[G. R. L.]
Supporting Information for
Disruption of groundwater system by earthquakes
Xin Liao1,2,*, Chi-Yuen Wang2,* and Chun-ping Liu1
1. Institute of Disaster Prevention, Beijing, China 101601
2. Department of Earth and Planetary Science, University of California, Berkeley, CA, U.S. 94709
* Corresponding authors: chiyuen@berkeley.edu, liaoxin19851224@126.com
Contents of this file
Text S1 to S5
Figures S1 to S3
Tables S1 to S2
Additional Supporting Information
No
Introduction
This Supporting Information contains the following three sections:
Supporting text:
1. Water level measurement
2. Tidal analysis
3. Groundwater flow to wells
4. Estimation of the coseismic increase of porosity
5. Estimation of transmissivity and permeability
Supporting figures:
1. Figure S1
2. Figure S2
3. Figure S3
1
Supporting tables:
1. Table S1
2. Table S2
Text S1. Water level measurement
As noted in the text, Jiangyou well is located in a remote area near the eastern border of
the Qinghai-Tibet Plateau. Water level in the well was measured with a float and
recorded on a chart recorder. The hourly water level was digitized daily from the chart by
an experienced staff. The recording paper was changed everyday and the water level
was digitized as soon as the chart was released from the recorder. The digitized data
was then delivered to a centralized location and archived.
The observational errors include both errors in water level and in time. The daily
cumulative error in water level is <5 mm, which is averaged to hourly values (<0.2 mm)
and distributed evenly to the observed values before archiving. An additional error is due
to the resolution of the naked eye, which is generally ~0.2 mm. Thus the error of well
water level is <0.4 mm, which is the sum of the recording error (<0.2 mm) and reading
error (~0.2 mm). The clock of the chart recorder is adjusted daily against a centralized
clock, which shows a daily cumulative error of 5 minutes, which is inconsequential for
the present study.
Text S2. Tidal analysis
We use Baytap-G [Tamura et al., 1991], a widely used and tested routine based on
Bayesian statistics, in the tidal analysis. The program analyzes a time series of water
level data, assuming that time variation in the data is due to a combination of the tidal
effect, the local air-pressure effect, long-term drift and offsets. The program solves for
the model parameters by minimizing the squares of the misfit to the model with
constraints on the model parameters. Baytap-G [Tamura et al., 1991] groups the tides in
12 constituents, Q1, O1, M1, P1S1K1, J1, OO1, 2N2, N2, M2, L2, S2K2, M3, where S1
and S2 are solar tides affected by the thermal radiation and barometric tides. Q1, M1,
J1, OO1, 2N2, N2, L2, M3 and O1 have much smaller signal-to-noise ratio than M2; thus
we select M2 tide in the present analysis.
Before tidal analysis, we removed step-like changes using water levels immediately
before and after the step and interpolated small gaps with the guide of the theoretical
strain tide [Tamura et al., 1991]. If the gap comprises more than 7 days, no analysis is
attempted for the segment. The data for water level were divided into 30-day segments
with a 23-day overlap. Because there is no barometric data near the Jiangyou well, we
did not make barometric correction. The effect of barometric pressure on the water level
M2 tide is likely to be small [Hsieh et al., 1987]. Moreover, since the Jiangyou well is
deep within the Eurasian continent and more than 1000 km from any coast, we did not
make ocean tide correction.
The phase shift of the water-level tide calculated by Baytap [Tamura et al., 1991] refers
to the theoretical strain tide and may be different from the local strain tide; thus a
correction for the phase difference is necessary. We estimated this difference by fitting
2
the data in Fig. 2 with a flow model (Equations S3 and S6, see below) and setting rw and
rc to the measured well radii (63.5 mm and 88.9 mm, respectively). The difference is
accounted for by adding a correction of 30o to the Baytap estimated phase shift. This
difference may be partly due to the effect of local topography and geologic heterogeneity
[Berger and Beaumont, 1976] and partly due to the partial opening of the Jiangyou well
to the aquifer (Figure S1), which results in a more negative phase shift than that if the
aquifer is fully open (Figure S2d).
Text S3. Groundwater flow to wells
We use the solution of Hsieh et al. [1987] for tidally induced radial flow of groundwater to
a well in a horizontal, laterally extensive, confined, isotropic and homogeneous aquifer
that is fully penetrated by the well. The application of this flow model to the Jiangyou
well, which is located in a geologically and geomorphically complicated area, can only be
considered as a first-order approximation.
For realistic well geometry and aquifer properties, the solution of Hsieh et al. may be
approximated as
𝑄
0
[𝐾𝑒𝑟(𝛼𝑤 ) + 𝑖𝐾𝑒𝑖(𝛼𝑤 )]exp⁡(𝑖𝜔𝑡)
𝑠𝑤 ≈ 2𝜋𝑇
(S1)
where 𝑠𝑤 is the drawdown at the well, which is related to the water level in the well (x)
and the pressure head in the aquifer (h) by h - 𝑠𝑤 = x, Q0 is the discharge of the aquifer
at the well, 𝜔 is the tidal frequency, Ker and Kei, respectively, are the zeroth order
Kelvins functions, 𝛼 w = (𝜔𝑆⁄𝑇 ) 1/2 rw , T and S, respectively, are the transmissivity and
storativity of the aquifer, and rw is the radius of the well (Figure S1).
Inserting the above solution into h – 𝑠𝑤 = x, Hsieh et al. [1987] obtained the following
relations between aquifer properties and the amplitude ratio (X/H) and the phase shift (𝜂)
between X and H,
𝑋/𝐻 = (𝐸 2 + 𝐹 2 )−1/2
(S2)
and
𝜂 = ⁡ −𝑡𝑎𝑛−1 (𝐹 ⁄𝐸)
(S3)
where X is the amplitude of tide of the water level in a well, H is the amplitude of the
fluctuating pressure head in the elastic aquifer responding to the tidal stress. For earth
tide analysis and for realistic values of rc, rw, T and S, E and F can be approximated by,
respectively [Hsieh et al., 1987],
𝐸 ≈ 1– (𝜔𝑟𝑐2 /2𝑇)Kei(𝛼𝑤 )
(S4)
3
𝐹 ≈ (𝜔𝑟𝑐2 /2𝑇)Ker(𝛼𝑤 )
(S5)
where rc is the inner radius of well casing. From Equation S2 we also have
𝑋 = 𝐻⁡(𝐸 2 + 𝐹 2 )−1/2
(S6)
There are limitations in using this method as noted in Xue et al. [2013]. First, the
estimated permeability is sensitive only to the volume within the drawdown cone around
the borehole. Assuming an effective radius r measured to 5% of the maximum
drawdown, we estimate r = 80 m for the present case. Given the relatively small
effective radius of sensitivity, the radial symmetry assumed in the model may be
reasonable even if significant heterogeneity exists in the study area [Xue et al., 2013].
Finally, the casing in the Jiangyou well is screened only to a section of the aquifer
(Figure S1) instead of to its full thickness. For this reason, a correction is needed, as
discussed below.
Existing studies [Hantush, 1961] show that, for partially penetrating wells, drawdown in
the well is affected by a ‘skin effect’, in addition to the wellbore effect described by Hsieh
et al. [1987]. This effect causes the groundwater flow near the wellbore to bend towards
the screened section and the flow path to increase, causing an additional drawdown.
Empirically, we assume that the drawdown of a partially penetrating well may be
expressed as:
𝑠𝑤′ = 𝛽𝑠𝑤
(S7)
where 𝛽 = (𝑠𝑤 + 𝑠𝑝 )/𝑠𝑤 , and 𝑠𝑝 is the drawdown produced by the skin effect.
′ , we plot for
Following the same procedure as in Hsieh et al. but replacing 𝑠𝑤 by 𝑠𝑤
different values of 𝛽 the relationship between amplitude versus phase shift in Figure
S2a. It shows that the relationships for different values of 𝛽 lie so close together that
they are nearly indistinguishable. Thus we may justify using Hsieh’s solution in Fig. 3 to
interpret the data from the Jiangyou well. Figure S2c and S2d show that both the
relationships between amplitude ratio and transmissivity and between phase shift and
transmissivity shift towards higher T with increasing 𝛽 . Thus the permeabilities estimated
with assumed 𝛽 =1, and cited in the text, likely represent lower bounds. Quantitative
evaluation of this effect is not made because the magnitude of 𝛽 for the Jiangyou well is
unknown and difficult to estimate without a full numerical solution.
Text S4. Estimation of the coseismic increase of porosity
The change of volume of a porous rock due to a change of pore pressure may be
expressed as dV/V = dP/K, where K is the bulk modulus of the porous rock.
Approximating mineral grains as incompressible, dV is then the change of pore volume.
Given the data in Figure S3, we obtained an order-of-magnitude estimate of dV/V ~ 10-5.
4
Text S5. Estimation of transmissivity and permeability
The transmissivity T of an aquifer is estimated by following the standard method (e.g.,
Elkhoury et al., 2006) of fitting the tidal data for phase shift 𝜂 with equation S3, using the
measured values of rc and rw and the approximated value of S. Permeability (k) is then
calculated from T based on the following relation
𝜇⁡𝑇
𝑘 = ⁡ 𝑏𝜌𝑔
(S8)
where b is the thickness of the aquifer, 𝜌 and 𝜇 are, respectively, the density and
viscosity of water, and g is the gravitational acceleration.
Supporting figures
Figure S1. Simplified log of the Jiangyou well. The well is 4076.5m deep and was cased
to the bottom. A screened section opens between 2645 and 3324.5 m below the surface
to a 680-m thick formation of quartz sandstone, which is confined by thick aquicludes of
5
shale both above and below. The diameters of the wellbore and the screen section are rc
= 88.9 mm; rw = 63.5 mm, respectively.
Figure S2. (a) Plot of amplitude (X) versus phase shift (𝜼). (b) Plot of the ratio between
X and H versus 𝜼 for different values of β, where H is the pressure head away from well.
(c) Plot of X/H versus transmissivity (T) for different values of β. (d) Plot of 𝜼 versus T for
different values of β.
6
40
Ku(GPa)
30
20
10
0
0
5
10
15
20
25
30
Porosity (%)
Figure S3. Laboratory data for 𝐾𝑢 ⁡for sandstones plotted against porosity (see Table S1
for tabulated data).
7
Supporting tables
Ku
(GPa)
19
26
19
20
1 atm
1 atm
1 atm
1 atm
16.00
8.30
13.00
14.00
0.62
0.5
0.5
0.61
5 Ruhr sandstone
2
1 atm
30.00
0.88
6 Weber sandstone
6
1 atm
25.00
0.73
7 Berea sandstone
19
10 MPa
15.80
0.75
5
33 MPa
17.9
0.86
9 Berea sandstone
21
33 MPa
16.4
0.38
10 Berea sandstone
21
35 MPa
14.1
0.49
6.87
11
12
13
14
15
16
17
18
19
21
11
3
11
10
16
8
14
7
41 MPa
0.1 MPa
80 MPa
80 MPa
13 MPa
13 MPa
13 MPa
13 MPa
13 MPa
17.5
17.38
29.20
25.71
15.72
14.07
13.10
15.30
13.16
0.41
0.46
0.28
0.34
0.6
0.41
0.47
0.43
0.42
20 108/111 shale
15
40 MPa
21.48
0.6
21 MUD shale
21
60 MPa
17.23
22 G-01 shale
23 G-02 shale
26
14
1 atm
1 atm
10.84
18.98
0.62
5
0.6
0.42
24 G-03 shale
10
1 atm
31.87
0.34
20.5
27.5
14
9.5
29
1 atm
1 atm
1 atm
1 atm
1 atm
17.17
10.09
20.70
27.24
10.45
0.5
0.69
0.42
0.35
0.54
7.09
7.99
8.18
8.74
9.43
5.77
6.16
6.58
5.53
12.8
9
10.7
7
6.51
7.97
10.8
3
8.58
6.96
8.69
9.53
5.64
1
2
3
4
Berea sandstone
Boise sandstone
Ohio sandstone
Pecos sandstone
8 Calgary sandstone
25
26
27
28
29
Berea sandstone
CRE shale
KIM shale
JUR shale
3492 shale
3506 shale
3525 shale
3536 shale
3564 shale
G-04 shale
G-05 shale
G-06 shale
G-07 shale
G-08 shale
Porosit
y (%)
BKu
(GP References
a)
9.92
4.15
6.50
8.54
26.4 Wang, 2000
0
18.2
5
11.8
5
15.3
Hart, 2000
9
6.22
Confining
Pressure
Rock
B
Hart and
Wang, 1999
Ortega et al.,
2009
8
Table S1. Complied laboratory data for Ku, B and porosity for sandstones [Hart and
Wang, 1999; Hart, 2000; Wang, 2000] and shales [Ortega et al., 2009]. Porosity was
measured under ambient condition; Ku and B were measured at different effective
pressures.
9
Earthquake
Time
(yyyy/mm/dd)
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
2006/05/03
2006/10/09
2006/11/15
2006/12/26
2007/01/13
2007/04/01
2007/06/02
2007/08/08
2007/09/12
2007/12/09
2008/01/09
2008/05/12
2008/07/05
2008/07/19
2008/08/30
2009/01/03
2009/01/03
2009/07/15
2010/06/12
latitude
(degree)
-20.187
20.654
46.592
21.799
46.243
-8.466
23.028
-5.859
-4.438
-25.996
32.288
31.002
53.882
37.552
26.241
-0.414
-0.691
-45.762
7.881
longitude
(degree)
-174.123
120.023
153.266
120.547
154.524
157.043
101.052
107.419
101.367
-177.514
85.166
103.322
152.886
142.214
101.889
132.885
133.305
166.562
91.936
Magnitude
(Mw)
8
6.3
8.3
7.1
8.1
8.1
6.1
7.5
8.5
7.8
6.4
7.9
7.7
7
6
7.7
7.4
7.8
7.5
Epicenter
distance
(degree)
93.37
17.63
39.65
17.26
40.50
64.12
9.38
37.76
36.40
93.94
16.59
1.47
40.51
31.12
6.12
41.79
42.27
95.60
26.75
Table S2. The listed earthquakes, taken from USGS earthquake catalogs from year
2006 to 2010, correspond to those that generated seismic waves energy densities
exceeding the threshold of 10-5 J/m3 at the Jiangyou well - a threshold for the minimal
seismic energy density required to induce a change of water level in wells [Wang and
Manga, 2010].
10
Additional references
Berger, J. and C. Beaumont (1976), An analysis of tidal strain observations from the
United States of America II. The inhomogeneous tide, Seismol. Soc. Amer. Bull.,
66(6), 1821-1846.
Hantush, M. S. (1961), Drawdown around a partially penetrating well, J. Hydraul. Div.,
87, 83-98.
Hart, D. J. (2000), Laboratory measurements of poroelastic constants and flow
parameters and some associated phenomena, Ph.D. thesis, The University of
Wisconsin - Madison, Madison, Wisconsin, USA.
Hart, D. J. and H. F. Wang (1999), Pore pressure and confining stress dependence of
poroelastic linear compressibilities and Skempton's B coefficient for Berea sandstone,
in Proceedings of the 37th U.S. Rock Mechanics Symposium, edited by Amadei et al.,
pp. 365-371, Balkema, Rotterdam, Netherlands.
Hsieh, P., J. Bredehoeft, and J. Farr (1987), Determination of aquifer permeability from
earthtide analysis, Water Resour. Res., 23, 1824–1832.
Ortega, J. A., F.-J. Ulm, and Y. Abousleiman (2007), The effect of the nanogranular
nature of shale on their poroelastic behavior, Acta Geotechnica, 2, 155–182, DOI
10.1007/s11440-007-0038-8.
Tamura, Y., T. Sato, M. Ooe, and M. Ishiguro (1991), A procedure for tidal analysis with
a Bayesian information criterion, Geophys. J. Internat., 104, 507–516.
Wang, H. F. (2000), Theory of Linear Poroelasticity, Princeton Series in Geophysics,
Princeton University Press, Princeton, New Jersey.
Wang, C.Y. and M. Manga (2010), Earthquakes and Water, Lecture Notes in Earth
Sciences, Springer, Heidelberg.
Xue, L. H.-B. Li, E. E. Brodsky, Z.-Q. Xu, Y. Kano, H. Wang, J. J. Mori, J.-L. Si, J.-L. Pei,
W. Zhang, G. Yang, Z.-M. Sun, Y. Huang (2015), Continuous permeability
measurements record healing inside the Wenchuan earthquake fault zone, Science,
340, 1555-1559, doi: 10.1126/science.1237237.
11