Chong Yue ,Chunheng Tng ,Wei Yn ,Xioong Pn ,Xueme Li ,Yuwen Tn ,Zongfeng Zhng,Tinlong Yu

a China Earthquake Networks Center,Beijing,100045,Beijing,China

b Earthquake and Volcano Prediction Research Center of Jilin Province Seismological Bureau,Changchun,130117,Jilin,China

c Fengman Seismostation of Jilin Province,Jilin,132108,Jilin,China

d Shuangyang Seismostation,Earthquake Administration of Changchun City,Changchun,130060,Jilin,China

Keywords:Water-tube tiltmeter at shuangyang seismostation Water level of shuangyang lake Finite element method Difference of the ground deformation

ABSTRACT This article analyzes the relationship between the water level and the water-tube tilting in Shuangyang lake,based on the differential deformation features reflected by the NS and EW components of the water-tube tiltmeter.The results show a good spatiotemporal consistency between the variation of water level and the NS tilt component,which is considered to be affected by the magnitude and duration of the water level variation in Shuangyang Lake.The article uses Landsat remote sensing image data to extract the water boundary of Shuangyang Lake,and takes advantage of the finite element numerical simulation method to build three-dimensional models for different geological structural conditions of the Shuangyang seismostation.The simulation results show that when the underground medium is granite,the effect of water level variation on the vertical displacement of the surface is non-directional.With a 50-m soil layer in Model 2,the simulated NS tilt variation is equivalent to the actual observed water-tube tiltmeter NS component when the water level variation is 0.44 m and 0.8m.When the variation of water level reaches 2.0m,the simulation result of the NS component is 79.6 ms,which is slightly larger than the observed result of 60.32 ms.However,the simulation results show that the variation of the EW component is significantly smaller than that of the NS one.Due to the fact that the Shuangyang lake is long in the NS direction and short in the EW direction,the existence of the soil layer tends to generate ground deformation along the NS direction in the vicinity of the lake after the increase of water level,thereby resulting in the difference of the ground deformation in the two directions.

1.Introduction

The crustal tilt observation of is one of the most sensitive means to reflect crustal deformation and the stress field.The current crustal tilt observation includes water-pipe tiltmeter,horizontal pendulum tiltmeter and vertical pendulum tiltmeter,and its measurement accuracy can reach 10-10—10-9(Niu,2017).Among them,water-tube tiltmeter is designed according to the principle that the water surface in the connecting pipe maintains a natural level.The longer connecting pipe results in a higher signal-to-noise ratio of the water-tube tiltmeter than the other two methods.The summary of past earthquake cases show that numerous crustal tilt anomalies appear before earthquakes (Lv,2010;Tang and Zheng,2018).At the same time,due to the fact that most of the stations are located in caves,sensitive crustal observations are susceptible to different interference factors such as close pumping,excavation,and reservoir storage (Li et al.,2011;Chu et al.,2015;Zhang et al.,2016),which interfere the determination of earthquake precursor anomalies.Therefore,in the actual data analysis process,quantitative calculation methods and means need to be combined to quantitatively calculate and determine the magnitude,direction,and difference characteristics of the data variation that may be caused by interference factors.

Since the installation of the Shuangyang crustal water-tube tiltmeter,the observation data have been continuously recorded and the instrument observation status has been in a stable state with low noise level(Yu et al.,2007).Prior to most of the earthquakes ofM5.0 or above in Jilin Province,the water-tube tiltmeter showed significant variations in the annual amplitude and anomalous changes in tidal factors (Tang and Zheng,2018),which further provides reference for our study of anomalies before earthquakes.However,the results corresponding to the earthquake show that the abnormal variation in the NS tilt component of the water-tube tiltmeter is the most significant,larger than the EW component.In addition,after the replacement of the water-pipe bowl in 2016,the NS component showed more times of rapid short-term southward variation in the rainy season in August every year,while the EW component did not vary synchronously.Such remarkable difference between the two tile components is anomalous and relevant research on the Shuangyang water-tube tiltmeter is needed.In order to analyze the short-term rapid tilt variation of the Shuangyang water-tube tiltmeter which is possibly affected by rainfall,we construct three-dimensional finite element models with different geological structural conditions in the study area,for the purpose of simulating the influence of the water level variation of Shuangyang Lake caused by rainfall on the NS and EW tilt components of the Shuangyang water-tube tiltmeter.Combining with the focal mechanism solution of moderate to strong earthquakes in the study area,the mechanism of the directionality associated with the water level of Shuangyang Lake and that of earthquake precursor anomalies are further discussed.

2.Overview of Shuangyang Station and characteristics its watertube tiltmeter

2.1.Shuangyang Station

Shuangyang seismic station is located on the west side of Beishan in Shuangyang District,Changchun City,Jilin Province and the ground surface around the station is relatively gentle (Fig.1).The water-tube tiltmeter is arranged inside the cave,and the depth from the opening of the cave is 129.2 m (Yu,2007).The lithology of the instrument installation platform is Yanshanian granite,which is relatively broken in the cave.The NE-trending Yitong-Shulan fault is located beneath the north side of the station.There are two minor faults exposed inside the cave,with NW strike and NE inclination.Furthermore,there is no artificial covering above the cave,and the thickest covering of the cave reaches to approximately 38 m.The cave is located on the hillside,after rainfall,the rainwater often flows rapidly along the river as there are no water storage areas under the mountain.The lake locates approximately 3.5 km to the southeast from the station,with an area of about 650 hectares(Fig.1(a)).Notably,the water level of the Shuangyang lake often rises due to the convergence of the water from adjacent basins after concentrated rainfall.

2.2.Characteristics of the Shuangyang water-tube tiltmeter

Since the replacement of the water-pipe bowl in 2016,the NS component of the water-tube tiltmeter has experienced rapid short-term changes several times;on the contrary,the EW component has not changed significantly in the same period from July to August when the rainfall is concentrated (as shown in Fig.2).The environmental interference factors around the station (Fig.1(b)) show that the main load impact caused by concentrated rainfall in this area is the Shuangyang Lake(Fig.1(a)).Other lakes are far from the station,so the article collects the water level data of Shuangyang Lake during the same period when the Shuangyang water-tube tiltmeter varies rapidly.

It can be seen from Fig.2 that there is a certain difference between the sampling rate of the water-tube tiltmeter and water level.Among them,the water-tube tiltmeter displays the whole point value data (24 sets of data a day),while the water level of Shuangyang Lake is the daily data at 8 o'clock(a set of data a day).The rapid variation of the water level(the black histogram in Fig.2) is lagging behind the rapid S-tilt of the NS component(the black curve in Fig.2),but the rapid S-tilt variation of the NS component is always accompanied by the rise of the water level.The better time consistency also further proves that the water level variations of Shuangyang Lake lead to short-term accelerated variations in the inclination of the Shuangyang water-tube tiltmeter.However,the water level variation of Shuangyang Lake has significant differences in influencing of the Shuangyang water-tube tiltmeter.The results of the EW component item are not significantly changed(the red curve in Fig.2)in the four time periods.During the period when the water level changes prominently,the variation of the EW component is equivalent to the single-day maximum variation amplitude of the solid tide(marked by the dotted arrow in Fig.2).By contrast,the four large variations of the NS component reach 24.12 ms,19.88 ms,30.93 ms,and 60.32 ms,respectively.In the short term,the variations of the NS component are all larger than the maximum daily variation of solid tide.At the same time,the variation characteristics of the water level of Shuangyang Lake suggests that the water level has a steep short-term rise and fall in 2016,the former of which has only lasted for 2 days,different from the water level features that gradually increase and then decrease in other years.This is the possible reason why the inclination variation of the NS component varies only 24.12 ms,while the water level variation reaches to about 1.36 m,which is smaller than the 30.93 ms variation caused by the 0.8 m water level variation in 2018.In addition,it can be seen that the inclination of the Shuangyang water-tube tiltmeter is affected by the magnitude and duration of the water level variation in Shuangyang Lake,and the water level may have exerted direction-dependent influence on the inclination of the water-tube tiltmeter in that the change of the NS component is significantly greater than that of the EW component.

Fig.1.Distribution of Shuangyang Station and the original data sequence diagram of Shuangyang water-tube tiltmeter.(a) Landsat remote sensing image;(b),(c) Original observation data of the NS and EW components of the Shuangyang water-tube tiltmeter.

In order to further analyze the reliability of the data during the rapid variation of the Shuangyang water-tube tiltmeter,the results of the M2wave tidal factor of the NS and EW components during the period of concentrated rainfall from June to September are calculated,as shown in Fig.3.The calculation results show that the M2wave tidal factors of the NS and EW components are relatively stable.The M2wave tidal factor of the NS component is around 0.53,and that of the EW component is around 0.46.To conclude,the rainfall around the station has not affected the instrument observation,and the data quality is reliable.

Fig.2.Time series diagram of the NS and EW components of the Shuangyang water-tube tiltmeter and the water level of Shuangyang Lake(a)2016-07-01-2016-08-13(b)2017-08-01-2017-08-30;(c)2018-08-01-2018-08-30;(d) 2019-08-01-2019-08-30.

3.Design of the models

3.1.Model parameters

This article focuses on simulating the load impact caused by the water level variation of Shuangyang Lake.The model is designed with a scale of 50 km length and 50 km width.In order to avoid the influence caused by the boundary effect of the model,Shuangyang Station is set to be located in the center of the model.Furthermore,the distance between the left and right sides of the model is 25 km,and the depth of the model is designed to be 10 km.Because the lithology of the foundation in the water-tube tiltmeter is Hercynian granite,the cave is not artificially covered,and the top of the cave is covered with a maximum thickness of 38 m.Considering the erosion of the rainfall on the top of the mountain,two models are designed in this article.Model 1 is a full granite model,while Model 2 is established with a 50-m overburden layer and an underlying granite layer (as shown in Fig.4(a)).We do not consider the impact of fault activity on the observation of the water-tube tiltmeter in the two models.

3.2.Boundary condition settings

The article uses Landsat remote sensing image data(resolution 30 m)to extract the water boundary of Shuangyang Lake,and selects the Shuangyang Lake boundary(Shuangyang Lake in Fig.3(a)) as the main load area of the model.Additionally,we count the results of the water level difference of the Shuangyang Lake when there is a short-term variation in Shuangyang water-tube tiltmeter from 2016 to 2019,and the four-year water level difference results are:1.36 m,0.44 m,0.8 m,2.0 m.We first convert the water level variation into a pressure load in an ascending order:0.4 m,0.8 m,1.36 m,2.0 m(calculate parameters:the water density is 103kg/m3,and the acceleration of gravity is 9.8 m/s2),and then we apply pressure loads on the surface of Shuangyang Lake sequentially in four analysis steps.The bottom of the entire model is fixed in the Z direction,the west and east sides of the model are fixed in the X direction and the north and south sides of the model are fixed in the Y direction.The surface of the model is set as free.Notably,we only consider the load effect caused by the water level variation of Shuangyang Lake.Regardless of gravity,the elastic body model is used for simulation calculation.Taking into account the different lengths of the water-tube tiltmeter,the length of the NS and EWcomponents are 33.18 m and 23.42 m,respectively.The outer boundary grid size of the entire model is 1km,and the grid is refined at the boundary of Shuangyang Lake,with a grid size is 50 m.Finally,a total of 81 714 grid cells are obtained for the entire model.The boundary condition setting of Model 2 and diagram of model meshing are shown in Fig.4.

4.Simulation results

The article obtains four kinds of water level loading effects on the displacement of the model through simulation.By using the displacement difference in NS and EW directions to the adjacent grid nodes(the distance between the two nodes is 50 m)along the Z direction on the surface of the model,we convert the displacement value to the inclination under the length of the NS and EW components.The simulation results are shown in Fig.5 and Fig.6.Fig.5 is a comparison diagram of the measured data and the simulated results,and Fig.6 is the results of the vertical displacement of the surface obtained by Model 1 and Model 2.Because the water level variation in this article is relatively synchronized with the instrument's“response”(except the variation was slightly smaller in 2016),we assume that the water level variation of Shuangyang Lake is the most important factor in the tilt variation of the Shuangyang water-tube tiltmeter.Using the water level variation of 0.44 m(2017)and 0.8 m(2018)as the input condition,the“response amount”of the NS component is utilized as a constraint to test different combinations of Young's modulus and Poisson's ratio (Yang et al.,2018;Ji Jingchen,2019;Zhao et al.,2019) and to obtain the model parameters closest to the variation.The Young's modulus and Poisson's ratio of the granite in Model 1 are 4＊109Pa and 0.25,respectively.While those in Model 2 are 1＊1010Pa and 0.25,respectively.The two parameters in the overburden layer are 1＊107Pa and 0.32,respectively.

In Fig.5,the circle dotted solid lines represent the NS components,the triangle dotted lines stand for the EW components,the red lines are the results of Model 1,the blue lines are results of Model 2,and the green lines are the actual observed results.The actual measurement results of the water-tube tiltmeter show that the NS component gradually increases with the increase of the water level variation (except for the 1.36 m in 2016).In contrast,the measured EW component varies slightly with the increase of the water level variation;however,the deformation trend and amount are significantly smaller than those of the NS component.When the underground medium is all granite (Model 1),the NS and EW components exhibit same deformation trend.The difference between the two simulated components is mainly caused by the length of the observation pipe.That is to say,when the underground medium is granite,the increase in the load induced by the rise of the water level shows no directional difference in the inclination amount of the water-tube tiltmeter.The vertical displacement results obtained from the simulation in Model 1 (Fig.6(a),Fig.6(b)) indicates that the maximum vertical displacement of the ground associated with the rise of the water level is mainly concentrated in the center of Shuangyang Lake.After the variation of the water level load,a near NS elliptical displacement contour with Shuangyang Lake as the center is formed.However,due to the high Young's modulus of the granite itself,the load variation caused by the water level has a lower impact on the surrounding vertical displacement.The contour results in Fig.6(b) show that the farther away from the boundary of Shuangyang Lake,the greater the distance between adjacent contours.Besides,the vertical displacement of the Shuangyang station exhibits no difference in the NS and EW directions.The NS and EW components of the Shuangyang water-tube tiltmeter show more consistent variation after the load varies,which is not consistent with the actual observation of the difference variation in the NS and EW components.

Fig.3.Tidal factor of M2 wave in the NS/EW component of the Shuangyang water-tube tiltmeter.

Fig.4.(a).Boundary condition setting of Model 2;(b).Diagram of model meshing.

Fig.5.Comparison diagram of the measured data and the simulated results.

When the model includes the 50 m overburden layer (Model 2),the variation in the simulated NS component is equivalent to the actual observation results when the water level variation is 0.44 m and 0.8 m.When the water level variation reaches 2.0 m,the NS-direction simulation result is 79.6 ms,which is slightly larger than the measured result of 60.32 ms.However,at this time,the variation of the EW component obtained by the simulation is significantly smaller than that of the NS component.The simulation result shows that the variation of the EW component is only 21.3 ms when the water level variation is 2.0 m.

The vertical displacement results obtained by the simulation show(Fig.6(c)and(d))that:affected by the presence of the overburden layer,the vertical displacement of the surface generated by the water level is larger than the displacement in Model 1,and the largest vertical displacement change is mainly concentrated in Shuangyang Lake.In the surrounding area,the vertical displacement along the boundary of Shuangyang Lake gradually decreases.The surface distribution of Shuangyang Lake is about 5.2 km long from north to South and 3.4 km wide from east to west,so the settlement and deformation characteristics around the lake are not uniform.As shown in Fig.6(d),it can be seen that the vertical displacement variation on the left and right sides of Shuangyang Lake(along the NS direction)are relatively uniform,while in the upper and lower areas of Shuangyang Lake(along the EW direction),the vertical displacement variation is characterized by inhomogeneous deformation.That is,when the overburden layer exists (inhomogeneity of the medium),the surface deformation will be uneven.However,when the Shuangyang Lake,which is long from north to south and short from east to west,changes the load due to the rise of the water level,the displacement along the NS direction will be greater than that of the EW direction.As a result,the Shuangyang water-tube tiltmeter can record the displacement variation in the NS direction,but there is no synchronous variation in the EW direction.

5.Discussion

The simulation results above show that when the subterranean medium is only composed of granite,there is no directional difference in the inclination variation of the Shuangyang water-tube tiltmeter when the Shuangyang Lake water level rises.However,when the model includes a 50 m overburden layer,compared with granite,the lower Young's modulus of the overburden layer will lead to more surface deformation.In Shuangyang Station,which is 3.5 km away from the boundary of Shuangyang Lake,the NS component variation obtained by Model 2 is equivalent to that of Model 1;however,due to the particular shape that the length of Shunagyang lake is long in NS and short in EW,the vertical displacement around Shuangyang Lake is much larger in the NS direction than in the EW direction.That is,Shuangyang Lake,which is mainly distributed in the NS direction,is more likely to cause deformation along the NS direction on the surface around the lake,while the east-west direction deformation is not obvious.In turn,the Shuangyang water-tube tiltmeter shows different deformation characteristics in its NS and EW tilt components.

Fig.6.Vertical displacement simulation results,(a)simulation results in Model 1,(b)enlarged view of Shuangyang Lake in Model 1,(c)simulation results in Model 2,(d) enlarged view of Shuangyang Lake in Model 2 (displacement downward is negative,up is positive).

Before many earthquakes ofM5.0 or above in Jilin Province,the NS component of the Shuangyang water-tube tiltmeter showed a decrease in annual amplitude;however,there were no obvious abnormal variation in the EW component.This article collects the focal mechanism solution results of shallow earthquakes aboveMW4.7 around the Shuangyang station since 2005(https://www.globalcmt.org/).The results show that the Qianguo earthquake in 2006,the Qianguo earthquake swarm in 2013 and the Songyuan earthquake in 2017,mainly occurred on the NEtrending fault named Fuyu-Zhaodong fault (Pan et al.,2018;Li et al.,2020).In addition,most of the faults are strike-slip faults.The results of GPS calculations show that the plane strain rate in this area from 2012 to 2017 is featured by NE-SW compression (Yu et al.,2016),which is consistent with the direction of the seismogenic faults of the aforementioned earthquakes.

In the northern part of Shuangyang station,there is a NE-trending Yitong-Shulan fault (as shown in Fig.7(b)).During the active process of this fault,secondary faults perpendicular to the fault (ie,northwestward)are often formed(the red dashed line in Fig.7(b))(Yu Zhongyuan,2016),which is more consistent with the fact that there are two northwest strike and northeast inclination minor faults exposed inside the cave.During the seismogenic process of the earthquake,the variation of the tectonic stress is more easily transmitted through the northwestward secondary faults.Then,the NS inclination occurs in the area,which is captured by the NS component of the Shuangyang water-tube tiltmeter,thereby exhibiting the feature of smaller annual amplitude variation(Fig.1(b)).In contrast,the variation in the EW component of the Shuangyang water-tube tiltmeter is not significant (Fig.1(c)),and the abnormal difference between the two tilt components before the earthquake has appeared.

6.Conclusion

Based on the differential deformation features of the NS and EW components of the Shuangyang water-tube tiltmeter after rainfall,the paper analyzes the possible influencing factors around the station,and determines the load factors caused by the water level of Shuangyang Lake.The relationship between the water level of Shuangyang Lake and the inclination of the Shuangyang water-tube tiltmeter is analyzed.Using Landsat remote sensing image data,this article extracts the boundary of Shuangyang Lake,and taking advantage of the finite element simulation method,three-dimensional finite element models with different geological structural are established.Finally,we obtain the difference in the influence of the load variation caused by the water level of Shuangyang Lake on the NS and EW components of the Shuangyang water-tube tiltmeter.Some major conclusions are listed as follows:

Fig.7.(a) Distribution of the focal mechanism solutions of historical earthquakes in Northeast China and (b) regional geological structure map of Shuangyang.

(1) From 2016 to 2019,the rapid southward variation of the NS component of the Shuangyang water-tube tiltmeter is consistent with the rapid variation of Shuangyang Lake water level.The tilt variation of the NS component is affected by the magnitude and duration of the water level variation of Shuangyang Lake,while the EW component is not greatly associated with the water level variation of Shuangyang Lake.

(2) When the underground medium is only composed of granite,the water level of Shuangyang Lake rises to form a near NS elliptical displacement contour around Shuangyang Lake.Same inclination displacements are formed in the NS and EW directions,indicating that the vertical displacement variations are not directionally dependent.

(3) After adding a 50 m overburden layer in Model 2,when the water level variation is 0.44 m and 0.8 m,the simulated NS tilt variation is equivalent to the actual observed inclination.When the water level variation reaches 2.0 m,the simulation result of the NS component is 79.6 ms,which is slightly larger than the measured 60.32 ms,and the variation of the EW component is significantly smaller than that of the NS one.The simulation results suggest that the existence of the overburden layer has led to the NS deformation on the ground surface around the Shuangyang Lake due to its special shape.Such deformation is thus reflected by the watertube tiltmeter which shows different deformation characteristics in the NS and EW components.

However,limited by the results of underground wave speed and borehole information in the area,the article makes necessary simplifications on the continuity,anisotropy,physical parameters,and fluctuations of the terrain.In addition,this article does not consider the influence factors such as underground fluids (Yang et al.,2019;Zhang et al.,2019).Through the comparison of the two sets of models,the mechanism of the difference between the NS and EW components of the Shuangyang water-tube tiltmeter affected by the water level of Shuangyang Lake is analyzed.Furthermore,the differences between the rapid variation after rainfall and the mechanism of the NS and EW components before the earthquakes are discussed.In the future,with the gradual improvement of the data quantity in the study area,further investigations will be conducted on the mechanism of earthquakes.

Acknowledgements

This study is sponsored by National Key Research and Development Program of China(2018YFC0807000);The Spark Program of Earthquake Technology of CEA(XH20070Y);The Earthquake Tracking Task of CEA(2021010221).