Earthquake Magnitude Probability and Gamma Distribution

The earthquake magnitude probability distribution is one of the underlying input data for certain earthquake analyses, such as probabilistic seismic hazard analysis. Nowadays, the method proposed by McGuire and Arabasz (1990) is commonly used for obtaining the (simulated) earthquake magnitude probability distributions. However, based on the observed earthquake data in 5 regions (Taiwan, Japan, California, Turkey, and Greece), the model did not fit the observation well. Instead, all of the case studies show that using the newly proposed gamma distribution can improve the simulation significantly compared to the conventional method.

Development of damage probability matrices based on Greek earthquake damage data

A comprehensive study is presented for empirical seismic vulnerability assessment of typical structural types, representative of the building stock of Southern Europe, based on a large set of damage statistics. The observational database was obtained from post-earthquake surveys carried out in the area struck by the September 7, 1999 Athens earthquake. After analysis of the collected observational data, a unified damage database has been created which comprises 180,945 damaged buildings from/after the near-field area of the earthquake. The damaged buildings are classified in specific structural types, according to the materials, seismic codes and construction techniques in Southern Europe. The seismic demand is described in terms of both the regional macroseismic intensity and the ratio αg/ao, where αg is the maximum peak ground acceleration （PGA） of the earthquake event and ao is the unique value PGA that characterizes each municipality shown on the Greek hazard map. The relative and cumulative frequencies of the different damage states for each structural type and each intensity level are computed in terms of damage ratio. Damage probability matrices （DPMs） and vulnerability curves are obtained for specific structural types. A comparison analysis is fulfilled between the produced and the existing vulnerability models.

Application of logistic regression model for hazard assessment of landslides caused by the 2012 Yiliang Ms 5.7 earthquake in Yunnan Province,China

Accurate assessment of seismic landslides hazard is a prerequisite and foundation for postdisaster relief of earthquakes.An Ms 5.7 earthquake occurring on September 7,2012,in Yiliang County,Yunnan Province,China,triggered hundreds of landslides.To explore the characteristics of coseismic landslides caused by this moderate-strong earthquake and their significance in predicting seismic landslides regionally,this study uses an artificial visual interpretation method based on a planet image with 5-m resolution to obtain the information of the coseismic landslides and establishes a coseismic landslide database containing data on 232 landslides.Nine influencing factors of landslides were selected for this study:elevation,relative elevation,slope angle,aspect,slope position,distance to river system,distance to faults,strata,and peak ground acceleration.The real probability of coseismic landslide occurrence is calculated by combining the Bayesian probability and logistic regression model.Based on the coseismic landslides,the probabilities of landslide occurrence under different peak ground acceleration are predicted using a logistic regression model.Finally,the model established in this paper is used to calculate the landslide probability of the Ludian Ms 6.5 earthquake that occurred in August 2014,78.9 km away from the macro-epicenter of the Yiliang earthquake.The probability is verified by the real coseismic landslides of this earthquake,which confirms the reliability of the method presented in this paper.This study proves that the model established according to the seismic landslides triggered by one earthquake has a good effect on the seismic landslides hazard assessment of similar magnitude,and can provide a reference for seismic landslides prediction of moderate-strong earthquakes in this region.

Probability-consistent earthquakes and probability-consistent conservative earthquakes

It is pointed out in this paper that the concept of scenario earthquake, expectant earthquake or proposed earthquake suggested by Kameda Nojima (1988) is not probability consistent due to unfit understanding for the aseismic design standard of probabilistic method. The corresponding concept proposed by QI FENG LUO meets the meaning of probability consistent, but it is still in a meaning of average so the result is not good enough. On the basis of above analysis, a concept of probability consistent conservative earthquakes is suggested. And a new method selecting aseismic objective earthquake with physical meaning is proposed on the basis of probabilistic method. After seismic hazard is analysed by certain control parameters, such as peak acceleration, we can determine the aseismic standard according to certain probabilistic level. Based on the attenuation law and the potential sources, we can find out some earthquakes or their combinations of magnitudes and distances. Such earthquakes or combinations are probability consistent for this control parameter. Based on above parameter, we suggest considering the destructive effects of other parameters (such as response spectrum), and selecting conservative earthquakes to replace the average earthquake and meet the requirements of aseismic design better.

Spatial and temporal synthesized probability gain for middle and long-term earthquake forecast and its preliminary application

The principle of middle and long-term earthquake forecast model of spatial and temporal synthesized probability gain and the evaluation of forecast efficiency (R-values) of various forecast methods are introduced in this paper. The R-value method, developed by Xu (1989), is further developed here, and can be applied to more complicated cases. Probability gains in spatial and/or temporal domains and the R-values for different forecast methods are estimated in North China. The synthesized probability gain is then estimated as an example.

Earthquake Probability of the“Seismic Gap”on the Longmenshan Fault

Using the layered viscoelastic medium model,this paper calculated the coulomb stress loading effect on the Lushan epicenter generated by the Wenchuan earthquake.Then combined with the rate-state friction law proposed by Dieterich J.(1994),we obtain the probability of an0 earthquake occurring in the vicinity of Lushan.The results show that the probability of0 earthquake of the Lushan region in 2013 is up to18%,indicating that the stress disturbance caused by the Wenchuan earthquake accelerated the Lushan earthquake.This paper also calculates the coulomb stress accumulation on the"seismic gap"generated by the two earthquakes of Wenchuan and Lushan,and combined with the background seismicity,gives the6.0 earthquake probability of the"seismic gap".Although there may be a certain error in the results because of the Dayi earthquake,selection of the medium model parameters and background seismicity,the seismic probability of the"seismic gap"is increasing.Thus,we think destructive earthquakes are still likely to occur in the"seismic gap".

Probability forecast of earthquake magnitude in Chinese mainland before A．D． 2005

A probability forecast method of earthquake magnitude, based on the earthquake frequency magnitude relation and the model of Bernoulli′s random independent trial, is applied to the earthquake risk assessment of seismic zones in China's Mainland before A.D.2005 in the paper. The forecasting results indicate that the probabilities of earthquake occurrence with magnitude 5 in seismic zones before 2005 are estimated to be over 0.7 in common and 0.8 in most zones; and from 0.5 to 0.7 with M =6; the maximum probability of earthquake occurrence with magnitude 7 is estimated at 0.858, which is also expected in Shanxi seismic zone. In west China's Mainland, earthquakes with magnitude 6 are expected to occur in most seismic zones with high probability (over 0.9 in general) ; the relatively high probabilities of earthquake occurrence (more than 0.7) with magnitude 7 are expected in the seismic zones surrounding the Qinghai Tibet plateau and south Tianshan seismic zone. A discussion about the result confidence and the relationship between the estimated probability and the possible annual rate of earthquake occurrence is made in the last part of the paper.

Study on the Recurrence Probability of Strong Earthquakes of Faults

Based on the physical model of Brownian passage time,the probabilities of recurrence of strong earthquakes on the major active faults in China are calculated in different predictive time spans,based mainly on the analysis of the earthquake preparation process before a strong earthquake occurs. Furthermore,the seismic risks on active faults are studied. The results show that the earthquake probabilities on the Xianshuihe fault,the Altyn Tagh fault,the east Kunlun fault and Xiaojiang fault are significantly greater than other faults in the Chinese mainland,which indicates that the level of stress accumulation on these faults are higher than on other faults. Therefore,these faults may have a seismic risk for strong earthquake in future.

Study of Nonlinear Earthquake Flow Functions and Their Application to the Space Increased Probability of Strong Earthquake (SIP)

The definition and abnormality discriminatory criteria of earthquake flow function are introduced in this paper based on the algorithm of Space Increased Probability (SIP). Nine earthquake flow functions were defined by the method. The retrospect test that applied the SIP algorithm with the nonlinear earthquake flow function to 7 earthquakes, which occurred from 1975 to 1989 in Eastern China, with a magnitude of 6 or greater depicted that 6 of the 7 strong earthquakes (86%) were located in the SIP areas, and the SIP covers about 32% of the total research time-space domain. These suggest that the R-value, an effective scale for earthquake forecast, is 54% and may imply that the nonlinear earthquake flow function introduced in this paper can be applied to the intermediate-term earthquake forecast research.

Application of Dangerous Probability Function in Risk Estimation of Surface Rupture Earthquake: Taking the Lingwu Fault in Ningxia Region as an Example

Based on the fitting on paleoearthquake data of intra-plate regions in the northern part of China and giving a statistical model of time interdependence, the potential damage earthquakes in a definite future period and characteristics of present shocks along the Lingwu fault have been analyzed by using dangerous probability function and some new data concerned. We have inferred that the fault has entered a period that earthquakes will probably occur. There exists a potential danger that a strong earthquake with M\-S7.0～7.5 will occur in 10～100a.

Discussion on the Relationship between “Anti-great Earthquakes” and Ground Motion with a Low Probability of Exceedance

In this paper we discuss the differences and relationship between"great earthquakes",rare ground motion,and very rare ground motion.Taking the Beichuan-Yingxiu potential seismic source zone in Longmenshan seismic belt as an example,we revealed the relationship between the effects of"great earthquakes"and rare ground and very rare ground motion.After pointing out scientific and technical problems in the current seismic fortification system,we suggest that very rare ground motion should be considered if we want to deduce the potential hazard of great earthquakes in the future.

Distribution of empirical recurrence intervals for segment-rupturing earthquakes onactive faults of the Chinese mainland

For the two main recurrence behaviors of segment-rupturing earthquakes on active faults of the Chinese mainland,this paper establishes corresponding empirical distributions forearthquake recurrence interval. The results show that, for the time-predictable recurrence, the normalized recurrence interval, T/Tt, obeys very well the lognormal distributions: LN (μ1=0.00, σ21 =0. 152), where, T is an observed recurrence interval, and Tt is the average recurrence interval that is correlative with the size of the preceding event. For the quasi-periodic recurrence, the normalized recurrence interval, T/T, follows the lognormal distribution : LN(μq=0.00, σ2q=0.242), where, T is the median of recurrence intervals for various cycles. A statistical test suggests that, there is no significant difference between the latter distribution, built by this paper, and the recurrence interval distribution for the characteristic earthquakes of the Circum-Pacific Plate boundaries (NB model). Accordingly, this paper combines these two distributions into one and obtains a more stable lognormal distribution :LN (μ = 0.00, σ2 = 0.222), for the quasi-periodic recurrence interval.

Study on the characteristics of earthquake's impact on cities

Firstly, the impact of historical earthquakes on 34 China province-level capital cities is evaluated by using historical earthquake catalog. The distribution of affected intensity shows, about 53% of cities have even not been affected by earthquake intensity VI, and 44% of cities have been hit by earthquake intensity VII to IX. For most of the cities, occurrence frequency of affected intensity VI is usually higher than that of affected intensity larger than VI, and the value of affected intensity with maximal occurrence frequency may be very different among cities. So both the maximal affected intensity and the affected intensity with maximal occurrence frequency should be taken into account when the prevention seismic intensity needs to be determined. Secondly, considering the incompleteness of records of historical earthquakes, a method of earthquake catalog computer simulation is introduced to study the features of affected intensity of big cities. 69 county-level cities of Fujian Province are selected to be statistical objects. The statistical result shows, for different risk levels the seismic intensity changes greatly among cities, the seismic intensity of 2% probability of exceedance in 50 years can be regarded as the characteristic affected intensity of city, and can be the basis of determining the city special earthquake prevention level and a proper indicator of future earthquakes impact on cities.

Problem and Improvement of R-values Applied to Assessment of Earthquake Forecast

The researches on the assessment of earthquake forecast are reviewed, then the R-value assessment is further developed theoretically in the paper. The results include the arithmetic of the R-values of earthquake occurrence under the condition that 'anomaly' occurred or no 'anomaly' occurred respectively, and the relation between the values. The distribution of Rvalue of a forecast method, corresponding to multi-status anomalies being independent each other, is also developed in the paper. The appropriate methods to estimate the R-values and extrapolate the occurrence probability of future earthquakes are also given in the paper.

Study on Medium- and Long-term Strong Earthquake Risk Along the Zhangjiakou-Penglai Fault Zone

The Zhangjiakou-Penglai fault zone lies in the northern part of North China Plain and extends along the Zhangjiakou-Huailai-Sanhe-Tianjin-Bohai Sea-Penglai-Yantai-North Huanghai Sea line, it is about 900 km long and some 250-km wide in a northwest direction. The 1679 Sanhe-Pinggu M 8.0 and the 1976 Tangshan M7.8 earthquakes occurred in the fault zone. In this paper an analysis of Gutenberg- Richter’s empirical relation and time process of historic and recent earthquakes along the eastern and western segments of the fault zone separated by the 117°line indicates that they obey a Poison process and, hence, a calculation from it yields a cumulative probability of strong earthquake occurrence along the two segments before 2010, i. e. the probability of M6.0 earthquake occurrence is 0.80 along the eastern segment and the probability of M7. 0 earthquake occurrence is 0.76 along the western segment of the fault zone.

Study on Integrated Recurrence Behaviors of Strong Earthquakes Along Entire Active Fault Zones in the Sichuan-Yunnan Region, China

Based on historical earthquake data, we use statistical methods to study integrated recurrence behaviors of strong earthquakes along 7 selected active fault zones in the Sichuan-Yunnan region. The results show that recurrences of strong earthquakes in the 7 fault zones display near-random, random and clustering behaviors. The recurrence processes are never quasi-periodic, and are neither strength-time nor time-strength dependent. The more independent segments for strong earthquake rupturing a fault zone has, the more complicated the corresponding recurrence process is. And relatively active periods and quiescent periods for earthquake activity occur alternatively. Within the active periods, the distribution of recurrence time intervals between earthquakes has relatively large discretion, and can be modelled well by a Weibull distribution. The time distribution of the quiescent periods has relatively small discretion, and can be approximately described by some distributions as the normal. Both the durations of the active periods and the numbers of strong earthquakes within the active periods vary obviously cycle by cycle, leading to the relatively active periods having never repeated quasi-periodically. Therefore, the probabilistic assessment for middle- and long-term seismic hazard for entireties of active fault zones based on data of historical strong earthquakes on the fault zones still faces difficulty.

Estimating the Degree of Earthquake Risk from Fault Characteristics

A theoretical model considering the relationship between fault characteristics and tectonic stress is proposed to quantify earthquake risk degree. The model is applied in practice to the fault along the southern margin of Weihe basin in Shaanxi Province, Northwestern China and fitted well with reality.

A Review on the Research Progress in Operational Earthquake Forecasting(OEF)in the World

In this paper,the research progress of the Operational Earthquake Forecasting( OEF) is introduced from the major areas of concern,the concept of probability gain,hybrid model development,and the application to earthquake disaster reduction. Due to the development of OEF based on the global "Collaboratory for the Study of Earthquake Predictability( CSEP) " plan,it provides a significant technical foundation for earthquake forecast modeling and a practical foundation for solving the actual problems in earthquake preparedness and disaster mitigation. Therefore, related research and technical ideas provide inspirational and referential significance for earthquake forecasting/prediction.

A Preliminary Study on the Probabilistic Estimation of Deaths from Future Earthquakes in North China

During the period from 1800 to 1989,the degree of fatalities(?from earthquakes in North China(Lat.34.0°-42.0°N,Long.107.5°-125.0°E)varied exponentially with the frequency of earthquake events(N),namely:N=37.71 exp(-0.72?(E-logD,D:deaths).For the periods from 1988 to 1998 and from 1999 to 2009,the probabilities for earthquakes to cause one thousand or more deaths in North China are estimated to be 0.37 and 0.50,respectively,by using the Gumbel’s extreme value theory.

Recurrence Behaviors of Earthquakes along the Kefallinia Transform Fault, Ionian Sea, Greece

We examined the whole strong earthquake recurrence behaviors of two fault zones along the Kefallinia Transform, Ionian Sea, Greece, using seismological data and statistical methods. Our data include 29 events with M 〉 5.5 for the period 1636 - 2003. We found different recurrence behaviors for the Kefallinia Fault Zone （clustering and time-predictable recurrence behaviors） and the Letkada Fault Zone （near random and non-slip-predictable or non-time-predictable recurrence nature）. The different modes may be attributed to： （a） segment interaction along-strike （Kefallinia） by static triggering and （b） the influence of fault systems to the north and east on the recurrence on Lefkada. Within the active periods, earthquake recurrence intervals are distributed in a more dispersed fashion, and can be fitted well by a Weibull distribution. In contrast, the distribution of the quiet periods is relatively less dispersed and difficult to describe by suitable probability functions.