Earthquake Reaearch in China  2017, Vol. 31 Issue (2): 188-200
Tidal Response Characteristics of the Well Water Level in the Sichuan-Yunnan Region
Gong Haobo1, Li Guangke1, Liao Xin2, Guo Weiying1, Chen Min1
1. Earthquake Administration of Chongqing Municipality, Chongqing 401147, China;
2. Institute of Disaster Prevention, Sanhe 065201, Hebei, China
Abstract: In this paper, the long time series data of the well water-level data of 12 wells in the Sichuan and Yunnan area is analyzed by the Baytap-G tidal analysis software, and well water level tidal response characteristic parameters (amplitude ratio and phase change) are extracted. We analyzed the features of the shape and stage change, and characteristic parameters of the tidal response of well water level before and after the earthquakes, which can provide a new method and approach to analyzing the response relationships between well water level and earth tide and barometric pressure. The results show that Luguhu Well and 9 other wells are affected by earth tides, and their well water level amplitude ratios and phases are relatively stable; the Nanxi Well and Dayao Well water level changes are affected by the barometric pressure combined with tide force, and their well water level amplitude ratios and phases are more discrete. The water level amplitude ratios and phases of Jiangyou Well, Luguhu Well and Dongchuan Well are significant to large earthquakes, and the relationship between seismic energy density and water level amplitude ratios and phases of M2 wave of the three wells are presented.
Key words: Well water level     Tidal response     Sichuan Yunnan Region

INTRODUCTION

There are many factors that cause a change of well water level. They include tectonic stress factors derived from geological activities and plate movements, as well as non-tectonic stress factors derived from natural and anthropogenic phenomena (earth tide, atmospheric pressure, rainfall, artificial water injection or pumping, etc.). The tectonic stress factors are generally non-periodic changes, but the non-tectonic stress factors generally have a certain change cycle and frequency. Among them, the earth tide and atmospheric pressure on the well water level is a periodic loading, the variation of the stress in the size, direction and amplitude is regular and periodic, and the change of the water level is caused by elastic deformation.

Many scholars have studied the influence of the tide(Bredehoeft, 1967; Hsieh et al., 1987; 1988; Zhang Zhaodong et al., 1991) and atmospheric pressure on well water levels (Weeks, 1979; Van Der Kamp and Gale, 1983; Rojstaczer and Riley, 1990; Zhang Zhaodong et al., 1986, 1989, 1993; Ding Fenghe et al., 2007; Zhang Ziguang et al., 2010). Based on the study of the response of the well level to the background signals of earth tide and pressure tide, we can obtain a quantitative study on the bearing pressure of aquifer, the characteristics of the aquifer medium, especially the fluid flow characteristics and its evolution with time (Hsieh et al., 1987; Doan et al., 2006; Elkhoury et al., 2006; Xue et al., 2013). It provides a reference for the further study of the hydrogeological conditions in the fault zone, the extraction of the stress and the change of the medium related to seismic activity and the prediction of the earthquake.

In this paper, based on the understanding of the normal dynamic change of well water level to stress, the tidal response characteristic parameters (amplitude ratio and phase change) of the 12 wells in the Sichuan-Yunnan area were calculated with Baytap-G tide analysis software (Ishiguro and Tamura, 1985), the characteristics of its shape and phase change, and the change before and after the earthquake were analyzed. In addition, the energy density is used to analyze the variation characteristics of the tidal parameters for different seismic responses in the same well. It provides a new method to analyze the response relationship between well water level and earth tide and barometric pressure.

1 SELECTED TIDAL EFFECT WELLS

The data of this paper comes from the precursor network database of the Earthquake Administration of Yunnan and Sichuan Provinces. There are many well water level observation points in the Sichuan-Yunnan area, and many years of continuous observation data. However, the stability and continuity of the data are different because of different observation conditions. The following principles should be followed when choosing a well: (1) the water level is stable and the data is accurate and continuous; (2) the well water level has a good response to the tides, and the changes of the day and month are mainly caused by the change of earth tide and atmospheric pressure. Based on the analysis of the dynamic change of water level, considering the distribution of the main tectonic zone and the caution area of Sichuan-Yunnan, and according to the results of the evaluation, 12 wells were selected in the study, 7 of which are located in Yunnan and the other 5 in Sichuan. Among them, the wells PZH and XC are the dynamic water level observation, the water level indicates the change of the head, and the other 10 wells have a static water level. The water level is defined as the distance between the liquid surface from the wellhead. The distribution of wells location is shown in Fig. 1. The basic conditions of each well point are shown in Table 1.

 Fig. 1 Selected well location and distribution of the Wenchuan earthquake epicenter

Table 1 Basic information of selected wells
2 CALCULATION OF TIDAL DYNAMIC CHARACTERISTICS OF THE WELL WATER LEVEL 2.1 The Calculation Method of Tidal Parameters of Well Water Level

The tidal amplitude ratio and phase change are the effective parameters to analyze the tide of well water level. The amplitude ratio is the ratio of the observed tidal amplitude to the theoretical tidal amplitude, and the phase change is the difference between the actual tidal phase and the theoretical tidal phase. Taking the ideal well aquifer system as the research object (Hsieh et al., 1987), considering that the aquifer is the most typical horizontal layered confined aquifer, at the same time, it is assumed to be a homogeneous isotropic elastic medium with continuous saturation and an isotropic permeability property. On this basis, the change of water pressure in the aquifer is considered as the harmonic disturbance, and the change of the well water level is the harmonic response, the amplitude ratio δ and the phase change φH-h:

 $\delta =|{{h}_{0}}/{{H}_{0}}|={{({{E}^{2}}+{{F}^{2}})}^{-1/2}}$ (1)
 ${{\varphi }_{H-h}}=\text{arg}\left({{h}_{0}}/{{H}_{0}} \right)=-\text{ta}{{\text{n}}^{-1}}\left(F/E \right)$ (2)

In the formula, h0 and H0 are respectively the tidal partial wave amplitude of the well water level with frequency of ω and the tidal wave amplitude of pressure head in aquifer; $E\approx 1-\omega r_{c}^{2}\text{Kei}\left(\alpha \right)/2T;F\approx \omega r_{c}^{2}\text{Ker}\left(\alpha \right)/2T;\alpha \approx {{r}_{w}}\sqrt{\omega S/T};$ S is water storage coefficient, the value of most confined aquifers is 10-3-10-5; T is hydraulic conductivity, ω is a tidal partial wave frequency of well water level and pore pressure; Ker and Kei are the real and imaginary parts of Kelvins function, respectively; rw is the radius of the pipe; rc is the radius of the well casing or the radius of the hole in the fluctuation range of well water level. Here, the essence of the pressure head is the pore water pressure head of the aquifer from the hole, which is the pressure head of the aquifer under undrained conditions; the δ indicates the ratio of the amplitude of the well water level to the pressure head amplitude of the aquifer under undrained conditions. According to the formula (1) and (2), the response of well water level to the pore pressure under undrained condition of aquifer, that is, the well water level tidal amplitude ratio and phase are affected by the aquifer hydraulic conductivity T, the water storage coefficient S, the well diameter parameter rc and rw, and the frequency of tidal signal ω.

In this paper, the Baytap-G program is used to conduct calculations. The advantage of this method is the estimation the regression coefficients of the tidal parameters, drift and meteorological time series using the iterative method, and the Bayesian information principle is used to estimate the optimal parameters, which improves calculation precision (Ishiguro and Tamura, 1985). The basic principle is to divide the time series of the well water level as follows:

 $y\left( t \right)=\sum\limits_{m=1}^{M}{{{\delta }_{m}}}\sum\limits_{n={{\alpha }_{m}}}^{{{\beta }_{m}}}{\left[ {{A}_{mm}}\text{cos}\left( {{\omega }_{mm}}t+{{\varphi }_{mm}}+\Delta {{\varphi }_{m}} \right)+Dr\left( t \right)+R\left( t \right)+h\left( t \right)+\varepsilon \left( t \right) \right]}$ (3)

In the formula, M is the number of waves, αm and βm are the beginning and ending of m wave groups in the tide table; Amm, ωmm, φmm are the theoretical amplitude, angular frequency and initial phase of the n tidal component in the m wave group, respectively. δm, Δφm is the tidal amplitude ratio and phase difference to be estimated for the first M wave group; Dr(t) is the long term trend; R(t) is the disturbance caused by meteorological factors; h(t) is the step variable caused by human factors or instrumental factors; ε(t) is the observation noise.

2.2 Calculation of Tidal Parameters of Well Water Level

In this paper, using the Baytap-G tidal analysis program, the data window length sets as 720h, and the sliding step is 360h. If the missing number is greater than 360h, the segment data is invalid and not used for tidal analysis. Normally, the results of each window are drawn at the beginning of the window length. According to the results of the preliminary analysis, the M2 wave amplitude ratio and phase difference of the 10 wells of the earth tide effect wells such as YA and the calculation errors are calculated (Fig. 2, Fig. 4). The amplitude ratio and phase of P1S1K1 wave and the calculation error are given for the combined effect of tide force and atmospheric pressure wells such as DY and NX (Fig. 3, Fig. 5). Select the southwest region in China (including Chinese and Myanmar border) where M≥6.0 strong earthquakes have occurred (excluding the Wenchuan aftershocks) and global impact of these wells in M≥8.0 huge earthquakes since 2007. The basic information of earthquakes is shown in Table 2.

 Fig. 2 Variation of M2 wave amplitude ratio and phase change of well water level with time The vertical line represents the date of the earthquake, see Table 2

 Fig. 3 Variation of P1S1K1 wave amplitude ratio and phase change of well water level with time The vertical line represents the date of the earthquakes, see Table 2

 Fig. 4 The calculation error of the amplitude ratio and phase change of the YA well water level

 Fig. 5 The calculation error of the amplitude ratio and phase change of the NX well water level

Table 2 The basic information of selected earthquakes
3 ANALYSIS OF TIDAL DYNAMIC CHARACTERISTICS OF WELL WATER LEVEL

It can be seen from the changes of the water level amplitude ratio and phase difference of 12 wells in YA and other wells (Figs. 2, 3), the amplitude ratios and phases of well water levels affected by earth tide are relatively stable, such as LGH, PZH, XC, DC; and the amplitude ratios and phases of the well levels affected by the combined effect of tide force and atmospheric pressure are more discrete, such as DY and NX. It is possible that the tidal wave of atmospheric pressure is mixed with other factors such as thermal effect, which complicates the tidal information. According to the calculation results, the response of the M2 wave amplitude ratio and phase difference of the JY, LGH, DC3 wells to large earthquakes is more significant. The results of these 3 wells are analyzed.

3.1 The JY Well

The JY well is in the southeast of the Longmenshan Fault Zone, the Fujiang River from the east through the well. This area is mainly for the third section of the Xujiahe Formation and the third section of the Leikoupo Formation, which has a relatively thick confining bed, and non-hydraulic connection with the nearby Fujiang and the creek. The well water level was recorded in the Wenchuan earthquake (epicentral distance of 157km), decreased by 14m during the earthquake, was in a seasonal change before the earthquake and after the earthquake showed a continuous increase, indicating that the aquifer was in compressed state. August 25, 2010 -August 15, 2011 broken for unknown reasons (Fig. 6). The variation of M2 wave amplitude ratio and phase difference of the JY well is consistent with the change of water level, which show three different changes, and the amplitude and phase of the change are basically synchronous.

 Fig. 6 The JY well water level

① In the Wenchuan earthquake, the amplitude ratio and the phase difference of the M2 wave in the well water level rise simultaneously, which reflects the dredging effect of the seismic wave, and the water conductivity of the aquifer is significantly increased. ② After the Wenchuan earthquake, the water level showed a rising trend, in mid-October 2009 to mid-November turning decline, and then continued to rise. The amplitude ratio and phase of M2 wave also appear to fall and then rise, and the amplitude change is more obvious, there is no significant earthquake in the vicinity of the well area before and after the change, and the reasons for the specific changes need to be further understood. ③ The amplitude ratio and phase of the M2 wave increased simultaneously after the records were restored in August 2011, and then changed steadily in a new state. At this time the water level showed a steady trend of rising, and the aquifer continued to be in a compressed state.

3.2 The LGH Well

The LGH Well is located in the north structural belt in the south of Sichuan, and the nearby rupture is very developed. The groundwater type in this area is divided into two types: loose accumulation pore water and deep bedrock structural fissure water. The well water level began to be observed in December 2007, recorded in the Wenchuan earthquake (epicenter distance of 442km), when the water level step rose about 0.02m (Fig. 7). The phase of the M2 wave of the LGH well in the Wenchuan earthquake also increased, and the coseismic phase shift was about 16.5°, and the increase was several times the background shift. After the earthquake, the M2 amplitude ratio and phase of the well water level decreased to a stable value. It is shown that the well bore-fissure flow exchange is accelerated under the action of seismic wave, so as to clear the fissure, the permeability increases and the phase increases and tends to a stable value, indicating that the phase is only affected by the seismic wave, not subject to structural stress changes.

 Fig. 7 The LGH well water level

During 2010-2013, the amplitude ratio and phase of M2 wave in the LGH well are affected by the MS7.1 earthquake in Yushu, the MW9.0 earthquake in Japan, the MS8.6, MS8.2 earthquake in the northern part of Sumatra and the MS7.0 earthquake in Lushan. The amplitude ratio and phase rose synchronously during the earthquake, and then recovered after the earthquake.

3.3 The DC Well

The DC well is located in the Xiaojiang fault, its surface 0-95.59m for the Quaternary alluvial product, moraine block stone layer, rich in water, and the surface of the root plant, with gravel sand constitute a diving aquifer; the surface of 0-95.59m is composed of Quaternary alluvial flood and moraine rock, rich in water, and the surface of the root plant, together with gravel sand constitute a diving aquifer; 95.59-491.16m is alluvial deposit and lacustrine deposit, and its water content is weak, as the relative confining bed; 491.16-600.87m is a fracture layer of basalt bedrock, fracture development, good permeability; 600.87-605.96m is limestone, and the water content is moderate; the observation of the aquifer is located at 557.42-600.16m, and the hydraulic relationship between the overlying strata is weak.

From January 2007 to May 2009, the water level is rising, from May 22, 2009 to August 23, 2011, the number is missing, the long-term change of water level is stable after August 2011 (Fig. 8). The amplitude ratio and phase of M2 wave in DC well are affected by the MS8.6, MS 8.2 earthquake in the northern part of Sumatra, the MS7.0 earthquake in Lushan, and the MS6.5 earthquake in Ludian. The amplitude ratio and phase rose synchronously during the Sumatra earthquake and the Lushan earthquake, and then recovered after the two earthquakes. The amplitude ratio and phase increased synchronously during the Ludian earthquake, and did not return to the previous level after the earthquake.

 Fig. 8 The DC well water level
3.4 Summary

The amplitude and phase response of the well water level to the tide are considered to be a measure of the unit water storage rate and hydraulic conductivity of the aquifer. The greater the permeability, the smaller the phase lag; the smaller the permeability, the greater the phase lag. It can be seen that NX, DY, YS, LC, GD and other wells have not changed or changed very little after several large earthquakes from the curves of the M2 amplitude ratio and phase of the well water level, indicating that the seismic wave did not cause a significant increase in the flow of groundwater between the wellbore and the aquifer. It can be deduced that the earthquakes did not affect the aquifer in the wellbore area during the study period, or the aquifer strain was not significant, and the permeability did not change significantly. Among them, the NX well water level had decreased coseismic response changes in the Wenchuan MS8.0 earthquake, Lushan MS7.0 earthquake, the Japan MW9.0 earthquake, Myanmar MS7.0 earthquake and other large earthquakes, and the changes were obvious. However, the amplitude ratio and phase of the M2 wave in NX well were stable during and after the earthquakes. It can be seen that coseismic water level change is not directly related to the amplitude ratio and phase change. In addition, the amplitude ratios and phases of the M2 wave in the 4 wells of PZH, XC, YA and FP have no obvious response to many earthquakes, but they are changed because of some other factors, so it is considered that the change of the amplitude and phase is not only related to the change of the aquifer conductivity caused by seismic wave. The impact of earthquakes on the water level of JY, LGH and DC wells is obvious and the amplitude ratio and phase of the M2 waves in the 3 wells are simultaneously increased. It shows that the seismic wave increases the permeability of the aquifer in the well area.

4 ANALYSIS OF CHARACTERISTIC PARAMETERS OF SINGLE WELL TIDE RESPONSE

The process of seismic wave propagation is the process of energy release. For the same observation well, the smaller the epicentral distance and the greater the energy release, the more obvious the change of the well water level. Therefore, the seismic energy density e(r) is introduced, that is, the seismic energy per unit volume after the earthquake releases energy. The relationship between seismic energy density e(r), epicentral distance r, and magnitude of M is as follows (Wang et al., 2008):

 $e\left( r \right)={{10}^{1.45M3.03\text{lg}r4.24}}$ (4)

According to the water level of M2 wave amplitude ratio and phase change characteristics, we selected the JY, LGH, and DC wells. The seismic distance of each well is calculated by using the selected seismic latitude and longitude, and then the relationship between magnitude and epicentral distance is analyzed by formula (4), and the logarithmic plot of magnitude and epicentral distance of each well is obtained (Fig. 9), which is used to determine the energy threshold of different earthquakes.

 Fig. 9 Relationship between seismic energy density distribution and magnitude and epicentral distance (a) JY well; (b) LGH well; (c) DC well

Fig. 9(a) shows the relationship between the distribution of seismic energy density and magnitude and epicentral distance in JY well. The horizontal axis represents the epicentral distance and the vertical axis represents the magnitude. Each solid box in the coordinate axis represents an earthquake. Here, a, b, c represented three earthquakes, that is the Wenchuan MS8.0 event, Lushan MS7.0 event and Japan MW9.0 earthquake (Table 2). The line in the figure is the energy density threshold of the formula (4), the magnitude is the same, the seismic energy density is negatively correlated with the epicentral distance, the epicentral distance is the same, and the seismic energy density is positively correlated with the seismic magnitude. Among them, the energy density of Wenchuan earthquake is the largest, e(r) =5.045J·m-3, and the change of permeability coefficient of aquifer is the most significant, followed by the MS7.0 earthquake in Lushan and the MW9.0 earthquake in Japan, but neither of these earthquakes caused an aquifer permeability coefficient change.

Fig. 9(b) shows the relationship between the distribution of seismic energy density and magnitude and epicentral distance in the JY well. The a, b, c, d, e, f represented the earthquakes, respectively, that is Wenchuan MS8.0, Lushan MS7.0, Japan MW9.0, Yushu MS7.1, the northern part of Sumatra MS8.6 and Nepal MS8.1 earthquakes (Table 2). These 6 earthquakes caused the variations of the amplitude ratio and phase change of M2 wave in the water level of LGH well.

Fig. 9(c) shows the relationship between the distribution of seismic energy density and magnitude and epicentral distance in the DC well. a, b, c, e and k represent the earthquakes, respectively, that is the Wenchuan MS8.0, Lushan MS7.0, Japan MW9.0, Yushu MS7.1, the northern part of Sumatra MS8.6 and Ludian MS6.5 earthquakes (Table 2). The data is missing for the Wenchuan MS8.0 earthquake and the Japan MW9.0 earthquake. The other 3 earthquakes caused the variations of the amplitude ratio and phase change of M2 wave in the water level of DC well.

The lower limit ofthe energy density that can cause amplitude ratio and phase change is 10-3J·m-3, which can be found by the changes of phases and amplitude ratios of M2 wave in JY, LGH, DC well water levels caused by coseismicity. In the previous study on the relationship between seismic energy density and earthquakes, the lower limit of the energy density which can cause the change of permeability coefficient of aquifer is about 10-4J·m-3(Wang and Manga, 2010). When the energy density is greater than 10-3J·m-3, the seismic wave energy can more effectively remove the obstacle in the fracture, which can more significantly cause the aquifer permeability coefficient changes. The results of this study are consistent with the above conclusions, but the threshold of each well is different, if the amount of seismic samples that can cause amplitude ratio and phase is sufficient, the seismic energy density threshold that can cause the aquifer parameters change can be determined more accurately.

5 CONCLUSION

Through the analysis of this paper, the following conclusions and preliminary understanding are obtained:

(1) From the calculation results of the M2 wave amplitude ratios and phases change of the 12 wells, it can be seen that the amplitude ratios and phases change of the well water levels affected by earth tide are relatively stable, such as the LGH well. And the amplitude ratios and phases change of the well levels affected by the combined effect of tide force and atmospheric pressure are more discrete, such as the DY and NX wells. It is possible that the tidal wave of atmospheric pressure is mixed with other factors such as thermal effect, which makes the tidal information become complicated.

(2) The calculation results of the amplitude ratio and phase change of well water level are affected by various factors, such as deformation caused by tectonic stress, seismic wave and data quality. The variation range of each well is different.

(3) NX, DY, YS, LC, GD and other wells have not changed or changed very little after several large earthquakes from the curves of the M2 amplitude ratio and phase change of the well water level, indicating that the seismic wave did not cause a significant increase in the flow of groundwater between the wellbore and the aquifer. In addition, the amplitude ratios and phase changes of the M2 wave in the 4 wells of PZH, XC, YA and FP have no obvious response to many earthquakes, but they are changed because of some other factors, so it is considered that the change of the amplitude and phase is not only related to the change of the aquifer conductivity caused by seismic waves. The impact of earthquakes on the water level of JY, LGH and DC wells is obvious, the amplitude ratio and phase change of the M2 waves in the 3 wells are simultaneously increased. This shows that the seismic wave increases the permeability of the aquifer in the well area.

(4) According to the relationship between the seismic energy density and the epicentral distance, the magnitude, the lower limit of the seismic energy threshold that can cause amplitude ratio and phase change is 10-3 J·m-3 in the JY, LGH and DC wells.

This paper has been published in Chinese in the journal of Earthquake, Volume 37, Number 1, 2017.

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1. 重庆市地震局，重庆 40l147;
2. 防灾科技学院，河北三河 065201