最大熵原理与地震频度-震级关系
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摘要
地震是一种随机事件 ,它的发生具有极大的不确定性 ,因而可以用熵来进行描述。地震以最无序的方式在各地发生 ,意味着地震熵达到了极大值。古登堡 (Gutenberg)和里克特 (Richter)根据资料和经验得出的地震频度 -震级关系式实际上是在给定的约束条件下 ,当地震熵取极大值时得到的一种负指数分布。文中从最大熵原理得出了同一形式的地震频度 -震级关系 ,使它的来源从理论上得到了解释
Entropy is a state function. Entropy increasing principle shows that under isolated or adiabatic condition the process of a system developed spontaneously from non equilibrium state to equilibrium state is a process of entropy increasing. The equilibrium state corresponds to the maximum entropy. In equilibrium state, the state of the system is most chaotic and disorder. Earthquake is a random event, the occurrence of which possesses extremely great uncertainty, and hence can be expressed by entropy. Earthquake occurs disorderly in different areas, implying that the seismic entropy has reached a maximum value. Therefore, magnitude distribution of earthquakes in one region for a certain time period can be expressed by the principle of maximum entropy. Assuming that M 0 is starting magnitude and AM-U is average magnitude, through the deduction we can get lg n= lg NAM-U-M 0+M 0AM-U-M 0-1AM-U-M 0M, where n is differential frequency, N is total number of earthquakes, and M is magnitude. The magnitude frequency relation proposed by Gutenberg and Richter according to seismic data and experience is expressed as: lg n=a-bM. Comparing the two equations gives a= lg NAM-U-M 0+M 0AM-U-M 0, b=1AM-U-M 0. Obviously, the Gutenberg Richter magnitude frequency relation is essentially a negative exponent distribution obtained by taking the maximum value of seismic entropy under a given constrained conditions. In this way the cause of magnitude frequency relation is theoretically explained.
Entropy is a state function. Entropy increasing principle shows that under isolated or adiabatic condition the process of a system developed spontaneously from non equilibrium state to equilibrium state is a process of entropy increasing. The equilibrium state corresponds to the maximum entropy. In equilibrium state, the state of the system is most chaotic and disorder. Earthquake is a random event, the occurrence of which possesses extremely great uncertainty, and hence can be expressed by entropy. Earthquake occurs disorderly in different areas, implying that the seismic entropy has reached a maximum value. Therefore, magnitude distribution of earthquakes in one region for a certain time period can be expressed by the principle of maximum entropy. Assuming that M 0 is starting magnitude and AM-U is average magnitude, through the deduction we can get lg n= lg NAM-U-M 0+M 0AM-U-M 0-1AM-U-M 0M, where n is differential frequency, N is total number of earthquakes, and M is magnitude. The magnitude frequency relation proposed by Gutenberg and Richter according to seismic data and experience is expressed as: lg n=a-bM. Comparing the two equations gives a= lg NAM-U-M 0+M 0AM-U-M 0, b=1AM-U-M 0. Obviously, the Gutenberg Richter magnitude frequency relation is essentially a negative exponent distribution obtained by taking the maximum value of seismic entropy under a given constrained conditions. In this way the cause of magnitude frequency relation is theoretically explained.
引文
冯利华.1998.物元分析在地震预报中的应用试验〔J〕.地震学报,20(6):635—639.
FENGLi hua.1998.Theapplicationtestofmatterelementanalysisinearthquakeforecast〔J〕.ActaSeismologicaSinica,20(6):635—639(inChinese).
李全林,于渌,郝柏林,等.1979.地震频度-震级关系的时空扫描〔M〕.北京:地震出版社.1—22.
LIQuan lin,YULu,HAOBai lin,etal.1979.Time spaceScanningofSeismicFrequencyMagnitudeRelation〔M〕.SeismologicalPress,Beijing.1—22(inChinese).
宁夏回族自治区地震局.1982.宁夏地震目录〔M〕.银川:宁夏人民出版社.172—274.
SeismologicalBureauofNingxiaHuiAutonomousRegion.1982.EarthquakeCatalogueofNingxia〔M〕.People’sPublishingHouseofNingxia,Yinchuan.172—274(inChinese).
王彬.1988.谈熵〔A〕.见:新疆维吾尔自治区科学技术协会编.熵与交叉科学.北京:气象出版社.19—22.
WANGBin.1988.TalkingaboutEntropy〔A〕.In:CommitteeofScienceandTechnologyofXinjiangUygurAu tonomousRegion(ed).EntropyandCrossScience.MeteorologicalPress,Beijing.19—22(inChinese).张学文,马力.1992.
熵气象学〔M〕.北京:气象出版社.114—125.
ZHANGXue wen,MALi.1992.EntropyMeteorology〔M〕.MeteorologicalPress,Beijing.114—125(inChi nese).
SilviuG .1977.InformationTheorywithApplication〔M〕.McGRAW HiLL .CO .293—301.
FENGLi hua.1998.Theapplicationtestofmatterelementanalysisinearthquakeforecast〔J〕.ActaSeismologicaSinica,20(6):635—639(inChinese).
李全林,于渌,郝柏林,等.1979.地震频度-震级关系的时空扫描〔M〕.北京:地震出版社.1—22.
LIQuan lin,YULu,HAOBai lin,etal.1979.Time spaceScanningofSeismicFrequencyMagnitudeRelation〔M〕.SeismologicalPress,Beijing.1—22(inChinese).
宁夏回族自治区地震局.1982.宁夏地震目录〔M〕.银川:宁夏人民出版社.172—274.
SeismologicalBureauofNingxiaHuiAutonomousRegion.1982.EarthquakeCatalogueofNingxia〔M〕.People’sPublishingHouseofNingxia,Yinchuan.172—274(inChinese).
王彬.1988.谈熵〔A〕.见:新疆维吾尔自治区科学技术协会编.熵与交叉科学.北京:气象出版社.19—22.
WANGBin.1988.TalkingaboutEntropy〔A〕.In:CommitteeofScienceandTechnologyofXinjiangUygurAu tonomousRegion(ed).EntropyandCrossScience.MeteorologicalPress,Beijing.19—22(inChinese).张学文,马力.1992.
熵气象学〔M〕.北京:气象出版社.114—125.
ZHANGXue wen,MALi.1992.EntropyMeteorology〔M〕.MeteorologicalPress,Beijing.114—125(inChi nese).
SilviuG .1977.InformationTheorywithApplication〔M〕.McGRAW HiLL .CO .293—301.
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