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The apparent lack of pre-seismic crustal deformation preceding the 2008 Ms8.0 Wenchuan earthquake has been the subject of debate. In this study, tiltmeter data recorded close to the earthquake epicenter were analysed using spectrum and wavelet analysis. Changes in the stress field before the earthquake were analyzed based on the Benioff creep release and changes in regional Global Navigation Satellite System (GNSS) baselines. The characteris-tics of far- and near-field seismicity and deformation processes were investigated using rock fracture experiments. The results show that during pre-seismic strain energy accumu-lation, there was a synergy between stress field changes both proximal and distal to the ep-icenter; moreover, we identified a strong correlation between Benioff creep release and shortening of the LUZH-GUAN GNSS baseline. During the sub-instability stage, the de-formation characteristics of different structural sectors differed; faults near the epicenter were in a highly locked state, and the deformation rate and wave spectra of main period waves obviously decreased. This reflects fixed point deformation driven by deep stress. These results are of great significance for understanding geophysical field observations, for clarifying pre-seismic deformation and for earthquake prediction.

The M_{S}8.0 Wenchuan earthquake of 12 May 2008 occurred along the NE trending Longmenshan fault zone, located in the center of an N-S seismic belt of the eastern Qinghai-Tibet Plateau, on the southeastern boundary of the Bayan Har block. According to seismo-geological research, a 240 km surface fracture zone formed along the Longmenshan central fault and front fault owing to the earthquake [

According to the characteristics of coseismic and tectonic deformation, the theory of earthquake prediction by monitoring fault pre-slip was first proposed in the 1960s [

The crustal stress field consists of in situ stress and transient stress. In situ stress, also known as static stress or absolute stress, is caused by tectonic movement over a long (geological) timescale. Transient stress, also known as dynamic stress, is mainly derived from crustal stress processes caused by the Earth's deep medium rheology, and short-term interaction of the Earth’s crust and mantle with seismic waves; transient stress fluctuates significantly. Slow earthquakes, which have periods of tens of seconds to hours or even days, and long-period deformation waves, which have periods of days to months, are reflections of the transient stress field [13 - 16]. In addition, variables such as the coseismic velocity field and gravity field, along with observations of ground tilt, strain, gravity, and Global Navigation Satellite System (GNSS) data can also reflect the transient stress field and its short-term characteristic in a given region [13 - 16]. For this reason, the characteristics of pre-seismic crustal deformation differ from those of coseismic or tectonic deformation. Improved understanding of deep earthquake dynamics has become a research focus [

Based on the analysis of pre-seismic deformation data from China, the USA, Japan, and the former Soviet Union, Wu et al. [

The tectonic setting and dynamic background of the Wenchuan earthquake have been studied by many authors [3 , 23]. The Wenchuan deformation observation station, located on the back fault of the Longmenshan fault belt, was the closest deformation observation station to the epicenter of the 2008 M_{S}8.0 Wenchuan earthquake (

Using the finite element numerical simulation method, Zhang et al. [_{S}8.1 Kunlun Mountain earthquake on 14 November 2001, and the effect on subsequent earthquakes. This event occurred on the western boundary of the Bayan Har block and the regional stress field was significantly affected, with seismicity in the epicentral region significantly enhanced. The 2008 Wenchuan earthquake, which occurred on the eastern boundary of the Bayan Har block, was likely triggered by the 2001 Kunlun Mountain earthquake.

Therefore, we chose the time-stamp of the M_{S}8.1 Kunlun Mountain earthquake as the starting point for our analysis, and the area of enhanced seismicity as our research area.

There is no set definition for the area of pre-seismic stress field variation related to large earthquakes. Xu [_{S} ≥ 5.5 earthquakes that occurred between the 2001 Kunlun Mountain and 2008 Wenchuan earthquakes. The map shows increased seismicity in southwest China, South China, and around Taiwan. At the same time, an ellipse-shaped seismic gap (hereafter, a “gap ellipse”) is also apparent (area within the red dashed line in

The M_{S}8.1 Kunlun earthquake epicenter was close to one end of the long axis of the gap ellipse. Enhanced post-seismic activity was centered around the Kunlun earthquake epicenter, and around Taiwan. The largest of these events occurred on 31 March 2002 (M_{S}7.5), 10 December 2003 (M_{S}7.0), and 26 December 2006 (M_{S}7.2). The epicenter of the Wenchuan earthquake was located in the center of the long axis of the ellipse; seismic activity was low before the earthquake.

A small number of CMONOC GNSS stations were established around the gap ellipse in 1999. The Luzhou (LUZH)-Guangzhou (GUAN) and Luzhou (LUZH)-Xiamen (XIAM) baselines are close to the long axis of the ellipse, the Luzhou (LUZH)-Delingha (DLHA) baseline connects the epicenters of the Kunlun Mountain and Wenchuan earthquakes, and the Luzhou (LUZH)-Kunming (KMIN) baseline is perpendicular to the long axis. Together, these baselines can reflect the characteristics of the stress field before the Wenchuan earthquake.

We used ground tilt data from the Wenchuan deformation observation station. A quartz pendulum tiltmeter was used for continuous tilt observations before the Wenchuan earthquake. The instrument was located in a cave with a depth of 25 m, a covering layer of 40 m, and an annual temperature difference of less than 0.3˚C. The tiltmeter, which had a distance of 5.0 m between the light spot and rod, was placed on a marble pier and produced an analog record from manual hourly values. Since October 2002, the tiltmeter has recorded a normal pattern with a stable change curve. From tidal analysis of EW and NS tilt, we found that the change in the tidal factor was relatively stable. The errors in the tidal factor in the NS and EW directions were 0.019 and 0.094, respectively, and the relative errors were within 1%. From long-term ground tilt data, the annual variation law of NS tilt is good and there was no significant anomaly before

the Wenchuan earthquake. In contrast, there was a significant change in the EW tilt. Owing to a westward blocking effect of the South China Plate, the EW tilt has dipped westward since the beginning of the observation period in October 2002.

To analyze the characteristics of seismicity before the Wenchuan earthquake, the strain energy released by the M_{S} ≥ 5.5 earthquakes was calculated using the empirical formula of energy magnitude (1), taking a 1-month window length and 1-month sliding step length for data in the China earthquake catalogue [

log E = 1.5 M S + 4.8 (1)

where E is the energy released by an earthquake with magnitude Ms. The cumulative Benioff creep at time t was calculated as follows [

ε = ∑ i N t E i (2)

where, N_{t} is the number of earthquakes occurring in the selected area before time t, and E i is the Benioff creep of the i-th earthquake. Cumulative Benioff creep ε can reflect the level of seismic energy release from blocks or faults [

Based on GNSS daily resolution results, several baselines around the gap ellipse were calculated, with the calculated length being the geodesic line between the two stations. The baseline length of the first day was set to zero so as to record relative change. At the same time, to filter out the influence of high-frequency information, the sixth order DB wavelet fitting result was adopted; that is, we filtered out high-frequency disturbances with periods of less than 64 days.

The discrete Fourier transform of a ground tilt data sequence { X ( k ) } can be expressed as:

f n = 1 N ∑ k = 0 N − 1 X ( k ) e − i 2 π k N n , n = 0 , ⋯ , N − 1 (3)

where n is the discretization of the time domain and k is the discretization of the frequency domain; both are periodic at N points. For each frequency n, the square sum of the real and imaginary parts of f_{n} (i.e., the spectral value) is the square of the wave amplitude corresponding to the frequency. The frequency or period corresponding to a higher spectrum value is the predominant period of the time series.

Firstly, a time interval with a good change trend was selected as the benchmark, and linear models of the Benioff creep data and GNSS baseline data were established. Filtering was performed to obtain two nearly stable but abnormal residual sequences, and the simplest correlation model was selected. The GNSS baseline residual was taken as the dependent variable, and the Benioff creep residual was taken as the independent variable. A regression model was established to obtain the regression coefficient and fitting error between the two residual series. If more than 95% of points were less than 2 times the mean square deviation, a normal distribution was assumed and the model was considered to be accurate.

Ground tilt observed at the Wenchuan station has obvious nonlinear characteristics that can be fitted by three linear segments with a reliability of α = 97.5% (

From October 2002 to the end of 2004 (moment A), the annual variation of the ground tilt showed stable westward movement; after moment A, the ground tilt rate decreased significantly, and the amplitude increased with time until the beginning of 2007 (moment B); from point B until to the Wenchuan earthquake (May 2008), the tilt rate was close to zero.

Fourier spectra of the linear change before point A and after point B were calculated (

According to the Benioff creep calculation (_{S}8.1 Kunlun Mountain earthquake, the release rate of seismic energy accelerated until mid-2004 (point A), after which it fell significantly, showing a long-term “deficit”; in the middle of 2007 (point B), which is regarded as the sub-instability stage [

The permanent LUZH GNSS station is ~200 km away from the Wenchuan earthquake epicenter. The LUZH-DLHA baseline approximately follows the direction of the major axis of the gap ellipse, and connects the active areas of the Kunlun Mountain and Wenchuan earthquakes. Over the long-term, the baseline has been in a state of extension (

The LUZH-KMIN baseline, which is approximately perpendicular to the major axis of the gap ellipse, showed a decrease in the rate of extension from the beginning of 2007 until the Wenchuan earthquake (

The XIAM GNSS station is located on the southeast coast of China, close to Taiwan. Taiwan sits at the junction of the Philippines and Ryukyu subduction tectonic belts. The southern and northern ends of Taiwan island are connected by NW trending transfer faults. Owing to the collision of the Philippine Sea Plate and Eurasian Plate, a compressional tectonic deformation zone, mainly represented by the central mountains, has formed on Taiwan island; this zone has a large number of NE nearly north-south imbricate thrust or overthrust structures, and intense tectonic deformation and seismic activity. These processes also affect the Taiwan Strait and southeast coast [32 , 33]. As shown in _{S} ≥ 5.5 were concentrated in mid 2002, the end of 2003

to mid 2005, and the end of 2006 to mid 2007. The LUZH-XIAM baseline extends approximately along the major axis of the gap ellipse; it mainly exhibits compression owing to the NW compression and collision of the Philippine Plate and the NW compression of the Indian Plate. During the intervals between these clusters, the baseline experienced rapid changes in compression (

The LUZH-GUAN baseline changed significantly before the Wenchuan earthquake. From early 2005 to mid 2007 it experienced rapid compression, which is rare in South China. However, from the end of 2007 until the Wenchuan earthquake the baseline experienced extension (

By comparing the variations in the Benioff creep (

To investigate this further, we converted the daily LUZH-GUAN baseline data into monthly sampling, with 1 sample per month. November 2001 was taken as the first value, i = 1; the Wenchuan earthquake month was i = 79, and December 2008 was the last month in the analysis (i = 86).

Based on the baseline and Benioff creep data before December 2004, a linear model was constructed and filtered to obtain the residual dL_{i}, dε_{i}:

d L i = Δ L i − ( 0.077 ⋅ i − 3.584 ) (4)

d ε i = ε i − ( 0.0552 ⋅ i + 2.7478 ) (5)

where, L i and d L i are the baseline relative value and residual value, respectively (both in mm); and ε i , d ε i are the standardized Benioff creep and linear filtering residual values, respectively (both in 10^{8}).

Correlation analysis yielded the following formulas:

d L i = 6.0 ⋅ d ε i + Δ i , i = 1 - 78 (6)

Δ i = d L i − 6.0 ⋅ d ε i , i = 1 - 78 (7)

where Δ_{i} is the fitting error of the LUZH-GUAN GNSS baseline based on seismic strain; its root mean square error is 1.7 mm and it obeys a normal distribution with 96.2% probability. According to the fitting results given in

After the Wenchuan earthquake, assuming that 50% of the earthquake energy was converted into strain energy, an energy balance can still be achieved with the model (8):

Δ i = d L i + 3.0 ⋅ d ε i , i = 79 - 86 (8)

The linear balance results are shown in _{i} over the whole process was zero, and the fitting error was 1.68 mm; the data obey a normal distribution with 96.55% reliability. In summary, our results show that the accumulation of strain energy (expressed as the shortening of the baseline) before the earthquake was balanced by the release of seismic strain energy during and after the earthquake.

By analyzing tilt data from the epicenter area, along with GNSS baseline and seismicity data from peripheral and distal regions, we obtained far- and near-field crustal deformation information for before and after the Wenchuan earthquake. From our analysis, we identified the distribution characteristics of crustal stress field changes before the earthquake, which provides an important basis for understanding the significance of geophysical field observations and for improving the layout of observation networks.

The ground tilt changes observed near the epicenter of the Wenchuan earthquake are consistent with normal pre-earthquake deformation, including a linear loading process (α), nonlinear strain accumulation (β), and pre-seismic sub-instability (γ). The linear loading process was consistent with the background

stress of the Wenchuan station, and the westward tilt reflects the joint action of Indian Plate compression and South China Plate resistance. The nonlinear change mainly reflects a slowing of the change rate, indicating a significant change in crustal properties or in the strain accumulation [

The characteristics of the pre-seismic sub-instability deformation identified in this study differ from the current understanding, and the sub-instability differed from the instability. Before and after the sub-instability stage, different structural areas played different roles in deformation. Based on 40 years of tilt and strain from Japan, Takemoto [

During strain energy accumulation, the change in the ground tilt of the Wenchuan earthquake epicenter area, the seismicity in surrounding area, and the change along large-scale GNSS baselines showed strong synergistic characteristics. Points A and B (marked in

Our results confirm that before some large earthquakes, it is difficult to observe accelerated deformation near the epicenter; however, observations in peripheral and distal areas may be more prominent. The Kunlun Mountain and Wenchuan earthquakes both occurred when long-term extension of the LUZH-DLHA GNSS baseline was reversed (i.e., there was a period of shortening); the Kunlun Mountain and Wenchuan epicenters were close to the DLHA and LUZH GNSS stations, respectively. This indicates that far-field stress disturbances may directly trigger some large earthquakes.

Finally, owing to the influence of deep fluid or plastic material flow, deformation observed under natural conditions usually reflects changes in the stress-strain field, and is characterized by spatial migration; therefore, it differs from coseismic deformation. Moreover, our results are also in contrast to the generally accepted understanding of crustal deformation characteristics before large earthquakes. The results of this study have significance for the improved understanding of geophysical field observations and the complexity of earthquake precursors; moreover, the results will help in innovating the idea of earthquake prediction.

We thank the First Monitoring and Application Center of the China Earthquake Administration for providing the GPS time series datasets. This research was funded by the National Key R&D Program of China, grant number 2018YFC1503606, and the National Natural Science Foundation of China, grant number 41330314.

The authors declare no conflicts of interest regarding the publication of this paper.