Mechanism of water level changes during earthquakes: Near field
versus intermediate field
Chi-yuen Wang1 and Yeeping Chia2
Received 7 April 2008; accepted 20 May 2008; published 19 June 2008.
[1] Using a new empirical relation among earthquake
magnitude, seismic energy density and hypocentral distance, we show that the documented water level changes during earthquakes occur across seven orders of magnitude of seismic energy density. Combining this relation with a global data set for water level changes, new data from Taiwan, and laboratory data for saturated sediments under cyclic loading, we show that at least two mechanisms may be important for inducing water level changes. Undrained volumetric change may be the dominant mechanism to cause the abrupt decrease or increase of water level documented in the near field, while an earthquake-enhanced permeability may account for the more gradual and sustained water level changes documented in the intermediate field.Citation: Wang, C.-Y., and Y. Chia (2008), Mechanism of water level changes during earthquakes: Near field versus intermediate field, Geophys. Res. Lett., 35, L12402, doi:10.1029/2008GL034227.
1. Introduction
[2] Several types of water level response to earthquakes
have been recognized [Roeloffs, 1998; Wang et al., 2004]: In the near field most documented water level changes show abrupt (step-like) coseismic increases (Figure 1a) [Wakita, 1975; Quilty and Roeloffs, 1997; Wang et al., 2001]. On the other hand, abrupt coseismic decreases in water level were documented in the immediate vicinity (<10 km) of the surface rupture of the causative fault of the 1999 Chi-Chi earthquake (Figure 1b) [Chia et al., 2001; Wang et al., 2001, 2004]. In the intermediate field, most documented changes are more gradual and can persist for days or weeks (Figure 1c); these are coined by Roeloffs [1998] as the ‘sustained’ water level changes. At even greater distances (the far field), only transient oscillations of the water level have been documented.
[3] Several mechanisms have been proposed to explain
these changes: (1) Static poroelastic strain of aquifers in response to fault displacement during earthquakes [Wakita, 1975; Quilty and Roeloffs, 1997], (2) earthquake-enhanced permeability [Rojstaczer et al., 1995; Roeloffs, 1998; Brodsky et al., 2003], (3) undrained dilatation and consolidation of saturated sediments [Wang et al., 2001], (4) resonant vibrations of wells [Cooper et al., 1965]. The poroelastic model was shown to predict water level changes during
earthquakes opposite in signs to that observed in some sedimentary aquifers [Roeloffs, 1998; Wang et al., 2001] and will not be discussed further here. The mechanism of resonant vibration occurs only with the right combination of well geometry and aquifer properties [Cooper et al., 1965] and will not be discussed here either.
[4] Here we examine the relative merit of the remaining
mechanisms. Undrained dilatation and consolidation both invoke volumetric changes. Earthquake-enhanced perme-ability, on the other hand, does not involve volumetric changes and is thus a distinct mechanism. Since different mechanisms require different amounts of energy to activate, we use a laboratory-derived energy criterion together with the distribution of seismic energy in the field to discriminate among the mechanisms. The result suggests that undrained dilatation and consolidation of sediments may be responsi-ble for the abrupt water level changes in the near field, while an earthquake-enhanced permeability may be respon-sible for the more gradual changes in the intermediate field. We use a global data set and new data from Taiwan to test the models.
2. Seismic Energy Density
[5] Using 30,000 strong-motion records for Southern
California earthquakes, Cua [2004] derived empirical rela-tions between the peak ground velocity with distance from the earthquake sources. From these Wang et al. [2006] derived e(r) = A/r3for soil sites, where e(r) is the seismic energy density at a hypocentral distance r and A is an empirical constant. In the near field, source dimension and rupture directivity, in addition to hypocentral distance, may significantly affect the dynamic strain. Thus the above relation can only be taken as a first-order approximation. Given this approximation, we have A = 3E/4p, and E is related to e(r) by
E¼4p 3e rð Þr
3
: ð1Þ
This relation is entirely empirical and thus includes both the geometrical and physical attenuation of the seismic energy. Combining this with Bath’s [1966] empirical relation between E and earthquake magnitude M, we obtain the following empirical relation among e, r and M:
log r¼ 0:48 M 0:33 log e rð Þ 1:4 ð2Þ
which was given without derivation by Wang [2007] and r is in km. Although strictly valid only for southern California, we assume it may be applied elsewhere in the absence of similar relations.
Here
for Full Article
1Department of Earth and Planetary Science, University of California,
Berkeley, California, USA.
2
Department of Geological Sciences, National Taiwan University, Taipei, Taiwan.
Copyright 2008 by the American Geophysical Union. 0094-8276/08/2008GL034227$05.00
[6] Plotting the above relation with log r against M at
constant e, we obtain the contours in Figure 2. Figure 2 also shows the relation between log r and M (red line) for r equal to one ruptured fault length (Wells and Coppersmith [1994] for all subsurface fault types). It shows that, at r equal to one ruptured fault length, e is10 J/m3[Wang, 2007]. For the
convenience of discussion we define the region within one ruptured fault length from the earthquake source as the near field.
[7] Many authors documented sustained water level
changes in the intermediate field [e.g., Roeloffs, 1998; Brodsky et al., 2003]. Referred as the ‘global data set’, these plot in Figure 2 across a range of e from 104to 100J/m3. Plotted also are the water level changes during the 1999 Chi-Chi and the 2006 Hengchun earthquakes; some of these plot at seismic energy densities in excess of 103J/m3. Taken together, the documented water level changes occurred across seven orders of magnitude in seismic energy density.
3. Dissipated Energy Required to Initiate Undrained Consolidation
[8] A great number of laboratory experiments has been
carried out by geotechnical engineers to study the consol-idation of sediments [e.g., Seed and Lee, 1966; Dobry et al., 1982; Vucetic, 1994; Hsu and Vucetic, 2004]. Using a wide variety of saturated sediments and a wide range of confining pressures, Dobry et al. [1982], Vucetic [1994] and Hsu and Vucetic [2004] showed that pore pressure begins to buildup when sediments are sheared to 10 cycles at a strain amplitude of 104. Yoshimi and Oh-Oka [1975] further showed that this result may not be significantly affected by the frequency of loading.
[9] The dissipated energy density required to initiate the
undrained consolidation in saturated sediments may be estimated from the experimental time histories of shear stress t and strain g by performing the following integration:
ed¼ Zt 0
tdg ð3Þ
where the integration extends from the beginning of the cyclic loading to the onset of pore-pressure buildup. For small strain prior to the onset of undrained consolidation, the cyclic experimental stress and strain may be approxi-mated byt = tosinq and g = go sin(q +8), respectively,
wheretoandgoare the corresponding amplitudes and8 is
the phase delay between stress and strain. Integrating (1) we have ed¼ Np 2 togosin8 ffi Np 2 mg 2 o8 ð4Þ
where N 10 is the usual number of cycles adopted in experimental study, m is the shear modulus measured at strain amplitude of 104. We list in Table 1 the available experimental data for the shear modulus and the damping ratio, together with the calculated edvalues. The calculated
ed range from 0.1 to 10 J/m 3
, reflecting the different potentials for sediments to consolidate under cyclic loading and the effect of different confining pressures under which the measurements were made [e.g., Ishihara, 1996]. Undrained dilatation requires a greater amount of energy to initiate [Luong, 1980]; but quantitative estimate of the threshold energy cannot be made because of insufficient data.
Figure 1. (a) Positive water level change in the Yuanlin I well during the 1999 Mw7.5 Chi-Chi earthquake. The well
is25 km from the hypocenter, thus in the near field, and 13 km from the surface rupture of the causative fault. The step-like coseismic water level increase is +6.55 m. (b) Negative water level change in the Liyu II well during the 1999 Mw7.5 Chi-Chi earthquake in Taiwan. The well is
20 km from the hypocenter, thus in the near field, but is only5 km from the surface rupture of the causative fault. The step-like coseismic water level decrease is 5.94 m. (c) Normalized sustained water level change in the BV well during the 1992 Mw7.3 Landers earthquake in California
[from Roeloffs, 1998]. The well is 433 km from the hypocenter and is thus in the intermediate field.
[10] Hazirbaba and Rathje [2004] showed that the
threshold strain required to initiate undrained consolidation in the field is the same as that in the laboratory. Thus it may be justified to compare the seismic energy density in the field with the laboratory-based dissipated energy required to initiate undrained consolidation; the latter is shown by the hachured band in Figure 2. Above the hachured band in the intermediate field, the seismic energy density is less than the laboratory-determined threshold energy required to initi-ate undrained consolidation; below the hachured band in the near field, the seismic energy density may be large enough to initiate undrained consolidation; within the hachured band, the seismic energy may cause the more sensitive sediments to consolidate, but not the less sensitive ones.
4. Model Testing and Discussion
[11] Since the seismic energy density in the intermediated
field is too small to initiate undrained consolidation, a distinct mechanism is required to explain the sustained water level changes at such distances (Figure 2). Several authors suggested that seismic waves may enhance rock permeability by removing precipitates and colloidal par-ticles from clogged fractures, which in turn may lead to gradual changes of water level in a nearby well hydrauli-cally connected to a local pressure source [Matsumoto et al., 2003; Brodsky et al., 2003]. Since an enhanced permeability can occur either up-gradient or down-gradient of a well, either positive or negative change of water level may be expected. Thus, if a sufficiently large number of
observa-tions are available, a statistically random occurrence in both the sign and the magnitude of the water level changes may be predicted. On the other hand, undrained consolidation of sediments around wells would produce water level increases in all wells. The strong contrast between the predicted behaviors permits the two mechanisms to be tested by documented field observations.
[12] We note that enhanced permeability may occur both
in the near field and in the intermediate field. In the near field, however, the effect of enhanced permeability is likely Figure 2. Hypocentral distance (in km) plotted against earthquake magnitude to show contours of constant seismic energy density and domains where different types of coseismic water level responses occur. The hachured band shows the laboratory-determined dissipated energy required to initiate undrained consolidation. Above the hachured band in the intermediate field, the seismic energy density may be less than the laboratory-determined threshold energy required to initiate undrained consolidation; below the hachured band in the near field, the seismic energy density may be large enough to initiate undrained consolidation; within the hachured band, the seismic energy may be sufficient to initiate consolidation in the more sensitive sediments, but not in the less sensitive ones. Red line shows the hypocentral distance of one ruptured fault length as a function of earthquake magnitude [Wells and Coppersmith, 1994]. Sustained water level changes in a global data set (see text) are shown in red circles; some represent multiple wells located in close proximity. Colored bars show the range of hypocentral distances for water level changes during the 1999 Chi-Chi M7.3 earthquake (labeled C) and during the 2006 M7.0 Hengchun earthquake (labeled H); red shows distances where both positive and negative changes occurred; blue shows distances where most changes were positive.
Table 1. Shear Moduli and Damping Ratios of Sediments, determined Under Laboratory Conditions and Cyclically Sheared to a Stain Amplitude of 104a
Samples Shear Modulus Damping Ratio (MPa) Dissipated Energy (J/m3) Undisturbed Fujisawa sand 100 0.07 1 Disturbed Fujisawa sand 40 0.02 0.1 Undisturbed Tokyo gravel, at a
confining pressure of 300 KPa
300 0.04 2
Undisturbed Tokyo gravel, at a confining pressure of 500 KPa
600 0.05 5
Reconstituted Tokyo gravel, at a confining pressure of 300 KPa
200 0.07 2
Reconstituted Tokyo gravel, at a confining pressure of 500 KPa
400 0.08 5
aDissipated energy is calculated using equation (4) with N = 10.
(Experimental values for the shear modulus and the damping ratio were read from Ishihara’s [1996] diagrams on p.143 and 145, and are thus approximate.)
to be obscured by the abrupt changes of water level due to undrained dilatation or consolidation. Thus the effect of enhanced permeability is revealed only in the intermediate field where undrained volume changes do not occur.
[13] In Figure 3a we plot the amplitude and sign of the
sustained water level changes as functions of distance to earthquake source for the global data set represented by red circles in Figure 2. A random distribution of the magnitude and the signs of these changes is apparent; the mean groundwater level change is 0.003 m and the standard deviation is 0.192 m. Thus the data is consistent with the enhanced permeability model.
[14] Over two hundred monitory wells in central Taiwan
documented the water level changes during the 1999 M7.5 Chi-Chi earthquake [Chia et al., 2001, 2008; Wang et al., 2001], providing a nearly continuous record of the signs and amplitudes of water level changes from a hypocentral distance of 20 km to 160 km (Figure 3b). Nine wells in the immediate vicinity of the surface rupture of the causa-tive fault showed abrupt coseismic water level decreases, consistent with the undrained dilatation model; at distances up to one ruptured fault length (85 km) but away from the surface rupture, the water level changes were all positive, consistent with the undrained consolidation model. At distances beyond one-ruptured fault length, negative changes appeared, which is consistent with the prediction of mechanism transition from undrained consolidation to enhanced permeability. During the 2006 M7.0 Hengchun earthquake which occurred offshore of southern Taiwan, a large number of monitory wells documented mostly pos-itive changes at distances up to one ruptured fault length, but both positive and negative changes at further distances (Figure 3c). No wells, however, were located close to the causative fault. Several earthquakes that occurred on eastern Taiwan [e.g., Chia et al., 2008] are not included in the present analysis because these earthquakes are separated from most monitory wells by the Central Ranges of the island, which may introduce complications to the seismic wave attenuation and thus to equations (1) and (2).
[15] The ranges of hypocentral distances for water level
changes documented during the Chi-Chi and the Hengchun earthquakes are plotted as colored bars in Figure 2 (marked by C and H, respectively). The change in color in each bar marks the transition in from locations with only positive changes to locations with both positive and negative changes (Figures 3b and 3c). In both case, this transition occurs close to the lower bound of the hachured band, i.e., at e 10 J/m3, consistent with the hypothesis that it
corresponds to a change in mechanism from undrained-consolidation to enhanced-permeability.
[16] Thus we may suggest that, in the near field, the
dominant mechanism for water level change is the un-drained volumetric change, while in the intermediate field it is an enhanced permeability. These mechanisms also provide simple explanations why the water level changes are abrupt in the near field and more gradual (and sustained) in the intermediate field and why a given well in the intermediate field shows consistently positive or consistently negative water level changes and similar time histories during different earthquakes [e.g., Roeloffs, 1998; Matsumoto et al., 2003]. The occurrence of undrained volumetric changes around a well in the near field causes an immediate pore pressure change, thus an abrupt water level change in the well. On the other hand, an enhanced permeability connects a well to a nearby pressure source (or sink); since the transmission of pore pressure from the source to the well Figure 3. Amplitude and sign of water level changes
during earthquakes plotted as functions of the hypocentral distance. (a) Water level changes in a global data set (see text). (b) Water level changes during the 1999 Chi-Chi earthquake. The upward arrow shows the distance equal to one ruptured fault length. Note that nine wells near the downward arrow documented abrupt decreases of water level as illustrated in Figure 1b. These wells are all located in the immediate vicinity (<10 km) of the surface rupture of the causative fault. (c) Water level changes during the 2006 Hengchun earthquake. The upward arrow shows the distance equal to one ruptured fault length.
requires time, water level changes in the intermediate field are more gradual, as explained by previous authors [e.g., Brodsky et al., 2003]. Furthermore, since the passageway with enhanced permeability may remain the same for a given well, one may expect a consistent sign of water level changes and similar time histories during different earth-quakes. The enhanced permeability, however, may decline with time due to re-clogging of the fractures by hydro-geological and/or biogeochemical processes.
[17] We note that the effects of rupture directivity, seismic
frequency, well depth, etc., may significantly complicate the simple picture presented above and need to be clarified in the future.
[18] Acknowledgments. We thank Michael Manga, Shemin Ge and an anonymous reviewer for helpful comments. Research is partly supported by the National Science Council of Taiwan (NSC-94-2116-M002-005) and the Water Resources Agency of Taiwan (MOEAWRA0960016).
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C.-Y. Wang, Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, USA. (chiyuen@berkeley.edu)
Y. Chia, Department of Geological Sciences, National Taiwan University, Taipei, 10617 Taiwan.
