Comparative study on the deviation characteristics of post-earthquakeintensity evaluation based on two intensity attenuation relationship models

Jing Ren ,Zhiqing Li ,Shuitng Hung ,Zhuntio Tn ,Yhui Chen ,Qi Yo ,Weiyu M

a China Earthquake Networks Center,Beijing,100045,China

b Earthquake Agency of Xinjiang Uygur Autonomous Region,Urumqi,830011,China

c Institute of Earthquake Forecasting,China Earthquake Administration,Beijing,100036,China

Keywords:Seismic intensity attenuation Deviation characteristics Disaster assessment

ABSTRACT We collect the isoseismal data of 488 earthquakes in western China and 182 earthquakes in eastern China after 1900.The least square method is used to establish two models of the seismic intensity attenuation relationship partitions in China,based on the major and minor axis ellipse models,and the area and the major axis radius,respectively.The two models are applied to the calculation of the intensity circle of the earthquake events with a magnitude MS ≥5.0 from 2008 to 2019,and the actual intensity is compared with the model intensity value as an indicator to verify the consistency between the actual intensity and the value from the empirical statistical model.Three real earthquake results are selected to calculate the major and minor axis and area of the ellipse using the two intensity attenuation relationship models.After comparison,we summarize the deviation characteristics of the intensity value,and put forward corresponding improvement suggestions.

1.Introduction

The rapid assessment of an earthquake disaster includes the information of the earthquake disaster area,casualties,and economic losses.In the earthquake emergency command system,the rapid assessment is also an important scientific basis for decision-making recommendations(Yang et al.,2005).Therefore,improving the accuracy of the rapid assessment results is vital for enhancing the government's response capabilities,especially for post-earthquake response and initial emergency command decisions.

In a rapid earthquake disaster assessment,intensity assessment is the important task.Currently,the commonly used method of rapid assessment of seismic intensity takes advantage of historical seismic intensity attenuation relationship and the main output information of earthquakes,such as ground motion observation records,aftershock distribution,seismic fault distribution,and focal mechanism solutions,to quickly evaluate and calculate the seismic intensity distribution and influence range in a few hours after the earthquake (Xu et al.,2012).It can be seen that the seismic intensity attenuation relationship is the basis and premise of intensity evaluation.The seismic intensity attenuation relationship is a statistical law describing the variation of intensity with magnitude(or the intensity of the meizoseismal area)and distance.The main factors affecting the intensity attenuation relationship include earthquake magnitude,focal depth,focal mechanism,seismic wave propagation medium and path,local site conditions,etc.(Zhang,2015).

At present,the commonly used intensity attenuation relationship model in China is the elliptical intensity attenuation relationship model.China has a vast territory with a number of seismic stations which have recorded massive historical seismic data.Many researchers have studied the attenuation relationship of seismic intensity in different regions with various geological settings,and obtained statistical relationships in each study area.For example,Wang et al.,2000 divided Chinese mainland into east and west regions by 105°E to determine the earthquake intensity attenuation relationship(Wang et al.,2000);Cui et al.,2010 used 96 isoseismal data from 48 moderate-strong earthquake events in South China in the 20th Century to fit earthquake intensity attenuation relationship,Wang et al.(2008) collected the intensity distribution map of 25 earthquakes in the moderate-strong earthquake regions of Central and South China from 1991 to 2006,and then coordinated with the seismic intensity distribution map of 9 earthquakes from 1918 to 1989 to refit the earthquake intensity attenuation relationship in Central and South China.

In addition to the elliptical intensity attenuation relationship,Lu et al.,2013 derived the“intensity attenuation relationship”based on the isoseismal area and the major axis radius according to the deduction equation.In their study,38 earthquakes with a magnitude 6.0 or higher were selected to conduct the fitting investigation.On this basis,this paper intends to use data from the same data source in the same region,to analyze the regression of the two aforementioned models,and study the deviation characteristics and the general trends of these two methods,thus exploring the general rule of earthquake intensity evaluation using these two models.

2.Selection of research area and research materials

2.1.Data of earthquake cases selected in the study

The data are mainly obtained from"The Catalogue of Modern China Earthquakes(1912-1990)" (Earthquake Disaster Prevention Department of China Earthquake Administration,1999),"China Earthquake Disaster Loss Information Collection (1966-1989)" (Earthquake Disaster Emergency Rescue Department of China Earthquake Administration,2015),"China Earthquake Cases 1966-2007",(Monitoring and Prediction Department of China Earthquake Administration,2001),"Compilation of Earthquake Disaster Losses in the Chinese Mainland (2001-2005)"(Earthquake Disaster Emergency Rescue Department of China Earthquake Administration,2010),"Compilation of Earthquake Disaster Losses in the Chinese Mainland (2006-2010)" (Earthquake Disaster Emergency Rescue Department of China Earthquake Administration,2015),the website of China Earthquake Administration and related documents,etc.

The selection of earthquake intensity data is based on the following principles:①Reliable source of earthquake case data ②The collected earthquake cases have clear isoseismal distribution maps ③The isoseismal maps of the seismic event must have sufficient reference points for accurate geographic coordinate registration and digitization.In order to avoid the correlation between intensityI(intensity is usually represented byI)and magnitudeMS,these two parameters are independently determined.Based on the above principles,488 earthquakes in western China and 182 earthquakes in eastern China were selected,all of which had a magnitude ofMS4.0 or higher since 1900,as shown in Table 1.

Table 1 Earthquake cases in China since 1900 selected in this study.

Firstly,following the practice of China's seismic intensity zonation map,we roughly divided China into eastern and western regions by 105°E longitude(Wang et al.,2000),the latter of which has been further divided into two sub-regions:southwest and northwest.The southwest region refers to the vast hinterland of southwestern China,including the southeast of the Qinghai-Tibet Plateau,the Sichuan Basin,and theYunnan-Guizhou Plateau.The research area includes Sichuan,Guizhou,Yunnan,Tibet,Chongqing,and Guangxi.The northwest region refers to the vast area from the west of the Greater Xing'an Mountains,to the north of Kunlun Mountain-Altun Mountain and Qilian Mountain.The research area includes Shanxi,Gansu,Qinghai,Inner Mongolia (west of 105°E),Ningxia and Xinjiang.Eastern China has also been subdivided into two sub-regions:Northeast and North China,Central and South China(Wang et al.,2000).The Northeast and North China region generally includes the North China and Liaodong regions,as well as most of the Bohai Sea and the Yellow Sea,to Daqing Mountain in the north,Liupan Mountain in the west,and Dabie Mountain in the south.The research area mainly includes Beijing,Tianjin,Hebei,Shanxi,Liaoning,Jilin,Heilongjiang,Shandong,Henan,and Inner Mongolia(East of 105°E)(Cui et al.,2010).The Central and South China region mainly includes Shanghai,Jiangsu,Zhejiang,Anhui,Fujian,Jiangxi,Hubei,Hunan,Guangdong,and Hainan(Wang et al.,2008).Fig.1 shows the division and the distribution of earthquake cases in this paper.

2.2.The measurement of major axis,minor axis and area data

Major axis steerable method is used to measure the major and minor axis data,which takes the radius of the longest direction of each isoseismal line as the major axis radius,and the direction perpendicular to it as the minor axis radius.Most of the collected and sorted seismic intensity isoseismals are irregular due to the differences of the seismogenic structure,topography and site conditions.When digitized,the intensity distribution,seismogenic fault map and topographic map of each earthquake are superimposed onto the original isoseismal line (if the line is incomplete in the original data,it is implemented to an ellipse),and the seismogenic fault trend and topographic conditions are considered as reference (Zhang et al.,2015).Finally,the major and minor axis radii,and area data of different intensities regions are extracted.

Based on the major and minor axis radius data of earthquakes in western China,the magnitude-distance relation diagrams (MS-R) obtained from the isoseismal data of the southwest and northwest regions were drawn,as shown in Figs.2 and 3,whereMSis the surface wave magnitude andRis the radius length of semi-major and semi-minor axes.It can be seen that theMS-Rdistribution in each statistical unit is ideal and suitable for statistical regression.According to the range of data measurement,it can be inferred that the applicable range of the attenuation relationship obtained by the regression is 4.0 ≤MS≤8.6 for magnitude and 0 ≤R≤1420 km for epicentral distance.

Figs.4 and 5 are respectively the magnitude-distance relationship diagrams (MS-R) according to isoseismal data in both North China,Central China and South China,whereMSis the surface wave magnitude andRis the radius length of semi-major and semi-minor axes.It can be seen from the figure that theMS-Rdistribution in each statistical unit is ideal and suitable for statistical regression.The applicable range of the attenuation relationship in Eastern China obtained by data regression is 4.0 ≤MS≤8.0 for magnitude,and 0 ≤R≤660 km for epicentral distance.

3.Establishment of elliptical seismic intensity attenuation relationship in the Chinese Mainland

3.1.Selection of elliptical intensity attenuation model

For each isoseismal line of the selected data,take the length of the major and minor axis radius.The seismic intensity attenuation relationship with the magnitude,and with the major and minor axis radius lengths of isoseismal line,are obtained based on the multiple regression analysis.The elliptical intensity attenuation relationship model which is most commonly used in China is chosen as following Equas.(Chen Dasheng et al.,1989):

Fig.1.Division map and epicenter distribution map of earthquakes.

Fig.2.The ratio of the actual intensity value to the intensity value calculated by two models respectively.

whereIis the seismic intensity,RaandRbare the major and minor axis radii,MSis the magnitude of the earthquake,R0is the near-field saturation factor,the parametersA,B,andCare the regression constants,and ε is the random variable that represents uncertainty in the regression analysis,which is usually assumed to be a normal distribution with a mean value of zero.

3.2.Model regression results

Fig.3.Distribution of magnitude-distance relation from the isoseismal data in Northwest China.

After applying the least square method for statistical regression,the regression coefficients of the seismic intensity attenuation relationship are obtained,as shown in Table 2.

4.Establishment of seismic intensity attenuation relationship based on area and the major axis radius in the Chinese mainland

4.1.Selection of seismic intensity attenuation relationship model based on area and the major axis radius

The attenuation Equa.of intensity attenuation with isoseismal line area,i.e.the empirical relationship between intensity and magnitude,distance and focal depth is generally established on the basis of the assumption that the intensity and the energy flow density of the ground motion field are logarithmically linear.(Lu et al.,2013),the major axis equation.is the same as the elliptical intensity attenuation relationship model,as shown in Equa.(1),and the area is shown in Equa.(3):：

Fig.4.Distribution of magnitude-distance relation from the isoseismal data in North China.

whereIrepresents intensity,MSrepresents surface wave magnitude,Arepresents isoseismal area(km2),A0represents area saturation factor,d1,d2,d3andd4are regression coefficients,and εArepresents regression variance.

4.2.Establishment of seismic intensity attenuation relationship based on area and the major axis radius

After applying the least square method for regression,a set of coefficients with the smallest variance is selected as the final regression coefficients,and the intensity attenuation relationship based on the intensity influence field area and the major axis radius is obtained.The coefficients are shown in Table 3 and Table 4.

5.Comparison of intensity evaluation and inversion based on two intensity empirical attenuation relationship models

5.1.Determination and evaluation of the intensity value

According to the above-mentioned seismic intensity attenuation relationship,seismic events with a magnitude ofMS5.0 and above since 2008 are selected,and the ratio of the actual intensity value to the intensity value calculated by the model is used as an indicator to verify the empirical statistical model and the actual intensity evaluation.The degree of coincidence is shown in Table 5.

In Table 4,the maximum intensity ratio calculated by the elliptical intensity attenuation relationship-major axis intensity attenuation relationship model is 1.344,while the minimum is 0.772.The median and average are 1.028 and 1.032,respectively.On the other hand,the maximum intensity ratio calculated by the elliptical intensity attenuation relationshipminor axis intensity attenuation relationship model is 1.261,while the minimum is 0.836.The median is 1.029,and the average is 1.029.

The intensity ratio is also calculated by the intensity attenuation relationship model based on area and the major axis radius.When the ratio is calculated based on area,the maximum value is 1.363,the minimum value is 0.635,the median is 1.028,and the average value is 1.032.The major axis radius in this model is the same as in the ellipse model.The maximum intensity ratio calculated based on the major axis in this model is 1.344,the minimum is 0.772,the median is 1.028,and the average is 1.032.

The variation tendency of the four values (maximum,minimum,median,and mean) obtained by the two methods are generally consistent,indicating some regularities when using the two methods to assess the intensity value.The actual intensity value is often slightly larger than the average intensity value.According to Table 4 and Fig.2,when estimating the actual intensity value based on the two intensity attenuation relationships,it is recommended to adjust the intensity value by 0.90–1.40 times.

Table 2 Regression coefficient of seismic intensity attenuation relationship in China.

Table 3 Regression coefficient of attenuation relationship between intensity and major axis radius.

Fig.2 is a comparison chart of the actual intensity value to the intensity value calculated by the two models.The chart indicates that the intensity ratio obtained from the major axis in Model 1 is slightly larger than that obtained from the minor axis.In Model 2,the intensity ratio obtained from the major axis is also slightly larger than the intensity ratio obtained from the area.This is because in the corresponding individual earthquake cases,such as the Wenchuan earthquake,the intensity isoseismal lines are narrow and elliptical with unique characteristics:the intensity attenuation along the seismogenic fault is extremely slow,and the intensity in the meizoseismal area is higher.Furthermore,the major axis scale of the isoseismal line exceeds the scale that can be predicted by the intensity attenuation relationship to a great extent.Meanwhile,the intensity attenuation is faster in the direction perpendicular to the seismogenic fault,and the minor axis length of the isoseismal line is very close to the length calculated from the intensity attenuation relationship(Xiao Liang,2008).

Fig.5.Distribution of magnitude-distance relation from the isoseismal data in Central and South China.

Comparing Model 1 and Model 2,the major axis regression equations used in Model 1 and Model 2 are both the major axis equations.in the ellipse attenuation relationship model;therefore,the regression coefficients and the deviation of the calculated intensity are the same.Additionally,in the elliptical intensity attenuation relationship model,the error caused by the minor axis calculation directly affects the error in area.Through the inversion and comparison of the intensity value,it can be seen that the intensity value ratio inverted from the Model 2 area model has a larger fluctuation than that from the model 1 minor axis model,possibly due to the fact that in the elliptical intensity attenuation relationship model,the area of the intensity circle is determined by the major axis and the minor axis.Therefore,the error of the major and minor axes will inevitably lead to the error of the area.In Model 2,the area value selected by the parameters participating in the fitting process is also measured on the basis of the elliptical intensity attenuation relationship model.Thus,the error fluctuation of the intensity value calculated by the area model is naturally higher than that calculated by the minor axis model.

5.2.Inversion comparison

Data from the earthquakes below were inverted based on the two models:theMS8.0 earthquake in Wenchuan,Sichuan(30.95°E,103.4°N)on May 12th,2008,theMS7.0 earthquake in Lushan,Sichuan(30.20°E,103.00°N) on April 20th,2013,and theMS6.4 earthquake in Payzawat County,Kashgar,Xinjiang (39.83°E,77.21°N) on January 19th,2020.

1.According to the China Earthquake Networks Center:On May 12th,2008,anMS8.0 earthquake occurred in Wenchuan,Sichuan (30.95°E,103.4°N),with a focal depth of 11 km.

It can be seen from Table 7 that for theMS8.0 earthquake in Wenchuan,Sichuan,the intensity of the meizoseismal area is XI degree,the maximum intensity value evaluated by the ellipse model is X degree,and the maximum intensity value evaluated by the area and major axis model is Ⅷdegree.For each area from VI degree to X degree,the corresponding major axis calculated by the attenuation relationship model is different from the official measurement data by 12 km,41 km,96 km,115 km,respectively.By contrast,the minor axis differences are 111 km,80 km,14 km,8 km,and the area differences are 138 459 km2,27 366 km2,19 355 km2,7 535 km2and 3 596 km2,which are up to 10 times different from the real earthquake data.For the results from the major-axis and area model,the major-axis differences are 12 km,41 km,96 km,115 km,and the area differences are 218 166 km2,48 057 km2,24 358 km2.The latter results are smaller than those calculated by the elliptical attenuation relationship model.2.According to the China Earthquake Networks Center:anMS7.0 earthquake occurred in Lushan,Sichuan (30.20°E,103.00°N) on April 20th,2013,with a focal depth of 13 km.

It can be seen from the Tables 8 and 9 that for theMS7.0 earthquake in Lushan,Sichuan,the intensity of the meizoseismal area is IX degree,the maximum intensity value evaluated in the ellipse model is Ⅷdegree,and the maximum intensity value evaluated by the area and major axis model is Ⅷdegree.For each area from VI degree to Ⅷdegree,the major axis calculated by the attenuation relationship model are different from the official measurement data by 105 km,43 km,10 km,7 km,respectively.On the other hand,the minor axis differences are 79 km,30 km,5 km,3 km;and the area differences are 4 351 km2,53 km2,764 km2.For the results from the major axis and area model,the major axis differences are 105 km,43 km,10 km,7 km,and the area differences are 8 075 km2,2 640 km2and 1 387 km2.The latter results are smaller than those calculated by the elliptical attenuation relationship model.

Table 4 Regression coefficients of the attenuation relationship between regional intensity and intensity influence field in China.

Table 5 A summary of the ratio of the actual intensity value to the intensity calculated by the model.

Table 5 (continued)

Table 5 (continued)

3.On January 19th,2020,anMS6.4 earthquake occurred in Payzawat County,Kashgar,Xinjiang (39.83°E,77.21°N),with a focal depth of 16 km.

It can be seen from the Table 10 that for theMS6.4 earthquake in Payzawat,Xinjiang,the intensity of the meizoseismal area is Ⅷdegree,the maximum intensity value evaluated in the ellipse model is Ⅷdegree,and the maximum intensity value evaluated by the area and major axis model is Ⅶdegree.For each area from VI degree to Ⅷdegree,the major axis calculated by the attenuation relationship model are different from the official measurement data by 1 km,32 km,23 km,the minor axis differences are 9 km,10 km,4 km;and the area differences are 2 448 km2,1 186 km2,224 km2.For the results from the major axis and area model,the major axis differences are 1 km,32 km,and 23 km,and the area differences are 4 882 km2,1 259 km2,and 246 km2.The latter results are smaller than those calculated by the elliptical attenuation relationship model.

Table 6 Major and minor axis length of each intensity area calculated by different models for the Wenchuan MS 8.0 earthquake.

Table 7 Area of each intensity area calculated by different models for the Wenchuan MS 8.0 earthquake.

Table 8 Major and minor axis lengths of each intensity area calculated by different models for the MS 7.0 earthquake in Lushan,Sichuan.

Table 9 Area of each intensity area calculated by different models for the MS 7.0 earthquake in Lushan,Sichuan.

Table 10 Major and minor axis lengths and area of each intensity area calculated by different models for the MS 6.4 earthquake in Payzawat,Xinjiang.

According to the estimation of the intensity value calculated by the two intensity attenuation relationship models and the inversion results of the real earthquake,it can be seen that there is still a certain deviation between the two values.The reason for this is that the actual intensity attenuation relationship is possibly affected by various factors such as source characteristics,deep structure,propagation medium,site conditions,building structure types,residential area distribution,and topography.In addition,the coupling effect between the parameters is ignored when using the regression analysis method,probably resulting in the deviation.

6.Conclusion

We collects the isoseismal intensity data of 488 earthquakes in western China and 182 earthquakes in eastern China after 1900,and uses the least square method to establish the partition model of the seismic intensity attenuation relationship in China based on the major and minor axis ellipse model and the area and major axis radius model.These results are then applied to the evaluation and calculation of the intensity circle of earthquake events from 2008 to 2019 with a magnitude aboveMS5.0,and the ratio of the actual intensity value to the model intensity value is used as an indicator to verify the degree of agreement.The results show that when using the two seismic intensity attenuation relationship models for intensity assessment,the actual intensity value is often slightly larger than the intensity value.Thus,we recommend to slightly enlarge the corresponding intensity value by about 1.03–1.40 times when using the two intensity attenuation relationship models to estimate the actual intensity value.

Two models are selected to carry out the inversion calculation (major and minor axis and area recalculation) for theMS8.0 earthquake in Wenchuan,Sichuan,theMS7.0 earthquake in Lushan,Sichuan,and theMS6.4 earthquake in Payzawat County,Kashgar,Xinjiang.All the results suggest that the accuracy of the elliptical intensity attenuation relationship model is higher than that of the other one,even though there is still a certain deviation from the real seismic results.The reason is that the seismic intensity attenuation relationship is affected by various factors such as source characteristics,deep structure,propagation medium,site conditions,building structure types,residential area distribution,topography,etc.This study provides different intensity attenuation relationships as complements,which can improve the credibility and accuracy of the intensity distribution of large earthquakes.Furthermore,the study provides a scientific basis to governments at all levels for earthquake emergency rescue after a large earthquake.

Based on the results of the seismic intensity attenuation relationship,the applicable magnitude range of the regional seismic intensity attenuation relationship in western China is suggested to be 4.0 ≤MS≤8.6 for surface wave,with a distance range of 0 ≤R≤1 420 km.Similarly,the applicable magnitude range of the regional seismic intensity attenuation relationship in eastern China is suggested to be 4.0 ≤MS≤8.0 for surface wave,with an epicenter range of 0 ≤R≤660 km.

Acknowledgement

This study is sponsored by the special fund of the Institute of earthquake forecasting,China Earthquake Administration(2020LNEF03)and China Earthquake Networks Center Youth Fund(QNJJ202105).