Earthquake Reaearch in China  2017, Vol. 31 Issue (1): 107-115
The Statistical Relationship between the Maximum Amplitude of the Body Strain Record and the Surface-wave Magnitude and Epicenter Distance
Jiang Jianing1, Wu Lijun2     
1 Zhangjiakou Central Station, Earthquake Administration of Hebei Province, Zhangjiakou 075000, Hebei, China;
2 Institute of Earthquake Science, China Earthquake Administration, Beijing 100036, China
Abstract: Based on the body strain record of Tiantanghe station from 2008 to 2014, we make a statistical analysis of the relationship between the maximum amplitude of the body strain record and the surface-wave magnitude, epicenter distance of the earthquakes, which occurred in the Chinese mainland and its surrounding areas with MS ≥ 6.0 and the rest of the world with MS ≥ 7.0. According to statistical results, we propose a statistical formula between the surface-wave magnitude of earthquake and the maximum amplitude of the body strain record, the epicenter distance:MS*=0.37lnAmax+0.57lnD+0.07. We can also derive a theoretical estimation formula for the maximum amplitude:Amax=e2.7(MS*-0.07)D-1.54. This demonstrates that the maximum amplitude of the body strain record increases exponentially with the increase of the surface-wave magnitude, and decreases with the increase of the epicenter distance, and shows a negative correlation with their product. We further discuss the necessity of adding instruments with high frequency sampling to earthquake monitoring, and dicuss the prospects for precise earthquake prediction in future.
Key words: Body strain     Seismic wave     Statistical analysis     High sampling rate     Earthquake monitoring     Earthquake prediction    


Because the deep burial of probes (300m-400m), Sacks body strains possess the features of little surface interference, working frequency bandwidth frequency responses from zero to more than 10Hz, and high sensitivity (Sacks et al., 1971; Tian Tao et al., 2014), and have unique advantages in crust deformation observation. This technology has helped gain great achievements in drilling strain observation in China (Su Kaizhi et al., 1993; Li Hailiang et al., 2010) and earthquake case studies (Gao Fuwang et al., 2004; Yi Zhigang et al., 2006; Wu Lijun et al., 2013; Wu Lijun et al., 2015b). Since digital transformation in 2001, the 6 stations in the Sacks body strain network have accumulated continuous and stable digital observation data for as long as 15 years. In 2007, some stations underwent the tenth "Five-year Plan" observation model transformation project, and instrument stability and operational ability of data collection and processing systems were greatly improved. This is significant for the utilization of Sacks body strain in the exploration of earthquake precursory micro dynamic information and also provides a necessary foundation for the identification of short and temporary pre-earthquake anomalies and earthquake prediction (Wu Lijun et al., 2015a).

In the study of drilling strain seismic waves, Niu Anfu et al. (2005) analyzed the coseismic deformation waves recorded from a number of strong earthquakes or typical earthquakes abroad and at home in 2003, and pointed out the relationships between the response delay time of the earthquake surface waves, amplitudes response and coseismic signal keeping time, and the distance from the epicenter and scales. Zhang Lingkong et al. (2009), on the basis of Sacks body strain seismic wave observation at the Baodi seismic station, explored the statistic relationship between the indicator increase with scale in seismic wave amplitudes within a given range of the epicenter and the power function attenuation with the epicenter distance increase. Tang Lei et al.(2011a, 2011b, 2013) conducted a series of analysis and exploration of the coseismic strain steps on the basis of drilling four component strain records. Zhao Nan et al.(2012, 2013) compared and analyzed the seismic waves recorded by the BBVS seismic detector and TJ-2 strain instrument and explored the similarities and differences of the seismic waves recorded by the two instruments and their relationships. Yang Yuewen et al. (2011), Guo Mingrui et al. (2012) extracted the earth global free oscillations excited by the Japan MW9.0 earthquake on the basis of the body strain observations.

The study of the largest amplitudes of deformation seismic waves plays a significant role in revealing the relationship between seismic energy and deformation. Anomalies of body strains before earthquakes have been widely proven by seismologists both abroad and at home. Therefore, the relationship between the deformation wave change in the earthquake and the earthquake focal can be an important way for earthquake precursors and short-impending predictions, and is an important starting point of short-impending prediction (Department of Monitoring and Prediction, China Earthquake Administration, 2007). Sacks body strain has a good earthquake reflecting effect in the earthquakes with M≥6.0 in the Chinese mainland and its surrounding regions and those over scale 7.0 in the world (Gao Fuwang et al., 1999; Yi Zhigang et al., 2005; Song Mo et al., 2010; Wu Lijun et al., 2015a). Thus, this paper makes a statistical analysis of the body strain seismic wave data at Tiantanghe Station (located in the Daxing district of Beijing). The body strain instrument has no zero drift and is not affected by the valves which ensures a good effect for the statistical research of the earthquake cases recorded. We have every reason to believe that it will be very beneficial for earthquake prediction to analyze the drill strain data in terms of earthquake responses and explore and obtain precursory anomalies information.

1 EARTHQUAKE CASE STATISTICS 1.1 Earthquake Catalogues

We downloaded the national MS 5.0 earthquake catalogue, the global MS 7.0 earthquake catalogue and the earthquake catalogue of the American National Earthquake Information Center (NEIC) and used the EQDown software (Lu Yuanzhong et al., 2002) for case statistics. We collected all of MS≥6.0 earthquakes in the Chinese mainland and its surrounding regions (longitudes: 70°-149°E, latitudes: 16°-55°N) and MS≥7.0 earthquakes in the world during 2008-2014. There were 339 earthquakes in the time and space concerned. The smallest scale is 6.0 with 44 earthquakes and the largest is MW 9.0 with 1 earthquake, the MW 9.0 earthquake in the vicinity of the east coast of Honshu Island, Japan on March 11, 2011. The earthquake with the shortest distance from the Tiantanghe seismic station is the earthquake MS6.7 at Minxian County, Gansu Province on July 22, 2013 with the epicenter distance of 1, 216km. The one with the largest distance is the M7.3 earthquake in the far sea off the coast of middle Chili on February 27, 2010 with the epicenter distance of 19, 409km.

Among the 339 earthquakes, there are 181 with magnitude from MS6.0 to MS 6.9, 150 with magnitude from MS7.0 to MS7.9, 7 with magnitude from MS8.0 to MS8.9 and 1 with magnitude of MW9.0.

1.2 Statistic Results of the Largest Amplitudes of the Body Strain Seismic Waves

The sampling interval of the body strains at Tiantanghe seismic station is one minute. The largest amplitude of seismic waves refers to the largest amplitude observed within the sampling interval. At 17:19 p.m. on February 12, 2014, an MS7.3 earthquake occurred in Yutian, Xinjiang. Fig. 1 is the seismic waves recorded by the Sacks body strain instrument. The seismic waves of the earthquake arrived at 17:30p.m. and the largest amplitude appeared at 17:36-17:37p.m. (Fig. 1(b)) with amplitude of 1408.6×10-9 lasting for one hour and seven minutes. The waveform first shows depression then extension next. There are subsequent radical changes. At 18:37p.m., it attenuated to the normal background value. The calculation reveals that the distance of the epicenter from Tiantanghe seismic station is 2, 976km.

Fig. 1 Calculation of the maximum amplitude

The epicenter distances and the maximum amplitudes of the 339 earthquakes were calculated in the aforementioned way. To ensure as much as possible the truth and objectivity of the results, the principles below were followed in the statistical process: (1) Earthquakes without reflection or without obvious reflection were not taken into account. (2) In the case of multiple strong aftershocks with M≥6.0, some of the aftershocks had short intervals in the time from the main shock and the body strain of the mainshock had a great influence in amplitude on the aftershocks. These aftershocks were not taken into account. For example, 26 earthquakes with M≥6.0, and 3 earthquakes of scale 7.0 took place within two days after the Japan MW9.0 earthquake on March 11, 2011. These 29 earthquakes were not taken into account. (3) Some of the earthquakes were double earthquakes or multiple earthquakes. For example, at 06:00a.m. to 07:00a.m. on October 8, 2009, 3 earthquakes with scales larger than 7.0, that is, 7.8, 7.9 and 7.2, took place in Vanuatu. The long lasting time of the seismic waves made it impossible to have them on the observation curves. In terms of time correspondence, we took the largest amplitude observed as the earthquake greatest amplitude. Generally speaking, coseismic amplitude response attenuates with distance, but because of the short lasting time of the near shock surface waves and the incompleteness of the far earthquake surface waves, the accurate largest amplitude of coseismic deformation is usually difficult to record and the attenuation that should have appeared becomes obscure or even opposite (Department of Monitoring and Prediction, China Earthquake Administration, 2007).

According to the aforementioned statistical principles, 184 earthquakes have good body strain seismic wave reflections (Fig. 2), among which there are 85 earthquakes of scales from 6.0 to 6.9, 91 earthquakes of magnitude from 7.0 to 7.9, 7 earthquakes of scales from 8.0 to 8.9 and 1 earthquake with M9.0. The smallest amplitude appears in the M9.0 earthquake in the vicinity of the east coast of Honshu island, Japan on March 11, 2011, with the amplitude of 41.4×10-9. The largest amplitude appears in the Wenchuan MS8.0 earthquake in Sichuan on May 12, 2008, with the amplitude of 48982.9×10-9.

Fig. 2 The station location and the epicentral distribution

We conduct the fitting of the scales, the epicenter distances and the largest amplitudes of the 184 earthquakes based on the Levenberg-Marquardt method and general global optimization (Fig. 3). The fitting results show the statistical relationship between surface wave scale MS* and the epicenter distance and the largest amplitude:

Fig. 3 The fitting results of earthquake magnitude
$ M_{\rm{S}}^* = 0.37\ln {A_{\max }} + 0.57\ln D + 0.07 $ (1)

where D is the epicenter distance in km, Amax is the largest amplitude with the unit of 10-9. The scale fitting variant σM=0.23, the correlation coefficient R=0.94 and the determination coefficient R2=0.88. The fitting result is good. The scale fitting mean square deviation and the result show that the fitting scale is close to the actual scale and can reflect the relationship between the scale and the epicenter distance and the largest amplitude. In seismology, Gutenberg (1945) proposed the surface wave scale MS as:

$ {M_{\rm{S}}} = \lg {A_{H\max }} + 1.656\lg \Delta + 1.818\;\;15° < \Delta < 130° $ (2)

where AHmax is the largest horizontal displacement with the unit of in μm; and Δ is the epicenter distance in degree. Equations (1) and (2) show that the largest amplitude of the body strain seismic waves fits well with the equation of the scale calculated from the epicenter distance and the equation in seismology, both being the function of the log of the largest amplitude and the log of the epicenter distance.

Fig. 4 shows the actual observations of the 184 earthquakes and the three dimensional curved surface of the scales based on equation (1) and the epicenter and the largest amplitude. It shows clearly the relationship between the three and the fitting effect.

Fig. 4 The measured results and the fitting results

The study of the response of the body strains seismic waves to the earthquake is significant for the analysis of the earthquake short-impending precursors and earthquake prediction based on short-impending precursors. The information of body strain impending anomalies is mainly distributed in the solid tide distortion or mutation that lasts for 1 to 10 days or within several hours (Zheng Jiangrong et al., 2005; Wu Lijun et al., 2015a, 2015c). The changes within the range is somewhat similar to seismic deformation, but is more complex than coseismic response. The key issue here is the short-impending precursor judgment and its relationship with future earthquake elements (Department of Monitoring and Prediction, China Earthquake Administration, 2007). Therefore, to explore the effects of the different coseismic scales and the epicenter distances on the body strains, the relationship equation between the largest amplitude and the epicenter distance can be as follows:

$ {A_{\max }} = {{\rm{e}}^{2.7}}\left( {M_{\rm{S}}^* - 0.07} \right){D^{ - 1.54}} $ (3)

where the definitions of Amax, MS* and D are the same as equation (1). It can be seen in equation (3) that the largest amplitude of body strain seismic waves increases in the scale of indicator function and reduces in the form of the power function with the increase of epicenter distance. The two show a multiple correlation relationship.


The statistical research found that there is some functional relationship between the largest amplitude of the body strain seismic waves and the epicenter distance. The scale statistic equation shows the function between the scales of the largest amplitudes and the epicenter distances. The equation proves that the largest amplitude of body strain seismic waves increases in the scale of indicator function and reduces in the form of the power function with the increase of epicenter distance. Despite the statistical relationship between the three, there are still affecting factors in theoretical calculation such as model residue, scale precision and epicenter distance residue. We believe that besides these factors, there are still three affecting factors. (1) The instrumental sampling rate is so low that it is difficult to record the largest energy value of the seismic waves. (2) The heterogeneity and anisotropy of the earth medium make it impossible to have the same amplitudes even if the largest amplitudes are caused by the same coseismic scales and the same epicenter distances. (3) The difference in the focal mechanism solutions can lead to the difference in the earthquake amplitudes in different directions. The result will be greatly improved if statistical analysis is done with largely increased sampling rates, and the precision of the functional equations will also be improved.

Although the digital deformation data with low sampling rates cannot completely reveal the focal information as an earthquake observation does, they still can reflect some characteristics of the earthquake propaganda process. The coseismic deformation features provide a new approach for the explanation and the identification methods of earthquake short-impending precursors (Department of Monitoring and Prediction, China Earthquake Administration, 2007). The strain seismic waves by high frequency sampling are more complete and the details are clearer (Yang Xuanhui et al., 2011). Lv Yongqing et al. (2011) compared the body strains and the broadband digitizer data, and found that the strain seismic waves recorded by the broadband digitizer are more precise and the seismic phase is clearer. Guo Yanping et al. (2012) found in their experiment of high sampling rate in drilling body strains that the 100Hz sampling in the TJ-2 body strain instrument can record complete seismic waves from near to very distant earthquakes. The frequency response changes have a good consistency. Under some binding circumstances, the strain seismic waves match well the seismic waves in the time domain and the frequency domain, but the S-wave recorded by the strain instrument is weak. Therefore, the increase of the sampling of the strains can make the statistical results more precise and reflect real coseismic information.

Seismologists have done much research and exploration on anomalies in deformation precursors and made a lot of significant achievements. They find that earthquake scales are connected to the lasting time and range of anomalies. Although the scales do not have absolute corresponding relationships with the anomaly amplitude, there is some statistical relationship (Department of Monitoring and Prediction, China Earthquake Administration, 2007). In recent years, a number of scholars have carried out research on the relationship between strain anomalies and the lasting time and the scales and epicenter distances (Chen Defu, 1993; С.И.Зубков et al., 1995; Jiang Jingxiang et al., 2008), and took this as an indicator in earthquake prediction tests (Jiang Jingxiang et al., 2003; Gao Fuwang et al., 2004; Yi Zhigang, 2005; Niu Anfu et al., 2008). These achievements, though still unable to explain all the observations, reveal some complicated micro dynamic information about earthquake preparation. It cannot be denied that these results are based on low sampling rates with some deviations and many objective phenomena, rules and theories cannot be revealed by these results. Qiu Zehua et al. (2013) found with an YRY-4 drilling strain instrument with the 100Hz sampling rate that P-wave strains do not only have surface strains, but also shear strains. This clarifies the nature of P waves and provides direct observation evidence. Seismic deformation wave study increases the theoretical possibility of explaining deformation short-impending precursors, extracting short-impending precursory information and locating potential earthquakes based on short-impending precursory signals (Department of Monitoring and Prediction, China Earthquake Administration, 2007).

If the present precursory observation technology cannot make an accurate judgment of the three elements of earthquake supported by the perfect theories, how can there be precise earthquake predictions? This leads to the current situation that the present earthquake prediction is empirically and statistically based but with strong predictor's personal experience (Zhang Guomin, 2013). However, it can be foreseen that in the near future, there will be systematical and theoretical research of focal earthquake preparation on the basis of precursory observations with high sampling rates and with the starting point of analysis of initial motions of precursory seismic waves, amplitude and velocity. Seismic waves and anomaly types will be set, while comprehensive quantitative indicators such as lasting time, range, amplitude, and precise earthquake preparation models will be made. All of these will help realize the accurate earthquake prediction and lead to a more challenging exploration.

ACKNOWLEDGEMENTS: We owe our greatest gratitude to the peer previewers and editors for their valuable advice and suggestions.

This paper has been published in Chinese in the journal of Technology for Earthquake Disaster Prevention, Volume 11, Number 3, 2016.

Chen Defu. Crustal Deformation Dynamics Observation and Study[M]. Beijing: China Ocean Press, 1993
Department of Monitoring and Prediction, CEA . Application of Digital Observation Data in the Short-term Earthquake Prediction and Study on the Precursory Physical Mechanism[M]. Beijing: Seismological Press, 2007
Gao Fuwang, Li Li, Han Fengyin. Borehole strain measurement in the Capital Circle Area and its anomalous changes shortly before earthquakes[J]. Earthquake, 2004, 24(1): 88–95.
Gao Fuwang, Liu Beishun. Volumetric strain variety character relations with an earthquake with MS6.0 in the Capital area, China[J]. Earthquake Research in China, 1999, 15(4): 370–376.
Guo Mingrui, Su Yanhong, Guo Yuqin, et al. Detection of earth's free oscillations in Japan MW9.0 earthquake by use of body strain observation at Datong seismostation[J]. Journal of Geodesy and Geodynamics, 2012, 32(Supp.): 32–34.
Guo Yanping, Qiu Zehua, Li Suhua, et al. On high sample rate of borehole volume strainmeter observation[J]. Journal of Geodesy and Geodynamics, 2012, 32(1): 51–55.
Gutenberg B. Amplitude of surface waves and magnitudes of shallow earthquakes[J]. Bull. Seism. Soc. Amer., 1945, 35: 57–69.
Jiang Jingxiang, Wang Zaihua, Li Chuan, et al. Borehole strain in anomaly and strong earthquake activity in Xinjiang[J]. Inland Earthquake, 2003, 17(2): 126–133.
Jiang Jingxiang, Xu Yangang. Prediction study on seismic intensity based on anomalous time of component-type borehole strain[J]. Inland Earthquake, 2008, 22(1): 6–13.
Li Hailiang, Li Hong. Status and development of borehole strain observations in China[J]. Acta Geologica Sinica, 2010, 84(6): 895–900.
Lu Yuanzhong, Li Shengle, Deng Zhihui, et al. Earthquake Analysis and Prediction System Based on GIS[M]. Chengdu: Chengdu Cartographic Publishing House, 2002
Lv Yongqing, Song Zhiying, Wang Zhenjiang, et al. Preliminary study on the concurrent observation of body strain with normal digitizer and broadband digitizer[J]. Earthquake Research in Shanxi, 2011(2): 17–21.
Niu Anfu, Ji Ping, Yan Wei, et al. An attempt to predict strong earthquake while the waiting time for forth coming earthquake with MS≥ 6.0 was breaking a historical records on the Chinese mainland[J]. Earthquake Research in China, 2008, 24(1): 61–66.
Niu Anfu, Zhang Jing, Ji Ping. Conseismic deformation response of strong earthquake[J]. Inland Earthquake, 2009, 19(1): 1–7.
Qiu Zehua, Chi Shunliang. Shear strain of P wave observed with YRY-4 borehole strain meter[J]. Earthquake, 2013, 33(4): 64–70.
Sacks I.S., Evertson D.W. Sensitive borehole strain-rate meters[J]. Carnegie Institution, Washington Yearbook, 1971, 68: 448–453.
Song Mo, Qiu Zehua, Tang Lei. Earthquake recording ability of borehole strainmeter[J]. Journal of Geodesy and Geodynamics, 2010, 30(Suppl.(Ⅱ)): 31–35.
Su Kaizhi, Liu Ruimin, Pei Yuzhen. Volume strainmeters in China[J]. Inland Earthquake, 1993, 7(2): 151–157.
Tang Lei, Jin Yan. Analysis of coseismic strain step observed by 4-component borehole strain meters in Sichuan-Yunnan Region[J]. Technology for Earthquake Disaster Prevention, 2013, 8(4): 370–376.
Tang Lei, Qiu Zehua, Guo Yanping, et al. Analysis on strain step caused by MW9.0 earthquake in Japan[J]. Seismological and Geomagnetic Observation and Research, 2011b, 32(6): 13–16.
Tang Lei, Qiu Zehua. Coseismic strain step of Wenchuan earthquake observed by 4-component borehole strainmeter[J]. Collected Works on Crustal Structure and Crustal Stress, 2011a(23): 114–124.
Tian Tao, Wang Junfei, Wang Wei, et al. Effect of coupling on the borehole strain observation[J]. Seismological and Geomagnetic Observation and Research, 2014, 35(3/4): 165–173.
Wu Lijun, Chen Zhengwei, Li Hangu, et al. Abnormal phenomena of body strain before large earthquakes[J]. Technology for Earthquake Disaster Prevention, 2015a, 10(1): 151–162.
Wu Lijun, Hu Lan, Dai Yaqiong, et al. Analysis of interference and earthquake cases for sacks body strain in Changping No. 200 station[J]. Inland Earthquake, 2015b, 29(3): 203–212.
Wu Lijun, Zhang Bo.. Features of impending anomalies of body strain before earthquakes at Changping station[J]. Earthquake Research in Shanxi, 2015c(4): 5–8.
Wu Lijun, Zhou Liming, Zhang Zhongwu, et al. Analysis of Sacks body strain interference at Dongsanqi Seismic Station and earthquake case study[J]. Journal of Institute of Disaster Prevention, 2013, 15(3): 41–44.
Yang Xuanhui, Yang Shuxin, Zhang Bin, et al. Strains recorded by seismic acquisition unit[J]. Earthquake Research in China, 2011, 27(1): 65–71.
Yang Yuewen, Ren Jia, Jiang Cuirong, et al. Detecting the free oscillation of the Earth excited by Chile M8.8 earthquake through the observational data of digital borehole dilatometer[J]. Seismological and Geomagnetic Observation and Research, 2011, 32(1): 33–38.
Yi Zhigang, Qiu Zehua, Song Mo. Analysis of data of digitalized borehole strain observation in Capital Area[J]. Journal of Geodesy and Geodynamics, 2006, 26(4): 53–58.
Yi Zhigang, Song Mo, Qiu Zehua. The value data recorded on hour by the China borehole strain networks for the Sumatra, Indonesia strong earthquake[J]. Collected Works on Crustal Structure and Crustal Stress, 2005(3): 25–40.
Yi Zhigang. Short term and imminent abnormality for borehole volume strain observation data[J]. Seismological and Geomagnetic Observation and Research, 2005, 26(Supp.): 178–185.
Zhang Guomin, Fu Zhengxiang, Gui Xietai.. An Introduction to Earthquake Prediction[M]. Beijing: Science Press, 2008
Zhang Guomin. Selected Papers of Earthquake Prediction Science Research[M]. Beijing: Seismological Press, 2013
Zhang Lingkong, Niu Anfu. On observation results of seismic wave of Sacks body strain[J]. Journal of Geodesy and Geodynamics, 2009, 28(5): 33–39.
Zhao Nan, Jiang Peichun, Li Gangfeng, et al. Preliminary analysis of earthquake wave recorded by BBVS system and TJ-2 volumetric strain variable wave[J]. South China Journal of Seismology, 2013, 33(2): 68–74.
Zhao Nan, Jiang Peichun, Zhang Guanghua, et al. Waveforms characteristics recorded by Lu'an station seismic observation system[J]. South China Journal of Seismology, 2012, 32(3): 81–87.
Zheng Jiangrong, Xu Guiming, Li Hongyu. Synthetical analysis of observation quality and response ability to strong earthquake of body strain metres of Jiangsu Province[J]. Journal of Geodesy and Geodynamics, 2005, 25(4): 63–68.
С. И. Зубков, С. Я. Секерж-Зенькович, Д. С. Секерж-Зенькович (translated by Liang Jincang). Relationship between strain precursors appearing time and earthquake magnitude and epicentral distance[J]. Translated World Seismology, 1995, (2): 19-23(in Chinese).
姜佳宁1, 吴利军2     
1 河北省地震局张家口中心地震台, 张家口 075000;
2 中国地震局地震预测研究所, 北京 100036
关键词体应变    地震波    统计分析    高采样率    地震监测    地震预报