Transfer functions of the well-aquifer systems response to atmospheric loading and Earth tide from low to high-frequency band

Authors


Corresponding author: G. Lai, Institute of Geophysics, China Earthquake Administration, No.5 Minzu Daxue Nan Rd., Haidian District, Beijing 100081, China. (cathy_313@163.com)

Abstract

[1] The transfer functions of the well-aquifer systems response to atmospheric loading and Earth tide can be used to calculate the well-aquifer properties. Due to the low signal-to-noise ratio, the study on barometric response at frequencies higher than 8 cycles per day (cpd for short) is almost blank. Using the recorded water level and barometric pressure as well as the corresponding theoretical tidal volumetric strain at 17 well stations in China, we obtained continuous barometric and tidal responses of the well-aquifer systems by cross-spectra estimation. It shows that the barometric responses are stable at low frequencies (0.1–0.5 cpd), while fluctuate at tidal frequencies (0.5–8 cpd). In the high-frequency band (8–30 cpd), by stacking the transfer functions to suppress the noise, we obtained stable barometric responses for the first time. According to the low- and high-frequency barometric responses, we can better judge whether the aquifers are confined in the timescale that we focused and whether the wellbore storage effect can be ignored, and expect to determine the fluid flow properties of the aquifers more reliably. For the three aquifers whose water table drainage and wellbore storage effects are ignored, we used the barometric and tidal responses to estimate their formation properties, which are consistent with previous results. The tidal strain sensitivities are related to the aquifer lithology, which are mainly controlled by the compressibility of the porous matrixes with different porosities and different aspect ratio fractures.

1 Introduction

[2] The water level in a well is a highly sensitive strainmeter, which can respond to external load, such as the Earth tide [Bredehoeft, 1967; Bodvarsson, 1970; Hsieh et al., 1987; 1988], atmospheric loading [Weeks, 1979; Van Der Kamp and Gale, 1983; Rojstaczer and Riley, 1990), fault activities [Wakita, 1975; Quilty and Roeloffs, 1997; Zhang and Huang, 2011], and seismic wave propagation [Cooper et al., 1965; Liu et al., 1989; Brodsky et al., 2003; Kano and Yanagidani, 2006; Wang et al., 2009; Kitagawa et al., 2011]. When there is no imposed dynamic stress, the well-aquifer system can be regarded as a stable linear system [Bendat and Piersol, 1986]. It is important to study the transfer functions of the linear system so as to determine the well-aquifer properties, which are significant for further study on its response to seismic wave propagation and the extraction of some reliable underground media and stress variations [Carr and Van Der Kamp, 1969; Johnson et al., 1973; 1974; Rhoads and Robinson, 1979; Hsieh et al., 1987; Doan et al., 2006; Burbey et al., 2011].

[3] The Earth tide and barometric pressure are two major continuous loadings on the well-aquifer system. When the aquifer is perfectly confined and has high lateral permeability and the well diameter is sufficiently small, the water level fluctuations related to Earth tide and barometric pressure changes can be expressed by a simple constant, known as the tidal sensitivity and barometric efficiency, respectively. These parameters can be obtained by the least square fit method and used for the estimation of the formation material properties [Jacob, 1940; Roeloffs, 1988; Rojstaczer and Agnew, 1989; Igarashi and Wakita, 1991]. However, most of the well-aquifers are not perfectly confined, and the permeability can be very low, so the simple constant is not enough to describe the frequency-dependent response of the water level in a well to Earth tide and barometric pressure [Rojstaczer, 1988a; 1988b; Rojstaczer and Riley, 1990].

[4] With both the Earth tide and barometric pressure as input signals, the water level as output signal, the transfer functions of the well-aquifer system carry lots of information about the properties of the well and the aquifer, and can be used to determine the well-aquifer properties and their variations over time. Rojstaczer [1988a] used the cross-spectra estimation to obtain the transfer functions of the water level response to atmospheric loading in the frequency band of 0.02–2 cycles per day (hereafter referred as cpd) in three wells and compared the results with the theoretical curves to get the fluid flow properties of the well-aquifer systems. Rojstaczer and Riley [1990] adopted a similar approach to study the response of a well tapping an unconfined aquifer to Earth tide and atmospheric loading. Quilty and Roeloffs [1991] used the average transfer function of the water level response to barometric pressure at frequencies lower than 1 cpd, to eliminate the frequency-dependent barometric effects from water level data. Doan et al. [2006] estimated the barometric response up to 8 cpd. Because the signals at high frequencies are quite noisy due to the lack of any large barometric pressure changes, the study on barometric response at frequencies higher than 8 cpd is almost blank. However, at high frequencies, the water level still responds to barometric pressure, and the response can be used to evaluate whether the wellbore storage effect can be ignored [Rojstaczer, 1988a], to determine the properties of the aquifer, and to extract some stress-related variations.

[5] In China, the digital transformation has been implemented to the Groundwater Monitoring Network, including hundreds of water level monitoring well stations, and the sampling interval of the observation data is one minute [The Monitoring and Forecasting Department of China Earthquake Administration, 2007]. Currently, a large number of waveform records are accumulated at these stations, which provide a basic database for studying the transfer functions of multiple well-aquifer systems. In this paper, we will extend the transfer functions to the high-frequency band and obtain the amplitude- and phase-frequency responses of the water level to barometric pressure from low to high-frequency band; we will also use this method to study the tidal responses in the intermediate frequency band and apply the obtained barometric and tidal response to the estimation of the well-aquifer properties.

2 Method and Data

[6] The well-aquifer system is composed of a well and an aquifer. The Earth tide and barometric pressure are loading on the well-aquifer system in different mechanisms (Figure 1). The Earth tide is loading on the matrix of the aquifer, and the response of water level to Earth tide is mainly controlled by the elastic properties and porosity of the porous matrix [Bredehoeft, 1967; Van Der Kamp and Gale, 1983; Rojstaczer and Agnew, 1989]. In the case of open wells, the barometric pressure is loading on the water surface of the well and the Earth's surface simultaneously. The response of water level to barometric pressure is much more complicated and often affected by the fluid flow in the system [Rojstaczer, 1988a; Rojstaczer and Riley, 1990].

Figure 1.

Idealized section of an open well tapping an unconfined aquifer response to Earth tide and atmospheric loading, revised from Rojstaczer and Riley [1990].

[7] For the well-aquifer system, the barometric pressure and Earth tide are two input signals that are dependent with each other at some frequencies. So we first calculate the ordinary coherence functions γxy2 among the water level, barometric pressure and Earth tide for each station. The definition of the ordinary coherence function is

display math(1)

where the Gxx(ω) and Gyy(ω) are the power spectra of two signals, and the Gxy(ω) is the cross spectra between them.

[8] The transfer functions of the water level response to barometric pressure and Earth tide for a well can be obtained by solving the following complex system of equations [Bendat and Piersol, 1986; Rojstaczer, 1988a; 1988b]

display math(2)

where BB and TT represent the power spectra of the barometric pressure and Earth tide, respectively; BT the cross spectra between atmospheric pressure and Earth tide; TB the complex conjugate of the BT; BW and TW the cross spectra between barometric pressure and water level and between Earth tide and water level, respectively; HB and HT the transfer function of water level response to barometric pressure and Earth tide, respectively.

[9] From equation (2), we can get that

display math(3)
display math(4)

[10] We considered the frequency band in which the water level is largely influenced by Earth tide as the intermediate frequency band (0.5–8 cpd), and the low and high-frequency bands correspond to f < 0.5 cpd and f > 8 cpd, respectively. It is a little different from Rojstaczer [1988a], for he divided them by the theoretical curves of the water level response to atmospheric loading, and the widths of the intermediate frequency band are different for different wells. In the intermediate frequency band, we calculate the transfer functions of the water level response to the Earth tide and barometric pressure from equation (3) and ((4)), respectively; in the low- and high-frequency band, the influence from Earth tide is small, so we just calculate the transfer functions of the water level response to barometric pressure from equation (3). The amplitude-frequency response (known as the tidal sensitivities and the barometric efficiencies) and the phase-frequency response correspond to the modulus and angle of the transfer function, respectively.

[11] To evaluate the stability of the obtained barometric efficiencies, we calculate the coefficient of variation (CV) at each frequency [Beyer, 1987]:

display math(5)

where σ is the standard deviation and inline image is the mean value. Then we estimate the mean CV in the low-, intermediate-, and high-frequency band, respectively, and use them to evaluate the stability of the barometric efficiencies in the three frequency bands for each station.

[12] By the end of 2007, the digital transformation implemented to the Groundwater Monitoring Network in China has been completed. The water levels in wells and the barometric pressures are measured by the LN-3 and the RTP-1 digital recorders, respectively, and the sampling interval of the observation data is one minute; all the wells are open with vented water level sensor [The Monitoring and Forecasting Department of China Earthquake Administration, 2007]. To get the transfer functions of the water level response to barometric pressure and Earth tide, we require the recorded data to be continuous, stable, not influenced by large earthquakes and rainfall, and the monitoring wells are located in different tectonic areas and have relatively detailed basic information. Finally, we picked out 17 stations from the Groundwater Monitoring Network of the China Earthquake Networks Center from 1 January (18 January for Jinhu well and 4 January for Taiyuan well) to 11 May (15 April for Taiyuan well) in 2008, the day before the great Mw 7.9 earthquake in Sichuan province. We checked the timing of each well and make clock corrections as necessary based on the initial response time of the water level to the Wenchuan earthquake.

[13] The distribution of the 17 observation wells are shown in Figure 2, and some basic information about the well-aquifer systems are shown in Table 1. Moreover, we calculated the corresponding tidal volumetric strain imposed by the solid Earth tide and ocean tide for each station by the “SPOTL” program [Berger et al., 1987; Agnew, 1997, 2012]. The water level, barometric pressure, and tidal volumetric strain waveform of the Xinghua well are shown in Figure 3a.

Figure 2.

Distribution of the 17 water level observation wells shown as the red solid triangles. The gray lines represent the faults [Deng et al., 2003].

Table 1. Some Basic Information About the 17 Observation Wellsa
Station Number and NameWell Diameter /mmWell Depth/mDepth of the Upper Aquifer Roof /mAquifer Thickness /mOpen Interval /mThe Lithology of the AquiferOverlaying Layer LithologyThe Standard Deviation of Regional Topographic Altitudes/m
  1. a

    The blanks mean the information is missing.

1 Xiuyan21925016.66 16.66–250GranodioriteGranodiorite47.54
2 Benxi1271213.46952.81260952–957MarbleQuartztes135.09
3 Ningjin 2003.781899  Dolostone 3.13
4 Linghai300153.716.912516.9–153.7Limestone and Dolostonesiliceous rock55.38
5 Xinghua15726802171.55092228–2680Limestone and DolostoneMudstone4.16
6 Taiyuan168765.78480  Limestone and Dolostone 70.15
7 Kunshan127676.03248428251.37–676.03Limestone and DolostoneGravel2.98
8 Suining108311.7613658136–311.76LimestoneMild clay8.73
9 Yutian134456.4300156 Limestone 21.81
10 Tangshan13520715486154–207LimestoneSandstone4.8
11 Jinhu14020001620.53801653.8–1659.4LimestoneGravel and mudstone2.31
12 Pingliang 610.27162.76  Sandstone 102.3
13 Zhouzhi902778.323413172778.3–2341SandstoneMudstone and Sandstone53.75
14 Nanxi219101.545.1 57.54–101.54Sandstone 56.89
15 Panjin139.71018.7458042086.49–1018.74SandstoneFine sandstone0.47
16 Dazu150108.745.546245.54–108.7MudstoneSandstone105.41
17 Linxia 200.1 5 Mudstone 156.69
Figure 3.

(a) The water level, barometric pressure, and tidal volumetric strain waveforms of the Xinghua well from 1 January to 11 May in 2008. The water level means the vertical distance from the mouth of the well down to the water surface inside the well, positive for decreasing water level. (b) The ordinary coherence functions among the three signals for the well. (c) The barometric efficiencies and phase shifts of the well from low- to high-frequency band (black dots). The blue, red, and yellow asterisks and vertical lines mark the average values and the 95% confidence interval, respectively. (d) The tidal volumetric strain sensitivities and the corresponding phase shifts of the well from the diurnal to semi-diurnal frequency band (black dots), the red asterisks represent the average tidal volumetric strain sensitivities and phase shifts, and the blue vertical lines show the 95% confidence interval. Negative phase shifts mean phase lag.

[14] During the analysis of the coherence functions, the window size and step size of the Hamming window are 30 days and 15 days, respectively. The ordinary coherence functions of the Xinghua well are shown in Figure 3b.

[15] During the analysis of the transfer functions, in the low-frequency band, we filter the preprocessed water level and barometric pressure data from 1 h to 12 days by a 2 pass second-order Butterworth band-pass filter. Then calculate the power spectra and the cross spectra with 216 min (about 45.5 days) as a record, while the window size and step size of the Hamming window are ~11.4 days and 5.7 days, respectively. In the intermediate frequency band, the filtered frequency band is 3 min - 3 days, with 215 min (about 22.8 days) as a record, and the window size and step size of the Hamming window are ~2.8 days and 1.4 days, respectively. In the high-frequency band, the filtered frequency band is also 3 min - 3 days. As the signal-to-noise ratio in the water level is low and the barometric signals are relatively weak, we stack the data taking 214 min (about 11.4 days) as a record with the window size and step size of the Hamming window 8.5 h and 4.3 h, respectively. The barometric and tidal responses of the Xinghua well are shown in Figures 3c and 3d, respectively.

3 Results

3.1 Ordinary Coherence Functions

[16] We estimate the ordinary coherence functions among the water level, barometric pressure, and tidal volumetric strain for all the stations. It shows that (Figure 4) in the low-frequency band (f < 0.5 cpd), the coherence functions between the water level and barometric pressure at most frequencies for most wells are greater than 0.9. For several wells, such as the Xinghua (Figure 3b) and the Kunshan (Figure 4a) well, the curves are flat and the values are close to 1; for several other wells, such as the Benxi and Panjin well (Figures 4b–4c), the curves decrease at some frequencies, which may be due to the effects of rainfall. The coherence functions for the Mudstone well are about 0.5 or less and fluctuate greatly (Figure 4d), reflecting a bad correlation between the two signals. The coherence functions between the water level and the Earth tide are almost less than 0.2, indicating that in the low-frequency band, the water level is mainly response to the barometric pressure, and the influence from the Earth tide is small at most frequencies.

Figure 4.

The ordinary coherence functions among the water level, barometric pressure, and tidal volumetric strain for the (a) Kunshan well (Limestone), (b) Benxi well (Marble), (c) Panjin well (Sandstone), and (d) Dazu (Mudstone) well.

[17] In the intermediate frequency band (0.5–8 cpd), because the water level and the Earth tide have consistent wave components, the coherence functions between them are close to 1 at diurnal and semi-diurnal frequencies. As the barometric pressure has small energy at the frequency of M2 and O1 wave, its coherence functions with water level at these two frequency points decrease obviously.

[18] In the high-frequency band (f > 8 cpd), the signal-to-noise ratio in the water level is low and the barometric signals are relatively weak. The coherence functions between the water level and the barometric pressure at most wells decrease with increasing frequencies. However, at the frequency of 20 cpd, the coherence functions between the water level and the barometric pressure are greater than 0.8 for the Xinghua and Kunshan well, indicating that the water level in these wells can well respond to the barometric pressure in the high frequency band.

3.2 The Barometric Responses From Low- to High-frequency Band

[19] The continuous barometric efficiencies and phase shifts in the low-, intermediate-, and high-frequency band and the corresponding mean CV for the 17 well stations are shown in Figure 5, and the 95% confidence intervals are also plotted on that. All negative phase shifts mean water level lags behind the barometric pressure, while positive phase shifts mean the water level leads. Overall, the barometric efficiencies and phase shifts in the low-frequency band are stable at most wells, which are consistent with the high coherence functions between the water level and the barometric pressure at low frequencies. In the intermediate frequency band, the barometric response fluctuates greatly at tidal frequencies, which can be influenced by the strong energy of the Earth tide. In the high-frequency band, by stacking the continuous transfer functions to improve the signal-to-noise ratio, we obtained the barometric response at each station, and most of the barometric responses are stable.

Figure 5.

The barometric efficiencies and phase shifts (black dots) and the corresponding mean coefficients of variation in the low-, intermediate-, and high-frequency band by cross-spectra estimation for all the stations. The blue, red, and yellow asterisks and vertical lines mark the average values and the 95% confidence interval in the three frequency band, respectively. Negative phase shifts mean phase lag.

Figure 5.

(continued)

Figure 5.

(continued)

Figure 5.

(continued)

Figure 5.

(continued)

Figure 5.

(continued)

Figure 5.

(continued)

Figure 5.

(continued)

Figure 5.

(continued)

3.3 The Tidal Responses in the Intermediate Frequency Band

[20] When people analyze the response of the water level to Earth tide, the responses of the M2 and O1 wave are often the optimum choices, for they have strong energy and are not contaminated by the barometric pressure [Rojstaczer and Agnew, 1989; Doan et al., 2006]. Here we get the continuous tidal volumetric strain sensitivities in the intermediate frequency band by cross-spectra estimation (see Figure 6). It turns out that at most wells the tidal responses are stable at semi-diurnal frequencies, while scatter at diurnal frequencies, which may be due to the K1 tide that is disturbed by resonances induced by the free core nutation and thermal effect [Doan et al., 2006].

Figure 6.

The tidal volumetric strain sensitivities and the corresponding phase shifts from the diurnal to semi-diurnal frequency band (black dots) for the (a) Kunshan well, (b) Tangshan well, (c) Pingliang well, and (d) Dazu well. The red asterisks represent the average tidal volumetric strain sensitivities and phase shifts, and the blue vertical lines show the 95% confidence interval. The tidal responses at semi-diurnal frequencies are more stable than those at diurnal frequencies. Negative phase shifts mean phase lag.

4 Discussion

4.1 The Reliability of the High-Frequency Barometric Response

[21] Since this is the first time we extend the transfer function method to the high-frequency band and obtain the high-frequency barometric response, it is necessary to make a resolution analysis whether it is reliable or not. Our tests are as following: two datasets are generated randomly obeying the standard normal distribution, and the length of the datasets is the same to that of the water level and barometric pressure (132 × 1440). We estimate the transfer function of the two datasets at high frequencies in the same method that we described in section 2. After testing 100 times, we found that the obtained barometric efficiencies are stable around 0.1, and the mean CV, which is used to evaluate the stability of the results, are up to 52.4%. However, in this work, the barometric efficiencies are 0.3–0.8 for most wells; except for the Dazu and Linxia well, the mean CV for the other wells are less than 33%, even low to 5%. The good continuity of the barometric response from low to high-frequency band is also a plus. So we conclude that the obtained high-frequency barometric responses are credible in our work.

4.2 The Stability of the Barometric Response and Its Influencing Factors

[22] Rojstaczer [1988a] has analyzed that under the condition that there is only horizontal groundwater flow between the aquifer and the borehole, the high-frequency barometric response is governed largely by the well radius and the lateral transmissivity of the aquifer. In order to discuss whether the high-frequency barometric response is related to the regional topographic variations, we chose a well-centered square region of 20 km × 20 km with a grid spacing of 30″ × 30″, obtained the altitudes at all grid points from the model “GTOPO30” [U.S.G.S., 1993], and calculated the standard deviation σH of the altitudes for each station (see Table 1). Then we compared the CV of the high-frequency barometric efficiencies with the σH (Figure 7). It shows that for the seven wells with σH less than 10 m, the CV of six wells are less than 13%, only the Tangshan well is exceptional. For the other ten wells with σH greater than 10 m, except for the Nanxi well, the CV of nine wells are greater than 13%. We speculate that where σH is large, the tectonic movement should be active; the aquifers were compressed and deformed and no longer of large lateral extent. Therefore, the high-frequency barometric loading may have a much more complex form and the half-space model could be insufficient. Besides, the barometric pressure fluctuations may not as stable as those in plain area, which could affect the stability of the results. We also made a similar comparison for the low-frequency barometric efficiencies (Figure 7). It seems that the stability of the low-frequency barometric response has little to do with the regional topographic altitude variations: the mean CV at 14 wells are less than 13%, and only the Dazu and Linxia well have large CV, which may be attributed to the Mudstone aquifers that have lower permeability.

Figure 7.

The mean CV (coefficients of variation) of the barometric efficiencies at low frequencies (blue circles) and high frequencies (red asterisks) vary with the standard deviation of the regional topographic altitudes for each well. The solid line corresponds to 10 m and the dotted line corresponds to 13%. It shows that for the 7 wells with σH less than 10 m, the CV of the high-frequency barometric efficiencies in 6 wells are less than 13%; for the 10 wells with σH greater than 10m, the CV of the high-frequency barometric efficiencies in 9 wells are greater than 13%, while the stabilities of the low-frequency barometric response have no similar relationship.

[23] From the responses at 17 stations, we can see that the stability of the barometric efficiencies and phase shifts is better in the low-frequency band, moderate in the high-frequency band, and worse in the intermediate frequency band. This is interpretable: in the low and high-frequency band, the influence from the Earth tide is small, so the barometric responses are more stable. However, due to the effects of the weak barometric changes, high ambient noises, topography, and some other factors, the stability at high frequencies is not as good as that at low frequencies. Fortunately, we can extract the high-frequency barometric response by stacking the continuous transfer functions. In the intermediate frequency band, the barometric efficiencies and phase shifts for many stations fluctuate greatly at tidal frequencies (see Figure 5). Doan et al. [2006] have discussed that when the Skempton's coefficient is equal to 0.8, the barometric pressure changes typically equal about 10% of the tides in the well. So we speculate that it is the strong energy of the Earth tide that causes the fluctuations of the barometric response at tidal frequencies. Rojstaczer [1988a] has estimated the fluid flow properties of the partly confined aquifers by fitting the barometric efficiencies with the theoretical curves in the low-frequency band and at several tidal frequencies. As it is of high possibility that the barometric efficiencies at the tidal frequencies are contaminated by the Earth tide, it should be more reliable to determine the fluid flow properties by combining the low-frequency barometric efficiencies with stable high-frequency barometric response. Because of its complexity, we will not estimate the fluid flow properties in this work.

4.3 The Tidal Strain Sensitivity and the Aquifer Lithology

[24] We picked out the average tidal strain sensitivities at f = 1 cpd and f = 2 cpd for all stations and gave the results in Figure 8 according to the station number. It shows that at most stations, the tidal strain sensitivities at f = 2 cpd are obviously greater than those at f = 1 cpd, which is consistent with previous work that the tidal sensitivities are greater for M2 tide than O1 tide [Rojstaczer and Agnew, 1989; Rojstaczer and Riley, 1990; Doan et al., 2006]. Rojstaczer and Agnew [1989] explained that by water table drainage, for water table drainage can cause more attenuation in the lower frequency band.

Figure 8.

The average tidal strain sensitivities at f = 1 cpd and f = 2 cpd for each station. The numbers in the horizontal coordinate represent the station numbers as is shown in Table 1. The tidal strain sensitivities are larger for Granodiorite and Marble, medium for most of the Dolostones and Limestones, and smaller for the Sandstones and Mudstones, which are mainly controlled by the compressibility of the porous matrixes with different porosities and aspect ratio fractures.

[25] As the tidal strain sensitivities are stable at semi-diurnal frequencies, we analyzed the relationship between the tidal strain sensitivity at f = 2 cpd and the aquifer lithology (Figure 8). It shows that the tidal strain sensitivities are larger for Granodiorite and Marble, medium for most of the Dolostones and Limestones, and smaller for the Sandstones and Mudstones.

[26] The relationship between the volumetric tidal strain ε and the areal strain εa is as following:

display math(6)

[27] Based on the constitutive relation of stress-strain for poroelastic media [Rice and Cleary, 1976), Rojstaczer and Agnew [1989] derived the expression of the water level w in a well response to the areal strain εa under static-confined condition, known as the areal strain sensitivity

display math(7)

where B is the Skempton's coefficient expressed as

display math(8)

and inline image is the drained compressibility for rocks

display math(9)

where α is an additional constant of the medium and can be taken to be [Nur and Byerlee, 1971]

display math(10)

and νu is the undrained Poisson's ratio of the formation [Rice and Cleary, 1976]:

display math(11)

[28] Besides, ρ is the fluid density, and g is the acceleration due to gravity; βf is the compressibility of the fluid; βu and β are the undrained and drained compressibility of the porous matrix, respectively. φ is the porosity and ν is the Poisson's ratio. For the fixed βu, βf, and ν, the areal strain sensitivity As increases with decreasing β and φ [Rojstaczer and Agnew, 1989].

[29] The porosityφ, Young's modulus E, and the Poisson's ratio ν of the Granodiorite, Marble, Limestones, and Sandstones are shown in Table 2 [Jumikis, 1983; Chen et al., 2009]. Based on the expression of the compressibility [Wang, 2000]

display math(12)

we calculate the compressibilities of the four types of Rocks and the results are also shown in Table 2. It shows that the porosity and the upper boundary of the compressibility of the Granodiorite and Marble are obviously smaller than those of Limestones and Sandstones, which can well explain why the tidal strain sensitivities for Granodiorite and Marble are larger than most of the Limestones and Sandstones. The tidal strain sensitivities of most Limestone and Dolostone aquifers are greater than Sandstone wells. That can be attributed to the different porosity and pore types of the two rocks, as the lower aspect ratio (width/length) fractures in the Limestones are more prone to deformation than the higher aspect ratio pores in the Sandstones. Note that the expression of the areal strain sensitivity in equation (7) is under static-confined condition; the correspondence between the calculated tidal strain sensitivity and the aquifer lithology indicates that, at f = 2 cpd, the water level response to Earth tide is hardly influenced by the water table drainage.

Table 2. The Porosity, Young's Modulus, and Poisson's Ratio of Four Types of Rocks [Jumikis, 1983; Chen et al., 2009] and the Calculated Compressibility
LithologyGranodioriteMarbleLimestoneSandstones
Porosity (%)0.5–10.5–22–205–30
Young's modulus(GPa)26–6959–8810–795–80
Poisson's ratio0.13–0.250.25–0.380.14–0.300.17–0.30
Compressibility(×10−10/Pa)0.22–0.850.08–0.250.15–2.160.15–3.96

[30] Theoretically, the barometric efficiencies should also be related to the aquifer lithology. As the barometric efficiencies fluctuate greatly at tidal frequencies and are stable in the low-frequency band (0.1–0.5 cpd) at most wells, we picked out the average barometric efficiency at f = 0.3 cpd for all the stations (Figure 9). However, there is no obvious relationship between the barometric efficiencies and the aquifer lithology. We speculate that in the low-frequency band, some of the wells are influenced by water table drainage, so the response to barometric pressure is much more complicated and may be related to the fluid flow properties.

Figure 9.

The average barometric efficiencies at f = 0.3 cpd for all the stations. The numbers in the horizontal coordinate represent the station numbers as is shown in Table 1. There is no obvious relationship between the barometric efficiency and the aquifer lithology, which may be due to the different mechanism of the water level response to barometric pressure compared to the Earth tide.

4.4 Estimation of the Formation Material Properties of the Aquifers

[31] Positive phase shifts are observed at some wells in this work (Figure 5). Previous works have explained this phase advance by the drainage at water table or the fluid diffusion near borehole [Rojstaczer, 1988a, 1988b; Rojstaczer and Riley, 1990; Roeloffs, 1996; Doan, 2006]. From Figure 5, we can see that the barometric efficiencies of the Ningjin well are greater than 1 in the whole frequency band, which means the magnitude of the water level fluctuations exceeds that of the barometric pressure changes, and this is theoretically impossible for a confined aquifer [Weeks, 1979]. It is reasonable to speculate that this well is tapping an unconfined or a partly confined aquifer and is strongly influenced by the air flow in the unsaturated zone [Rojstaczer and Riley, 1990]. The barometric efficiencies of the Tangshan well at low frequencies are significantly smaller than those at high frequencies, and the phases at low frequencies are positive, which could be due to water table drainage, for this well is a partly confined well [Shi et al., 2007]. The barometric efficiencies of the Yutian well decrease with increasing frequencies from intermediate to high-frequency band, which may be due to the wellbore storage effect [Rojstaczer, 1988a]. For the Kunshan and Jinhu well, the barometric efficiencies are stable over the whole frequency band. The high-frequency barometric efficiencies are nearly a constant, indicating that the influence from the wellbore storage effect can be ignored. However, there is an obvious downward trend for the barometric efficiencies from low to intermediate frequency band, and the reason needs to be further analyzed. The barometric responses of the Dazu and Linxia well scatter heavily over the whole frequency band with large mean CV, which may be attributed to the Mudstone aquifers that have lower permeability and its complex topography.

[32] Ignoring the fluctuations at tidal frequencies, the barometric efficiencies of the Xinghua, Suining, and Panjin well change very slightly (less than 0.1) from low to high-frequency band, and the phase responses at high frequencies are around zero, indicating the influence from the water table drainage is small and the wellbore storage effect can be ignored, and the barometric efficiency in the high-frequency band can be considered as the static-confined barometric efficiency (Rojstaczer and Agnew, 1989). According to Roeloffs [1988], the barometric efficiency under static-confined condition can be expressed as:

display math(13)

[33] Combining equation (13) with equations ((6))–((11)), we can calculate the compressibilities of the porous matrix β, the Skempton's coefficient B, and the porosity φ of the confined well-aquifers by [Igarashi and Wakita, 1991]:

display math(14)
display math(15)
display math(16)

and the one-dimensional specific storage Ss can also be calculated by [Rojstaczer and Agnew, 1989]:

display math(17)

[34] We set ρ = 103kg/m3, g = 9.8N/kg, βf = 4.4 × 10− 10Pa− 1, and ν = 0.25 as Rojstaczer and Agnew [1989] did, set βu = 1.5 × 10− 10Pa− 1 for the Panjin well and βu = 2 × 10− 11Pa− 1 for the other wells, substituted the tidal strain sensitivity at f = 2 cpd and the barometric efficiency at f = 20 cpd of the wells to equations ((14))–((17)), and thus obtained the rough estimations of the aquifer properties (Table 3), which turned out to be consistent with Chen et al. [2009]. These parameters are useful for geophysicists and hydrologists.

Table 3. The Tidal Strain Sensitivity, Barometric Efficiency, and the Calculated Aquifer Properties for the Confined Well-Aquifers
StationTidal Strain Sensitivity (mm/10−9)Barometric EfficiencyMatrix Compressibility (Pa−1)PorositySkempton's CoefficientSpecific Storage (m−1)
Xinghua1.390.753.74 × 10−1110.0%0.295.5 × 10−7
Suining2.030.487.64 × 10−119.7%0.587.7 × 10−7
Panjin0.520.462.39 × 10−1018.5%0.621.2 × 10−6

5 Conclusions

[35] By stacking the continuous transfer functions of the water level response to barometric pressure to improve the signal-to-noise ratio, we obtained the high-frequency barometric responses for the first time. The barometric responses are stable in the low-frequency band while fluctuate greatly at tidal frequencies, which can be attributed to the strong energy from the Earth tide. For the partly confined or unconfined aquifers, the fluid flow properties are expected to be determined more reliably by fitting the barometric efficiencies both in the low- and high-frequency band, than just in the low-frequency band and at several tidal frequencies [Rojstaczer, 1988a], as it is of high possibility that the barometric efficiencies at the tidal frequencies are contaminated by the Earth tide.

[36] According to the stable barometric responses in the low- and high-frequency band, we can better judge whether the aquifers are confined in the timescale that we focused and whether the wellbore storage effect can be ignored. For the three well-aquifers whose water table drainage and wellbore storage effects are ignored, the porous matrix compressibility, the porosity, the Skempton's coefficient, and the specific storage coefficient have been determined, and the values are consistent with previous results [Chen et al., 2009].

[37] The tidal strain sensitivities at f = 2 cpd are larger for Granodiorite and Marble, medium for most of the Dolostones and Limestones, and smaller for the Sandstones and Mudstones, which are mainly controlled by the compressibility of the porous matrixes with different porosities and different aspect ratio fractures. There is no obvious relationship between the low-frequency barometric efficiencies and the aquifer lithology, which may be due to the different mechanisms of the water level response to barometric pressure compared to the Earth tide.

Acknowledgments

[38] This work made use of GMT and MATLAB software. The groundwater level and barometric pressure data are from the Groundwater Monitoring Network of the China Earthquake Networks Center. The authors sincerely thank Baoshan Wang, Emily E. Brodsky, and the two reviewers for their constructive comments and suggestions. They also thank Duncan C. Agnew for providing the “SPOTL” program for calculating the tidal volumetric strain and Yuan Huang for providing the basic information about the well-aquifers. This work was supported by the National Natural Science Foundation of China with Grant No.41174040.

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