Source duration of stress and water-pressure induced seismicity derived from experimental analysis of P wave pulse width in granite
Geological Survey of Japan, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan
Corresponding author: K. Masuda, Geological Survey of Japan, National Institute of Advanced Industrial Science and Technology, AIST, Tsukuba Central 7, Tsukuba 305–8567, Japan. (email@example.com)
 Pulse widths of P waves in granite, measured in the laboratory, were analyzed to investigate source durations of rupture processes for water-pressure induced and stress-induced microseismicity. Water was injected into a dry granite sample under constant axial stress of about 70% of fracture strength and a confining pressure of 40 MPa. After the effects of event size and hypocentral distance were removed from observed pulse widths, the ratio of the scaled source durations of water-pressure induced and stress-induced microseismicity was 0.52. The difference in the scaled source durations between water-pressure induced and stress-induced microseismicity suggests that water-pressure induced microseismicity involves a greater rupture velocity or a more equidimensional fault geometry than stress-induced microseismicity. These results suggest that pulse width analysis of P waveforms can be used to distinguish water-pressure induced events from those induced by regional stress and to characterize the faulting process.
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 Much evidence suggests that fluids in the subsurface are intimately linked to faulting processes [e.g., Hickman et al., 1995; Masuda et al., 2012]. Studies of seismicity induced by water injection are thus important for understanding the trigger mechanisms of earthquakes as well as for engineering applications such as hydraulic fracturing of rocks at depth for petroleum extraction. Determining the cause of seismic events is very important in seismology and engineering; however, water-pressure induced seismic events are difficult to distinguish from those induced by purely tectonic stress. To investigate this problem, we analyzed the waveforms of acoustic emissions (AEs) produced in the laboratory by both water-pressure induced and stress-induced microseismicity.
 The duration of rupture is a fundamental characteristic of earthquakes that is useful for understanding mechanisms of faulting [Vidale and Houston, 1993]. We investigated the source duration of microseismicity in a rock sample by considering pulse width broadening of the initial part of the P wave. Pulse width, defined as the interval between the initial break and the first subsequent zero crossing of the P wave waveform, can be expressed by the empirical law of Gladwin and Stacey :
where τ is the pulse width, t is time, Q is the anelastic parameter, C is a constant, and τ0 is the initial pulse width at the source at t = 0. The initial pulse width τ0 is source dependent. The pulse width method has been applied to estimate the source durations of natural earthquakes [Harrington and Brodsky, 2009], fault dimensions [Tselentis, 1998], and Q−1 [Ohtake, 1987].
 We used a right circular cylinder (100 mm long and 50 mm diameter) of Inada granite (grain size 3–10 mm ) for our experiment. An equispaced receiver array comprising 20 piezoelectric transducers of 2 MHz resonant frequency was cemented to the surface of the cylinder, which was then sealed in silicone rubber in a configuration similar to that of Masuda et al. [1990, 1993]. Most of the observed pulse widths used in our analyses were between 0.5 µs and 1.3 µs, the lower end of this frequency range corresponding to the resonance peak of the piezoelectric sensor. There may be some other resonance peaks in this range, but they are not as sharp and narrow as the peak in the range near the resonance frequency; therefore, we could confidently compare rupture duration data in dry and wet states [e.g., Benson et al., 2008; Burlini et al., 2009]. An axial load was applied to the dry sample at a constant rate of increase under a confining pressure of 40 MPa. One hour after initial loading, the axial load reached 410 MPa (about 70% of fracture strength) and was then held constant for the remainder of the experiment. Figure 1 shows the number of AEs observed per minute during the experiment. About 4.5 h after reaching peak stress, AEs caused by differential stress had ceased. Distilled water was then injected at 17 MPa pressure into the base of the cylinder until fracture occurred. The experimental system cannot measure the volume of water injected. The number of AEs gradually increased in the first 2.5 h of water injection, after which their number increased rapidly. The difference in AE activity before and after water injection suggests that the later AEs were triggered by water flow. Therefore, we regarded the AEs between 1.0 and 5.5 h (Figure 1) as stress-induced microseismicity and those after 5.5 h as water-pressure induced microseismicity. In this microfracturing process, effect of static fatigue such as brittle creep and stress corrosion might be important too [e.g., Heap et al., 2011].
 We recorded the AE waveforms of magnitudes exceeding the threshold level of the recording system and measured P wave velocities at approximately 15 min intervals. We determined the hypocenters of AE events (Figure 2) by automatically picking the first arrivals of the P waves using the technique of Masuda et al. [1990, 1993] and plotted hypocenters that were determined with probability errors smaller than 2 mm [Schubnel et al., 2003; Lei et al., 2004]. A weak clustering of stress-induced AEs was apparent before water injection (Figure 2a). After water injection, stronger clustering was observed in the same part of the sample (Figure 2b). Events in these clusters were selected for waveform analysis.
 For waveform analysis of AEs, we used waveforms recorded at a receiver sufficiently distant from the hypocenters (see Figure 2) to minimize the effect of the incident angle on the detector and eliminate uncertainties due to nonsource effects such as site effects and instrument characteristics. We selected those events for which hypocenters were determined from 18 or more P wave arrivals and then rejected events for which the amplitude of the initial pulse was clipped or too small to be read. These criteria were met by 75 stress-induced events and 303 water-pressure induced events. Figure 3 shows examples of P waveforms from these AEs. Pulse widths were measured from the waveform traces plotted from the digital data. The sampling rate of the data acquisition system was 50 ns, so the resolution for τ was ±0.05 µs. The amplitudes A of the initial portions of the waveforms were used to estimate the magnitudes of events.
 Figure 4 shows pulse width τ plotted against hypocentral distance for stress-induced and water-pressure induced AEs. Before water injection started, the sample was completely dry. After water injection, the degree of infiltration could not be determined. However, because the wave paths were restricted to the central part of the sample (Figure 2), it is sufficient to know whether the central part of the sample was wet or not. Similar water injection experiments in our laboratory during which we calculated P wave velocity tomography of samples during water migration [Masuda et al., 1990, 1993] have demonstrated that the central portion of the sample is infiltrated quickly and nearly uniformly. Therefore, we assumed that our wave paths represent transmission through uniformly wet rock. By assuming a constant P wave velocity before and after water injection, equation (1) becomes
where r is hypocentral distance and αi (i = D in the dry state and W in the wet state) is a constant.
 To investigate the source duration of the rupture process, we estimated the pulse width at the source (τ0) and normalized it by event magnitude to obtain a scaled pulse width at the source (τ*). We eliminated the effects of event size and the distance between events and receivers as follows.
5.1 Size Effect Correction
 We corrected for event size in a manner similar to that of Vidale and Houston . Theoretically, pulse width is proportional to the cube root of the event moment M0 [Kanamori and Anderson, 1975],
M0 is defined as
where μ is the shear modulus, D is average fault dislocation, and S is fault area. The amplitude of the source time function, A*, is proportional to moment rate M˙0, which can be approximated as moment divided by τ [e.g., Harrington and Brodsky, 2009]. Thus,
 We also assume that
where A0 is the amplitude at the source, as defined in section 5.2. Then,
 If we assume that the proportionality constant in equation (7) is unity for simplicity in calculation, from equations (3) and (7), the scaled pulse width τ* is given by
 Then, we obtain
5.2 Distance Effect Correction
 In stressed rock samples, tensile cracks open preferentially normal to the maximum compressive stress direction and randomly distributed within that plane. This creates a case of horizontal transverse isotropy [e.g., Benson et al., 2007]. These tensile cracks can grow stably [Scholz, 2002]. Shear-type cracks inclined to the maximum stress direction also propagate by the generation of tensile cracks as schematically shown in Scholz [2002, Figures 1.11 and 1.18]. During a loading to failure, tensile cracks are dominant, except just before macroscopic failure [e.g., Lei et al., 2004; Stanchits et al., 2006]. In stressed homogeneous rocks, S wave velocity shows acoustic birefringence or splitting, with vertically polarized S waves always being faster than horizontally polarized S waves [e.g., Stanchits et al., 2006]. These observations suggest that vertically oriented tensile cracks show horizontal transverse isotropy. Therefore, in applying a distance correction to the observed data, we chose to ignore the direction of radiation and discussed the results as some effective values. The distance correction is in the following linear relation between the logarithms of the seismic amplitude A and the hypocentral distance r, commonly used to determine earthquake magnitudes [e.g., Masuda, 1992]:
where a and b are constants and
 And if r = 1, then
 We assume that A (at r = 1, in mm) ≈ A0 (at r = 0). In other words we use A (at r = 1) as a normalized amplitude defined as A0. Because the error of AE hypocenter determinations is 2 mm, our assumption of A ≈ A0 would not affect the results of distance correction. Equation (11) can then be written as
5.3 Scaled Source Duration
 From equations (9) and (14), we can calculate the initial pulse width as
 From equations (15) and (2), we can calculate the recorded pulse width as
 To estimate τ*, a, and αi (i = D or W), we applied a least squares fit of equation (16) to each data set of stress-induced and water-pressure induced microseismicity. The scaled pulse widths τ* with their standard deviations are 0.50 ± 0.51 µs in the dry state and 0.26 ± 0.74 µs in the wet state. Although the difference in calculated values for τ* is marginally significant, there is indeed a difference between dry and wet states. Because we assumed a proportionality constant of 1 in equation (7), we can discuss only the ratio of the scaled pulse width τ* of water-pressure induced to stress-induced microseismicity, which is about 0.52. The source duration of water-pressure induced microseismicity is definitely shorter than that of stress-induced microseismicity; it is an important finding that the difference exists and is detectable. As discussed by Madariaga , the scaled pulse width measured in this study is proportional to the duration of the rupture:
where Ts is the source duration, which is roughly equivalent to L/v,
where L is the characteristic length of the fault and v is the rupture velocity. Equation (18) indicates that source duration should be inversely proportional to rupture velocity and proportional to fault length. The observed decrease in scaled pulse width from 0.50 to 0.26, then, would require that rupture velocity increased by 92%, that fault length decreased by 48%, or that both changed by smaller amounts. Therefore, it appears that some elemental microfaulting processes changed after water injection.
 Rupture velocity is sometimes assumed to be proportional to S wave velocity [e.g., Vidale and Houston, 1993], but S wave velocity does not nearly double after water injection [e.g., Kitamura et al., 2006; Schön, 2011]. Instead, rupture velocity may be faster in the wet state than in the dry state because water may reduce the friction between crack surface contacts or grain boundaries [e.g., Scholz, 2002]. Faulting, as a result, might propagate faster in the wet state.
 It is also possible that fault geometry changes in the wet state. The reduced friction between surfaces within wet rock makes it easier for contact surfaces to slide over each other. This in turn might create a more homogeneous stress distribution, and crack propagation may result in a more equidimensional (less elongate) fault geometry.
 Laboratory observations of stress and water-pressure induced microseismicity in the same sample of Inada granite showed a large decrease in scaled source duration following the injection of water. This decrease suggests a difference in the fault processes of stress-induced and water-pressure induced microseismicity. Our results suggest that pulse width analysis of P waves from microseismic events observed in the field can distinguish water-pressure induced seismicity from stress-induced seismicity and be used to characterize faulting processes.
 T. Satoh and O. Nishizawa contributed to the initial stage of this study. Constructive reviews of P. Benson and S. Stanchits were very helpful in improving of the manuscript.
 The editor thanks Philip Benson and an anonymous reviewer for their assistance in evaluating this paper.