotwain，I．M．（1990），Diagnosisoftimeofincreasedprobabilityofstrongearthquakesindiferentregionsoftheworld：AlgorithmCN，Phys．EarthPlanet．Int．61，57－72．〔26〕Wang，SH．B．，Bai，G．CH．，Wang，G．Y．，1993．Themodelofdoubleboundsofstochasticstressinseismicriskanalysisoffaults．ACTASEISMOLOGICASINICA，6，4，1005－1012．〔27〕Wang，Sh．B．，Yao，Zh．X．，1997，theearthquakepredictionmethodbymeansof“extendingprobability”method，expectedtobeshownin“theFourthWorkshoponNoninearDynamicandPrediction”．〔28〕Wang，Sh．B．，Yao，Zh．X．，1997，thespace－timecohenrenceofearthquakesinastrikefaultzone，expectedtobeshownin“theFourthWorkshoponNonlinearDynamicandPrediction”．
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