Earthquake Research in China  2020, Vol. 34 Issue (3): 394-405     DOI: 10.19743/j.cnki.0891-4176.202003002
Study on the Criterion of the Correlation between Deformation Precursors and Earthquakes
NIU Anfu, ZHAO Jing, YAN Wei, ZHANG Jing, ZHANG Lingkong, YUAN Zhengyi, YUE Chong     
China Earthquake Networks Center, Beijing 100045, China
Abstract: The relationship between pre-seismic anomalous changes and earthquakes is one of the most basic information to comprehend the process of earthquake preparation and conduct earthquake prediction research. However, few researchers have carried out relevant investigations for a long time. In this paper, the distribution characteristics of deformation anomalies before the Wenchuan earthquake are analyzed, and the widespread distribution area is discussed. Based on previous studies, we improve the relationship between anomaly duration t and magnitude M by introducing distance D. The new model is characterized by lower magnitude fitting error, making it possible to establish the correlation between deformation precursors and earthquakes. The correlation standard between precursors and earthquakes here is defined as Niu's criterion, which is applied to analyze and interpret the relationship between the short-term anomalies of Hongliuxia fault leveling and the Wenchuan and Jiuzhaigou earthquakes.
Key words: Earthquake     Deformation precursors     Correlation criterion    


The main objective of the precursor observation of an earthquake is to capture the possible pre-sliding displacement before the earthquake rupture, for the purpose of making earthquake prediction. However, numerous observations indicate that it is challenging to record prominently anomalous deformation in the vicinity of the epicenter of earthquakes, thus the concept of minimum precursory distance has been proposed by some scholars (Takemoto S., 1991; Niu Anfu et al., 2009, 2012, 2013). In addition, several questions are also remarkable: Where can we record the anomalous deformations before the earthquake? What is the maximum distance? How to establish the relationship between some far-field precursory anomalies and earthquakes? These problems are the most basic topics in understanding the earthquake process and prediction, which are mostly limited to experience in the past.

Due to the existence of a time difference between the pre-earthquake anomalies and the corresponding earthquakes, the relationship between precursors and earthquakes is uncertain. Therefore, the debate regarding the precursory problem has never ended in the international seismological domain. (Mortensen C.E. et al., 1976; Takemoto S., 1991; Linde A.T. et al., 1992; Bakun W.H. et al., 2005; Bilham R., 2005; Amoruso A. et al., 2010; Sun Wenke, 2012). Facing to the continuous debate, Niu Anfu (2005) propose the 'last minute' problem for short-term earthquake prediction in order to realize the 'seamless connection' between precursors and earthquakes by establishing the relationship between the characteristics of deformation anomalies. Classifying the typical abrupt deformation anomalies observed in the Chinese mainland, it is found that there is no moderately earthquake activityies around Panzhihua Station after a sudden variation of the ground tilt and ground stress for 1-4 days. Besides, major earthquakes occur frequently in Gansu and Qinghai areas with distance ~1 000 km in 10 days, and the correlation rate is 12/13(Niu Anfu, 2007). Such phenomenon contains profound scientific significance. First, the short-term change of the terrain not only reflects the state of local deformation, but also indicate a kind of tectonic force that can be transmitted in the deep crust for a long distance, i.e. in-situ stress wave (Niu Anfu, 2017); Second, although Panzhihua Station is generally far away from the epicenter of the earthquakes, the distribution of the epicentral distances are relatively concentrated, and the time of the earthquake occurrence relatively ranges in a time interval.Therefore, the study may be meaningful for short-term earthquake predictions.


Mogi K., (1993) put forward the model of spatio-temporal distribution map in the classification of precursors. According to the region, the precursors can be divided into three types: ① the short-term and impending earthquake precursors near the epicenter, which mainly reflect the acceleration process under the action of stress before the rupture; ② the short-term precursors far away from the source, which are mainly caused by the dynamic energy exchange between the source and far-field area; ③ the long-term precursors related to the accumulation of deformation and strain, such as expansion, steady slip of aseismic fault, long-term stick slip of seismic fault in the source area, local fracture in stress concentration area, and fault slip, which are widely distributed.

According to the calculation of deformation field caused by point source or static dislocation source, it is found that the ground tilt and strain decrease inversely with the cube of epicentral distance, and the ground tilt and strain decrease to below 10- 9 at the place about 10 times the radius of source body from the epicenter. According to the observation accuracy of ground tilt, strain and the scale of earthquake rupture, the precursor distance for MS≥5.0 earthquake is considered as 100 km, for MS≥6.0 earthquake as 200 km and for MS≥7.0 earthquake as 350 km. At present, this correlation method is widely used, but the problems of information integrity are still unsolved. The present method adopts the idea of distance constraint and time non-constraint, which is not suitable for the case that there is energy exchange between the source body and the external environment.

In fact, due to the difference of frequency response of instruments and dynamic characteristics of crustal deformation, it is limited to understand the deformation process related to earthquakes based on the thought of epicentral distance constraint and time non-constraint. The short-term variation of crustal deformation is different from structural deformation, and it has the characteristics of fluctuation. Its manifestation may either be steady-state or aseismic slip associated with the friction-slip-induced fault-slipping velocity(Miao Ali et al., 2012), or the unstable brittle fracture caused by the fault slip during nucleation (Das S. et al., 1981; Zhu Shoubiao et al., 2009), i.e. earthquake. The former is the precursor we intend to study, and the latter is the original P-wave of the earthquake.

The crust deformation observed is the integration of various periodic waves through the gain of tilt, strain, gravity and fault measurement instruments. In the situation of high sampling rate and accuracy, the earth tide and co-seismic deformation together with deep crustal stress disturbance can be recorded. The recorded results S can be divided into four parts: ① deformation related to tectonic activityies, mainly including some long-term changes, expressed by Ss; ② short-term and imminent precursory related to the process of earthquake preparation and nucleation, expressed by Sn, which may not be observed within the minimum precursory distance; ③ stress wave in the crust Sw, ④The interference Sd caused by the change of observation instrument, site environment and meteorological environment. Therefore, S can be represented as:

${\rm{S}} = {\rm{Ss}} + {\rm{Sn}} + {\rm{Sw}} + {\rm{Sd}} $ (1)

Here, Ss+Sn represents the long-term and short-term changes near the observation site, which may be weak due to the limitation of instrument frequency response and the characteristic of pre-seismic deformation.

The stress wave Sw is based on the flow of soft materials in the deep crust. The concept of long-period deformation wave proposed in the 1970s has attracted close attention. Many scholars have studied the existence, detection and mechanism of deformation waves (Bott M.H.P. et al., 1973; Anderson D.L., 1975; Scholz C.H., 1977; Meyer K. et al., 1988; Feng Deyi et al., 1993; Niu Anfu et al., 1995; Wang Shengzu et al., 2000; Takahashi K. et al., 2005; Niu Anfu, 2017). Since Molnar (Molnar P., 1975; Molnar P. et al., 1978) and Tapponnier P. et al., (1976) put forward the concept of slip lines in the lower layer of the lithosphere, the fluidity of the asthenosphere has been accepted by scholars and used to construct the plastic flow network of the continental crustal movement. The network provides the path of the stress wave propagation, and it directly affects the crustal deformation and seismicity in China (Luo Zhuoli et al., 1995; Wang Shengzu et al., 2000).

The triggering time of stress wave Sw to earthquake is limited, which can be obtained by case study (Niu Anfu, 2017). On this basis, the relationship between precursory anomalies and earthquakes is established, satisfying the constraints of time and distance. Although the distance may be far, it is still possible to find the rule of magnitude, distance and anomaly characteristics, which is beneficial to the earthquake prediction.


Some scholars have studied the anomalies before the Wenchuan earthquake. However, the results suggest that there are only few anomalies near the epicenter, and most of them are distributed in the peripheral areas (Zhang Shuliang et al., 2009; Niu Anfu et al., 2012, 2013, 2020). Whether some anomalies are related to the Wenchuan earthquake is worthy of further investigations. Therefore, this paper will discuss the characteristics and significance of the distribution of precursory anomalies in combination with seismic activities.

According to the characteristics of historical seismicity, the Wenchuan earthquake is located in the enclosed area of M7.0 earthquakes in the North-South Seismic Belt (Chen Zhangli et al., 2009). This is a long-term seismic gap. After the Kunlun Mountain earthquake in 2001, some large deformation anomalies have been observed in the North-South Seismic Belt, including the Longdengba Fault baseline and Guzan strain at the Xianshui River Seismic Belt, Tonghai fault leveling on Xiaojiang Fault, Hongliuxia leveling and Wudu strain on Qilian Mountain Seismic Belt. Besides the baseline between Guangzhou and Luzhou GNSS stations can also form a gap together with the seismic activities of M≥5.5 in southwest and southeast China(Fig. 1). There is no earthquake and deformation anomaly within the so-called elliptical gap as shown in Fig. 1, so it is consistent with the model proposed by Chen Yong (2008).

Fig. 1 Seismic activity before the Wenchuan earthquake and deformation sites of significant anomalies The ellipse shows a boundary without earthquakes and anomaly sites, yellow and red circles denote the earthquakes with MS≥5.5 for the period from November 14th, 2001 to the Wenchuan earthquake. Grey, red and green rectangles show all deformation measurement sites, deformation anomaly sites and GNSS stations, respectively

According to the characteristics of the elliptical gap, the baseline between Luzhou and Guangzhou GNSS stations is approximately oriented in the long-axis of the ellipse. Fig. 2 shows the results of de-noising analysis of the third-order DB wavelet of the baseline, in which the dotted line represents the fitting trend of the baseline. The baseline shows rapid compression with a speed of 12 mm/a in the period of 2005-2007, which is rare in South China. At the end of 2007, the baseline began to rapidly recover until the Wenchuan earthquake. After the earthquake, the baseline soon recovered to the original trend. The baseline changing process verifies the rationality of the elastic rebound theory.

Fig. 2 The Luzhou-Guangzhou GNSS baseline change (Dashed line shows compress)

Fig. 3 shows the M-t and Benioff strain of the seismicity inside and outside of the ellipse gap (inside-after the Wenchuan earthquake, outside-before the Wenchuan earthquake), and the sliding step length is 1 month. It can be seen from the comparison between Fig. 2 and Fig. 3 that during 2005-2007 when the baseline was rapidly shortening, the seismicity outside of the elliptical gap was significantly weakened, and the Benioff strain was in deficit. The relationship shows that the strain accumulation is related to the seismicity in the whole area, indicating several widely distributed deformation precusors.

Fig. 3 The M-t for earthquakes with M≥5.5 out of the ellipse gap (a) and Benioff strain with the slip window length 1 month (b). The dashed line shows the tendence from 2002 to 2004

A significant anomaly before the Wenchuan earthquake is observed at the Hongliuxia fault leveling site, which is nearly 1 000 km away from the epicenter of the Wenchuan earthquake. This site is located in the Qilian Mountain Seismic Belt, and is not directly related to the fault where the Wenchuan earthquake occurred. Besides, no major earthquake is felt before and after the anomaly around the site. After removing all possible interferences, the reason and mechanism of the short-term change on the fault leveling at Liujiaxia site are noteworthy to be investigated. The leveling observation at Hongliuxia site was started in 1999, and there are four survey endpoints, among which the leveling of edge ES (E-endpoint and S-endpoint) is characterized by rapid change. This edge is perpendicular to the Qilian Mountain northern fault oriented in NWW. The sampling periodicity is not consistent. From May 2005 to December 2012, the observation was conducted every two months. After that, it increased to every four months. Before the Wenchuan MS8.0 earthquake, the measured leveling was rapidly changed for 8 months with an amplitude of 2.2 mm. Similar anomaly repeated before the Jiuzhaigou earthquake. In the period of July 2016 to November 2016, the leveling broke through the original trend of gradual decline, and turned to increase rapidly for 4 months, with a range of 3.2 mm. When significant abnormal changes were observed in November 2016, repeat measurement was conducted with a similar range. Then, additional investigations were conducted once every two months until the occurrence of the Jiuzhaigou MS7.0 earthquake on August 8th, 2017.

The distances between the leveling site and the Wenchuan and Jiuzhaigou earthquake are 1 150 km and 950 km respectively, which are beyond the traditional understanding for the distance of precursors. However, only few scholars have analyzed the nature and mechanism of the changing patterns.

In order to establish the relationship between the characteristics of deformation precursors and earthquakes, Niu Anfu (2003) proposes the formula regarding abrupt anomalous deformation and the corresponding magnitude in the duration of 15-180 days without considering the influence of the epcientral distance

$M = 1.36{\rm{log}}T + 3.786 + {\varepsilon _0} $ (2)

Where, ε0 obeys normal distribution, σ(ε0)=0.35.

For the far-field short-term anomalies, distance correction can be applied for Equa. (2). Introducing half wave length D0 = 290 km, by the least square method we get the following equation

$M = 1.36{\rm{log}}T + 0.543{\rm{log}}\left({D/{D_0}} \right) + 4.161 + {\varepsilon _1} $ (3)

In the equation, ε1 obeys the normal distribution, σ (ε1)=0.28. The wavelength represents the length of stress wave (Niu Anfu, 2017), which is close to the 5° ring of seismic activity (Xu Shaoxie, 2006).

It is obvious that the magnitude fitting variance of Equa.(3) is significantly better than that of Equa.(2), and it can be applied to both near-field and far-field, indicating that Equa.(3) provides an important possibility for establishing the relationship between deformation precursors and earthquakes. According to the precursory characteristics, the magnitude of the target earthquake can also be estimated. If the magnitude error is within 2 times of variance, the anomaly is considered to be related to the earthquake with 95% reliability. This identification method is defined as the criterion of the correlation between precursors and earthquakes, called Niu's criterion.

According to the characteristics of the leveling anomaly of Hongliuxia site and the epicentral distance, the estimated magnitude of the Wenchuan earthquake is 7.79, and the estimated magnitude of the Jiuzhaigou earthquake is 7.27. Both of them are within 2 times of magnitude fitting variance, suggesting that two significant anomalies of Hongliuxia leveling is related to the Wenchuan earthquake and Jiuzhaigou earthquake with 95% reliability.


According to the theory of plate tectonics, mantle convection is the main driving mechanism of plate motions. The mantle is composed of hot materials with high temperature. Due to the difference of density and temperature in the mantle, the solid part of the mass can also flow. Mantle convection is a complex system, which not only conducts heat, but also hot materials. Mantle convection can rise from the core mantle boundary to the bottom of the lithosphere to form a whole mantle convection circle. Another scenario is the laminar convection, in which hot materials in upper and lower mantle may form convection circles separately. Under the influence of mantle convection, plastic flow can occur in the crust under long-term stress. Due to orogeny and volcanism, and under the action of gravity, the crust slips laterally and invades into the ocean. Tapponnier P. et al., (1976) utilize slip line field to simulate the structure of the Asian continent. Taking India as the stamping block, plenty of large strike-slip faults can be modeled by slip lines. Tapponnier P. et al., (1977) also investigate active faults and tectonics in China. Based on the epicenter distribution of the earthquakes with MS≥6.0, the surface rupture zone of strong earthquakes, focal mechanism solutions and active tectonic data, Luo Zhuoli et al. (1995) delineates the present-day structural slip lines in the Chinese mainland, which are the zones of the concentrated release of maximum shear stress and shear strain concentrated release, and control the spatial distribution framework of seismic activities and tectonic movements. The network basically consists of two clusters of logarithmic spiral curves with symmetry axis of central Himalayan arc to Baikal Lake. Wang Shengzu et al. (2000) also outline the plastic flow network in Chinese mainland, and the block boundaries are basically consistent with the important slip lines. The distribution of slip line field shows the main channel of the mass flow or stress wave propagation in deep crust.

In order to explain that there is no precursor or shadow abnormal activity before the Wenchuan earthquake, Teng Jiwen et al. (2008) analyze and discuss the deep process of preparation, development and occurrence of this earthquake. The preliminary study shows that under the collision and compression of the Indian Plate and Eurasian Plate, the eastern structure of the Himalayas orogenic belt is pushed to the NNE direction and wedged into the northeast margin of the Qinghai-Tibet Plateau, forcing the materials in the deep of the plateau to flow eastward. Meanwhile, the materials in the middle and lower crust and mantle selects the low velocity layer and low resistivity layer (20-25 km deep) as the first slip surface, the top surface of the above mantle asthenosphere is the second slip surface. Under the barrier of 'rigid' materials in the deep of Sichuan Basin, the materials in the deep of the crust encounters at a high angle at Longmenshan Fault, triggering the earthquake.

The effect of the deep mass flow on the Wenchuan earthquake is stronger than fault slip (Zhang Peizhen et al., 2008), making significant deformation. The former can be simulated by the fluid motion model, which contains numerous waveforms of fluid movement. Here, long waves (similar to Ocean tsunami)are selected as examples (Wu Yungang et al., 2011; Niu Anfu, 2017). It is assumed that the horizontal and vertical components of the flow velocity are expressed as u (x, y, t) and v (x, y, t), respectively, and the height of the free surface is η (x, t). Its two-dimensional continuity equation is expressed as:

${u_x} + {v_y} = 0 $ (4)

Among them, ux and vy are partial derivatives. Kinematic condition on free surfaces is:

${\eta _t} + u{\eta _x} - v = 0\left({y = \eta } \right) $ (5)

The bottom boundary condition is:

$ u{h_x} + v = 0\;\;\;\;\;\;\;\;\left({y = - h\left(x \right)} \right) $ (6)

By integrating and simplifying, we can obtain the Equa.(7) below:

$ \frac{{\rm{d}}}{{{\rm{d}}t}}\left({u \pm 2c} \right) = - g{\rm{s}} $ (7)

Where, $ s = \frac{{\partial (- h\left(x \right)){\rm{ }}}}{{\partial x}} $, which is the slope of the bottom boundary; $ c = \sqrt {g\left({h + \eta } \right)} $, which is the velocity of fluid propagation. Due to the inclusion of the nonlinear term, long wave equation is different from the small amplitude wave. The velocity of the long wave is related to the wave height. The higher the wave height, the higher the wave speed. Therefore, in the process of propagation, the long wave shape will change, and the wave front becomes steeper, which is an important feature of the long wave (Fig. 5).

Fig. 4 The leveling anomalies measured at Hongliuxia site prior to the Wenchuan and Jiuzhaigou earthquakes

Fig. 5 The sketch for bottom boundary effects on mass flow

Similar to the characteristics of long wave motion, the shape of the bottom boundary of mass flow in the deep crust is an important factor affecting stress transfer. When the bottom boundary is up-warped or the channel is narrowed, either the deformation is intensive or the strong earthquake is triggered. This is consistent with the rock fracture test and theoretical results (Das S. et al., 1981; Zhu Shoubiao et al., 2009; Miao Ali et al., 2012).

Tectonically, the Wenchuan earthquake, the Jiuzhaigou earthquake and the Hongliuxia leveling observation site are not on the same block (Fig. 6). However, in terms of the gravity distribution (Shen Chongyang et al., 2009) and the slip line network (Wang Shengzu et al., 2000), they are all located in the channel where deep crustal materials flow readily and stress transfers more efficiently. Based on long wave propagation model, it is not difficult to understand the dynamic significance of some significant deformation anomalies before earthquakes. The large earthquakes or significant deformation anomalies are strongly associated with deep mass flow in a special way.

Fig. 6 The tectonic distribution of Hongliuxia levelling site, Wenchuan and Jiuzhaigou earthquakes Blue lines show the block boundaries, red circles denote the earthquakes more than MS6.5

At the eastern margin of the Bayan Har block, the Lushan MS7.0 earthquake (Lushan earthquake)on April 20th, 2013, and the MS6.6 Minxian-Zhangxian earthquake (Minxian-Zhangxian earthquake) on July 22nd, 2013, also occurred in the studying period. The time interval between two earthquakes is 4 months. Because the pre-seismic observation period of the Hongliuxia leveling is 4 months, it is difficult to identify the anomalies before every earthquake. From this point of view, the deformation anomaly is still limited by the conditions of seismicity or the regional overall stress level, and there may not be the same precursory phenomenon before each earthquake.


The earthquake precursor study in this paper refers to the anomalies related to earthquakes in a period before the event. Such anomalies are mainly caused by the mass flow in the deep crust, thus having a large distribution area. Previous studies suggest that precursors are usually associated with the steady-state sliding, unsteady sliding and fracture nucleation process of faults (Dieterich J.H, 1979; Das S. et al., 1981; Zhu Shoubiao et al., 2009; Miao Ali et al., 2012). The precursor distance is artificially restricted within a certain range, and the relationship between precursors and earthquakes cannot be truly reflected. The long-term observation facts show that the steady-state fault sliding or aseismic sliding is not the end of the process, revealing an information window of stress wave transmission path. Although there is no earthquake near the abnormal site in a short term, it may be followed by an earthquake in another area. Besides, the unsteady fault slip and fracture nucleation process usually directly lead to the earthquake rupture. In this case, time-dependent deformation should be seismic P-wave, which is not regard as precursory anomaly.

It is an inevitable problem to judge the correlation between far-field precursors and earthquakes. According to the statistical relationship between the acceleration duration of deformation anomaly and the epicentral distance and magnitude of an earthquake, it provides an important index for distinguishing the relationship between the anomaly and the target earthquake. Meanwhile, the statistical relationship also provides an algorithm for estimating the seismic risk level of the study area.

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