JOURNAL OF GEOPHYSICAL RESEARCH, VOL.???, XXXX, DOI:10.1029/, 1 2 3 Fluid related deep low-frequency earthquakes resonant with the Rayleigh waves from the 2004 Sumatra-Andaman earthquake Masatoshi Miyazawa 4 Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto, Japan Emily E. Brodsky 5 Department of Earth Sciences, UC Santa Cruz, California, USA Masatoshi Miyazawa, Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto 611-0011, Japan. (linen@eqh.dpri.kyoto-u.ac.jp) Emily E. Brodsky Department of Earth Sciences, UC Santa Cruz, CA 95060, USA. (brodsky@pmc.ucsc.edu)
X - 2 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR 6 Abstract. The large surface waves from the 2004 Sumatra-Andaman earth- 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 quake dynamically perturbed the upper mantle structure in Japan and triggered periodic deep-low frequency seismic events in eastern and western Shikoku, western and central Tokai and the Kii peninsula. This occurrence of triggering may give insight into the mechanism of the recently discovered deep lowfrequency seismic events. Volumetric changes from the short-period (15 30 sec) Rayleigh waves with vertical extension and horizontal compression, play an important role in the triggering. Building on previous results that the event signals become increasingly strong with increasing dilatation, we compared the dilatation due to the Rayleigh waves, to signals from triggered events at the 30 km depth source regions, and observed clear relationships. There is an exponential relationship between the signal amplitude from triggered events and the dilatation, especially significant at the source region. The observations constrain the source mechanism of the deep low-frequency events. We suggest a possible source model that combines fluid and frictional processes. The dilatation strain opens fractures and promotes fluid flow. The fluid enters the fault zone and promotes slow slip. In this model, the fluid dehydrated from the subducting slab promotes the event excitation, which is consistent with the models suggested from geochemical results. Our result provides some of the first clear evidence from seismic data that the deep low-frequency events may have fluid-flow processes.
MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 3 1. Introduction 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Until the last decade in 20th century, dynamic triggering of earthquakes by transient stress perturbations had been a dubious matter with only circumstantial evidence. More recently, high density seismic networks have been deployed, and as a result we have had many clear observations of remote triggering of earthquakes from large teleseisms. Despite many observations, we still have challenges to investigate. For example, we would like to know if there is a common threshold to excite earthquakes and if so what it is. What is the mechanism of the triggering? When are earthquakes excited? The 2004 Sumatra-Andaman earthquake (Mw 9.1 9.3) was a huge event and the surface wave amplitudes measured in Japan were comparable to or a few times as large as those from the Denali earthquake (Mw 7.9) in 2002 that contributed to the triggering around North America that was investigated in many papers [e.g., special issue of Bull. Seism. Soc. Am., 2004]. Hence, we investigate the triggering from the Sumatra event in order to provide new information on the key issues of triggering threshold and triggering mechanism. Miyazawa and Mori [2006] showed that periodic triggering of deep low-frequency events in western Japan was due to the Rayleigh waves from the Sumatra event, and suggested that the triggering is well correlated with the large tensile dilatation at the source regions (Figures 1 and 2). These initial observations distinguished the tremor from the ordinary events triggered in Alaska that were promoted by shear failure [West et al., 2005]. The mechanism of the deep low-frequency earthquake/tremor is still unclear. Geochemical studies suggest that the flow of fluid dehydrated from the subducting slab should play an
X - 4 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 important role in excitation [e.g., Toriumi and Inui, 2001; Omori et al., 2004]. Furthermore, the low-frequency nature of the seismic signals is sometimes taken as evidence of fluid source [Obara, 2002]. However, low-frequency signal could potentially be made by either fluid movement [Seno and Yamasaki, 2003; Katsumata and Kamaya, 2003] or slow shear faulting [Obara and Hirose, 2006; Shelly et al., 2006]. In this paper, we follow up on the initial observation by carefully analyzing the strain field and quantifying the spectral and amplitude relationships between strain at the source and the resulting tremor. These observations will lead us to more definitive evidence for the role of fluids in deep low-frequency tremor excitation. This paper begins with a review of prior observations of triggered tremor combined with a discussion of the most salient first-order features. We then derive the strain changes in the tremor source regions due to the Sumatra seismic waves. By comparing the spectrum of the triggered and input signals, we determine which frequencies of the Rayleigh waves are capable of triggering the events significantly and what strain changes are relevant. On the basis of these results, we proceed to more carefully investigate the functional dependence of the amplitude of the tremor on the input dilatation given various assumptions about the spatial distribution of sources. Finally, we discuss the physical implications of our results both for standard rate-state models and a more complex scenario involving fluid-mediated fault slip. 2. Observations 2.1. Overview of triggered tremor 67 68 Miyazawa and Mori [2006] used High Sensitivity Seismograph Network (Hi-net) to un- cover non-volcanic deep low-frequency events triggered by the Sumatra earthquake. By
MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 5 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 filtering the continuous waveforms, they found discrete episodes of low-frequency tremor that correlated well with the packets of the Rayleigh waves (Figure 1). They established that the dilatation at the source region correlated well with the triggering (Figure 2). When the strain had peak values of about 10 7, strong triggering was observed. They located hypocenters by using a modified envelope correlation method [Obara, 2002; Miyazawa and Mori, 2005], which measures travel time differences between the envelopes by using cross-correlations of the envelope time series for a range of time lags. We relocated the hypocenters using a double-difference method [Waldhauser and Ellsworth, 2000] and a velocity model JMA2001. The source locations are shown by red circles in Figure 3 and the sources located at depths of 30 to 40 km, which correspond to the regions where the deep low-frequency earthquakes have episodically occurred (yellow circles in Figure 3) above the subducting Philippine Sea plate. The events seem to have occurred in five clusters: western and eastern Shikoku, western and central Tokai and the Kii peninsula. Like other example of low-frequency tremor, the triggered episodes were predominately shear waves as inferred by the apparent velocity and large amplitude in horizontal components (Figures 1 and 4), and had large amplitudes for waves from 1 to 15 Hz (Figure 5). Figure 4 shows the largest event observed in western Shikoku as an example. The waveforms (2 16 Hz) observed at each epicentral distance are shown for each component. Two dotted curves of earlier and later arrivals roughly show P and S wave arrivals assuming the origin time is 0 on the scale shown. The large wave packets travel at S wave velocity, while we can find arrivals of subtle proceeding signal in vertical components which seem
X - 6 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 to be on the P wave arrivals. The proceeding signals may be P waves, and/or S waves from another triggered event. We do not always observe them for other triggered tremors. An interesting feature of the waveform is that the large packets of tremors are almost symmetrical at each station. To see if this is caused by path effects, we looked at large earthquakes (M 4) that occurred in a similar but slightly deeper location (depth 40 km) near the plate boundary or in the subducting slab. The earthquakes radiated waves with similar frequencies to the tremor, but amplitudes several thousand times larger. For the earthquakes, the onsets of P and S waves are clear. In contrast, the waveforms of the tremor in Figure 4 show emergent arrivals even at the distant stations and on high-frequency components. This feature distinguishes the events from ordinary tectonic earthquakes and implies that the triggered tremors likely produce mostly S waves in some continuous or repeated process. Figure 5 shows an example of the Fourier spectra of vertical and horizontal components from 1400 to 2400 sec (see Figure 1) at stations with almost the same epicentral distance from the Sumatra event, KWBH and IKNH, where the tremors have been observed and have not, respectively. The ratios of the same components for two stations are shown in the bottom. The spectra lower than 1 Hz almost correspond to each other, while there are large differences in ranges higher than 1 Hz, which are especially significant in the horizontal component. Note that a peak around 20 Hz in the horizontal component is known noise due to resonance of the borehole. For some large triggered events, even in the frequency range around 1 Hz, the signal to noise ratio is high enough to see the particle motion. Figure 6 shows the particle motions of three large events. The vertical amplitudes are as small as 1 µm/s, which
MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 7 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 is comparable with the background noise. Their principal axes of the particle motions are NW-SE, WNW-ESE, and N-S, respectively, which are almost perpendicular to the 40 km depth contour line of subducting Philippine Sea plate boundary at each site as estimated from the seismicity. These events may occur on or above the plate boundary. Higher-frequency waves do not show as clear an orientation from the particle motion. If the source model of the triggered events is equivalent to a double couple model, we can observe P waves at the stations located in the compressional/tensional quadrant of the focal mechanism, which are along northwest and southeast directions at some distances at western Shikoku. In Figure 4, we observed clear proceeding signals in the vertical component at southeast stations (e.g., at distances of 20 km and 36 km), which are probably P waves. However, as the early phases are still unclear at other stations and are not common to the other smaller events, possibly due to poor signal-to-noise ratios, we focus on the later, larger packets by using only horizontal components in waveform analyses. Figure 7 shows short-period and long-period root-mean-square (RMS) envelope waveforms from representative examples of each of the clusters in Figure 3. The short-period waveforms are constructed from waveforms filtered with a pass-band of 2 16 Hz and show the activity of triggered events, and the long-period waveforms are the envelope waveforms of Love and Rayleigh waves filtered with a pass-band of 0.01 1 Hz. The seismicity seems to correspond to the amplitude of surface waves. At the western Shikoku and the central Tokai regions, the events are more actively triggered than other three regions. Relationships between origin-time and local magnitudes are shown in Figure 7 by small solid circles, where the magnitudes are compared with the envelope waveforms of Love and
X - 8 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR 138 139 140 141 Rayleigh waves filtered with a pass-band of 0.01 1 Hz. The amplitude of Rayleigh waves (gray line) rather than Love waves (dotted line) appears to correlate with the triggered event magnitude. In the following sections, we will attempt to quantify and expand upon this apparent correlation. 2.2. Strains at depth 142 143 144 145 146 147 148 149 150 151 Miyazawa and Mori [2006] examined the strains at the source regions estimated by continuing the wavefield observed on the surface to depth using a kernel for one cycle of surface waves, and found that events were synchronized with large extensions. Here we investigate the strains at depth for the full spectrum using appropriate kernels for continuous waveforms. To extrapolate the observed dilatational strains to depth, we use solutions for Rayleigh wave equation for a simple half-space structure [e.g., Lay and Wallace, 1995], and calculate the displacements and then the resulting strains. We take positive for radial and vertical directions. The strain changes across radial and vertical directions, e rr and e zz, are given by e rr = A 0 k 2 cos(kr ωt) [ exp( ω ˆη α z) + 1 ( ) ] c 2 2 β 2 exp( ω ˆη 2 β z) e zz = A 0 k cos(kr ωt) [ cω ˆη 2 α exp( ω ˆη α z) + ω ( ) ] c 2 2c β 2 exp( ω ˆη 2 β z) (1) (2) 152 153 respectively, where
MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 9 ηˆ α = 1 c 1 1 2 α 2, ˆη β = c 1 2 β2, (3) 154 155 156 157 158 159 160 161 A 0 is a constant coefficient, k is the wavenumber, ω is the angular frequency, r is the radial distance, z is the depth, α is P wave velocity, β is S wave velocity and c is the phase velocity of the Rayleigh wave. We assume α = 8.7 km/s, β = 5.0 km/s, and c = 3.5 km/s. When we change these velocities within reasonable ranges, the results show little differences. The dilatation, or volumetric strain change, V/V is approximately given by e rr + e zz. Ideally, there is no-contribution to e rr and e zz, from Love waves. To calculate strains beneath a station, we directly estimate the phases and amplitudes 162 from the observed vertical component u obs z while Miyazawa and Mori [2006] use only 163 164 equations (1) and (2) for each cycle of the surface waves. Since the vertical particle motion at the surface is u z z=0 = A 0 k cos(kr ωt) [ c ˆη α + 1 ( )] c 2 2c ˆη β β 2, (4) 2 165 166 167 168 169 170 e rr /(u z z=0 ) and e zz /(u z z=0 ) include neither A 0 nor the sinusoidal function. We obtain the predominant period of the surface wave at arbitrary time to give k and ω, assuming that the period is unique and the surface wave is not dispersed during the cycle. Hence, we much more accurately have the computed strain changes, e rr and e zz, beneath the station at arbitrary depth as
X - 10 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR e rr u obs z u z z=0 e zz u obs z, u z z=0 (5) (6) 171 172 respectively. Similarly, u r / z (= u r,z ) and u z / r (= u z,r ) at arbitrary depth are given 173 by [u r,z /(u r z=0 )]u obs r and [u z,r /(u r z=0 )]u obs r, respectively. 174 175 176 177 178 179 180 181 182 183 184 185 186 Examples of the resulting strains and stresses are shown in Figures 2(b) and (c) for a station KWBH in western Shikoku. When the events are significantly triggered, the amplitudes of the surface waves at depth are 0.1 0.5 as large as the amplitude at the surface. If the triggered events are faulting along the subducting plate, we can obtain the stresses on the fault plane. The Philippine Sea plate approximately subducts in the NW-direction, which is almost perpendicular to the radial direction from the Sumatra event. Assuming the fault plane is parallel to the plate boundary, we get that the stresses on the fault plane from the surface waves are a few kpa at most, while those from the S waves are 10 kpa. However, clear triggering is only observed during the arrivals of the surface waves. Furthermore, when large triggering was observed, shear stresses from the Rayleigh waves are very small compared to the normal stresses (Figure 2c). Therefore, shear stress does not appear to be an effective agent for triggering. 2.3. Spectra 187 188 Now that the strains are corrected for depth, we can investigate the efficiency of trig- gering of the wavefield as a function of frequency. Since the body wave and Love wave
MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 11 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 observations indicate that dilatation is more effective than shear in triggering, we compare the observed triggering during the surface wavetrain to the Rayleigh waves rather than the Loves waves. In Figures 1 and 2, significant triggering was observed for 21 sec Rayleigh waves around 1900 sec, but little triggering occurred at earlier times even though the waves have similar amplitudes in displacement. This may indicate short-period Rayleigh waves are much more capable of exciting deep low-frequency events. Both the amplitude and the period of Rayleigh waves may contribute to the dilatation changes at the deep low-frequency source region. Figure 8(a) shows the Fourier spectra for the vertical displacement, velocity, and acceleration of Rayleigh waves recorded at a broad-band seismic network (F-net) station, TSA. Dominant amplitudes are observed at periods (T) of 20 sec and 25 sec. Clear early arrivals of Rayleigh waves (1400 1500 sec) with periods of 35 50 sec also have large amplitudes in displacement. Using equation (1) and (2), we obtained the largest positive dilatational strain changes and corresponding two normal strains (in vertical and radial directions) from the Rayleigh waves at a depth of 30 km, where the deep low-frequency sources are approximately located (Figure 8b). Amplitudes are normalized by the largest vertical displacement at the surface, which can help us to understand the relative strains for frequency at depth (equations 5 and 6). The dilatation V/V becomes larger for longer period and has a peak value around T = 50 sec, while e rr and e zz have the large values around T = 17 18 sec. The sign of e rr changes if the period is longer than 38 sec, where the direction of particle motion changes.
X - 12 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 Figures 8(c) (c ) combine Figures 8(a) and (b) with the relationship between period T and strain for the example of TSA and four other stations representing each of the cluster regions. We use data recorded at F-net stations in Figure 3. Figure 8(d) indicates the largest amplitudes of triggered deep low-frequency events during the passage of the Rayleigh waves as a function of the corresponding predominant periods. The figure is constructed by taking the maximum period of the spectra of the time-series in a 100 sec moving Gaussian window and plotting it against the amplitude of root-mean-square envelope waveforms of deep low-frequency tremors for the time series in the same window. The indicated period does not necessarily indicate that of the Rayleigh waves which actually triggered the event, because secondary peaks may play a role. From Figures 8(c) (d), the peak of surface wave strains at T = 20 and 25 sec correspond to tremor peaks. For shorter periods, we observed significant deep low-frequency amplitude at T = 17 sec at KWBH, however the corresponding peak in strain is very small. At HRKH, the largest peak appears at shorter period and does not correspond with any peaks of the surface wave spectrum in that region (KMT). For long-periods, the maximum dilatation is large for period of T = 40 sec and greater, but the tremor excited by this frequency range is small. In the western Tokai region (WTR and URSH), strong triggering has also observed around T = 34 38 sec where e rr is very small. It seems that both absolute values of e rr and e zz are more similar to the tremor than the dilatation. Also, the acceleration (Figure 8a) seems to most closely follow the spectral form of the deep low-frequency signal with strong triggering at short-periods and weak triggering at long-periods.
MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 13 2.4. Dilatation amplitude and triggered amplitude 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 The simplest way to investigate the quantitative relationship between event triggering and surface waves, is to compare the amplitude of the strain components in the Rayleigh waves, to the local event magnitude. The magnitude calibration includes attenuation of waves propagating through the structure, and may therefore be an improvement on simply comparing the peak amplitude. Figure 9 shows the relationship between event magnitude and the largest dilatation observed during the event excitation. The larger amplitude waves seem to be capable of triggering events with large magnitude, but small events also occur during the large amplitude surface waves. This is also seen in Figure 7, where some event magnitudes are plotted lower than the envelope waveforms. As a result, we could not find a clear relationship with magnitude using this method. We therefore proceed to investigate the relationship between signals from triggered sources and strain changes ( V/V, e rr, and e zz ), considering both the amplitude and the phase rather than just the peak amplitude that is used for magnitude. We can obtain the strain changes during arrivals of Rayleigh waves, by using equations (5) and (6) with the appropriate periods and the observed vertical displacement waveforms. As discussed above, we use the horizontal components in order to focus on the clearest, largest packets of tremor for each triggered event. Seismic waveforms observed at a station above the triggered event region would be ideal for this purpose. We use the Hi-net data rather than the F-net data, because the denser Hi-net network has more very near the triggered deep low-frequency source regions (Figure 3). The Hi-net seismometers have natural periods of 1 sec, and they may not be suitable to get the actual particle motions for long-period waves such as from the Sumatra
X - 14 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 earthquake without additional calibration. By matching the Hi-net records with nearby F-net records, we calculate that the Hi-net amplitudes should be about 4.5 times as large as specified by the standard calibration. We also apply this calibration to make surface wave envelopes in Figure 7, but not in Figure 8 because we cannot calibrate the amplitude for a wide frequency range. From the determination of the event locations shown in Figure 3, the hypocenters appear to locate at almost the same region in each of five clusters. The relocated hypocenters still have significant errors in depth. In the following two sections we consider two possibilities: Either the hypocenters are co-located in each cluster or they are not. We will show that the results are not sensitive to either assumption. 2.4.1. Assuming tightly clustered events Here we assume that in each cluster of events, individual sources are separated by much less than the wavelength of the incoming surface waves. We use waveforms observed at 5 Hi-net stations shown in Figure 3 (diamonds). The source location is assumed to be the mean location of each cluster. We then compare the tremor amplitudes with the triggering strains by shifting the observed surface waves at the station closest to the epicenter (corrected for depth) to the source location. The timeshift is computed by combining the travel time for the tremor and the phase shift of the surface waves resulting from the propagation from the tremor epicenter to the observation station. Miyazawa and Mori [2006] found that triggering correlated with peak amplitude of volumetric strain changes. When we relocated the hypocenters, the result is almost the same. Figure 10 shows the relationships between the strain changes at the source region
MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 15 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 and the deep low-frequency signals at the 5 regions. The dilatations span ±3 10 7. In 4 regions except for the eastern Shikoku region (IKWH), we find a clear relationship that large dilatation excites both large and small tremor signals while the small dilatation only excites small tremors. As a result, the mean tremor amplitude generally increases with dilatation (solid line) as does the variance (shaded region). The horizontal strain e rr is small when the dilatation is large, but the vertical strain e zz is large. At eastern Shikoku, the trends seem to be opposite to the other regions. However, the relocated hypocenters are not robust and include large location errors, since the signal-to-noise ratios are very poor among the 5 regions (Figure 7), then the result may not be resolved. In the right portion of Figure 10, the averages of signal amplitudes are fit by 2 and 3-dimensional polynomials and exponential functions for volumetric strain changes. An n n-dimensional polynomial for x is given by a i x i, where larger n fits the data beti=1 ter. An exponential function for x is given by ae bx + c. The standard deviations of the residuals between the functions and observations are indicated in parentheses. In every region, though the polynomial functions match the observations better, the differences are small. To address the small signal under the compression, the exponential model is also reasonable as the differences between models are small. Motivated by the correlation between acceleration and tremor spectra in Figure 8, we also obtain the relationship between the vertical acceleration at source regions and the deep low-frequency envelopes at the same 5 stations (Figure 11). We apply the same timeshift procedure as above. The acceleration is given by ü z ü z z=0 ü z obs. (7)
X - 16 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 The values are within ±1.3 mm/s 2 which is considerably smaller than gravitational acceleration. Because of the phase difference by π from u z or e zz, the negatively large acceleration corresponds to the large signal amplitude except for IKWH. The standard deviations are large for large mean signal amplitudes and small for small ones. At URSH the peak value does not appear at the negatively largest acceleration as well as in Figure 10. From Figure 8(a) acceleration and Figure 8(d) KWBH, the peak values seem to correspond to each other and the acceleration has much better relationship with the deep low-frequency amplitude than dilatation V/V. Nevertheless we find large variances as we did for the dilatation (Figure 10). In Figure 8(d) we draw the largest amplitude of triggering for period and exclude other small ones, which can cause the amplitude to be variable when we take all the signals into account (Figures 10 and 11). The acceleration may apparently and incidentally explain the event amplitudes well. 2.4.2. Assuming multiple-locations The hypocenters obtained above (Figure 3) still have errors (especially in depth) and it is possible that their separation is significant compared with the wavelength of the surface waves. To deal with this possibility, we pursue a different approach to the analysis. Instead of assuming that the pulses co-locate, we consider each pulse separately as a separate event that must be shifted in time relative to the others in order to derive the correct phase relationship with the incoming wave. To investigate the relationship as above, we should deterministically give appropriate timeshifts for each event. We select well-relocated events with small location errors to minimize the timeshift errors. We compare the beginning of the wave packet with a calculated dilatation at the source.
MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 17 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 The symmetric nature of the wave packets and the slowly arising amplitude of the arrivals suggest that the tremor envelopes reflect source time functions (see section 2.1). However, we cannot discount the possibility that the envelope shape after the peak is independent from the effect of the structure during the propagation. Then it is reasonable to correlate the first half packet before the peak with the dilatation in this way. Figure 12 shows the relationships, in which we use the 17 clear deep low-frequency events (9 in western Shikoku, 1 in the Kii peninsula, 2 in western Tokai, and 5 in central Tokai) with large signal-to-noise ratios (for example, see the numbered events in Figure 7). The event amplitudes are large for the positive volumetric strain and the vertical expansion, and for the radial compression. For each event in gray lines, the exponential curves in solid lines are fit by using a least square method. The curves are similar to those in Figure 10, however some events have different trends. For example, in the volumetric strain, the amplitudes become large when strains become small. Even in these cases we still observe large amplitudes in the positive strain range. These variations partially explain why the average peaks do not appear at the positively largest dilatation and/or the negatively largest acceleration (Figures 10 and 11). Since the location errors in depth still include about 5 km or more, even though we use the double-difference method for the relocation, the error in the applied timeshift may be resulting in the different trend. As a result, it is more difficult to discern the exact relationship between triggering strains and tremor amplitudes than it was in the previous section. However, the general trend is still the same. Given the greater error in individual locations, we take the results here to confirm our earlier interpretation with the caveat that the precise relationship between triggering
X - 18 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR 344 345 strains and tremor amplitude may be much less well constrained if the tremor events are not well located. 3. Discussion 346 347 348 349 350 The key observations of triggered low-frequency events are: (1) The low-frequency events are triggered by dilatation and probably not shear strain/stress. (2) The efficient dilatational waves for triggering have large normal dilations and radial compressions at 30 km depth. (3) There is an exponential relationship between the amplitude of the imposed dilatational strain and the triggered event amplitude. 3.1. Trigging mechanisms 351 352 353 354 355 356 357 358 359 360 361 362 We will now discuss the relevance of these observations to possible triggering mechanisms in the triggering process. 3.1.1. Tensile failure The firs problem, the observation that expansion excites tremor may be most easily explained if the deep low-frequency events are tensile (mode I) cracks. The expansion due to the Rayleigh waves is usually anisotropic because vertical and radial strains are not usually uniform (e.g., Figure 8), and then a stress difference appears to trigger the event. However the deep low-frequency tremor mainly produces shear waves. The opening crack is capable of producing shear waves but the amplitude is smaller than or comparable to P waves. We could not find strong evidence that the observed waves included dominant P waves. Therefore, a shear stress in the source seems to be required. 3.1.2. Shear failure
MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 19 363 364 To evaluate the shear crack triggering, the calculation of Coulomb failure function changes CFF = τ µ( σ p) (8) 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 is a powerful tool, where τ, σ, and p are shear stress, normal stress, and pore pressure changes, respectively, and µ is a frictional coefficient. However, direct application of equation (8) does not explain our observations for two reasons. Firstly, the triggering correlates well with dilatational strains, but not shear strain oriented parallel to the fault. Since µ is generally less than 1, the shear stresses should have correlated even better than the extensional if the direct application of equation (8) were appropriate. The problem can be observed qualitatively by observing that the S- and Love waves seem not to trigger tremor but the Rayleigh waves do. More quantitatively, the change in shear strains only correlates with the deep low-frequency amplitude with a normalized cross-correlation of 9% when we assume the shear slip along the plate boundary, whereas as the extensional strains correlate at 22%. Secondly, the correlation between amplitude of the deep lowfrequency events and the amplitude of the strain change seen in Figures 10 and 12 is not explained by equation (8). The simple Coulomb failure model predicts failure of an indeterminate size as a result of a strain change. Each of the problems can be dealt with by adding intermediate steps in the triggering process. The first problem, correlation with dilatation or normal extensional strains, can be explained by adding fluids to the process. Dilatation opens cracks and pores allowing fluids to flow from regions of high pressure to those of low pressure.
X - 20 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 The model has the attraction of easily explaining the sign of the correlation. Compression closes cracks and prevents fluid flow; expansion opens cracks and increases flow. In fracture-dominated systems, fluid flow rates are very sensitive to crack aperture. For instance, for infinite planar cracks in an otherwise impermeable medium, the permeability is proportional to b 3, where b is the aperture [Snow, 1969]. The change in crack aperture is proportional to the dilatation strain σ so the change in flow rate increases with the applied extensional strain. The flow of fluid into a fault zone can then weaken the surface by increasing the pore pressure (equation 8) as well as decreasing the normal stress, and promoting failure. Considering the correlation between the significant triggering and the vertical expansion, we can expect much fault weakening if the fault is close to being horizontal. This model is similar to that proposed for long-range earthquake triggering by Brodsky and Prejean [2005]. Miyazawa and Mori [2006] suggested something similar. They proposed friction weakening model from the relationship between dilatation and signals in the partially melted heterogeneous structure. The model assumes the source is a crack fracture and the fluid exists partially and heterogeneously in the structure. It is ideally supposed to be undrained due to long-period strain changes in the homogeneous media, however pressure changes cannot be uniform over the heterogeneous structure unsaturated with fluid, where minor pressure differences could be caused. Then, due to large dilatation, the tiny amount of fluid dehydrated from the subducting slab, instantly and slightly moves to the dry fault region, suddenly reduces the friction on the fault, and thus accelerates the fracture. In case of the compression, the fluid going away from the fault plane or the shortage of fluid supply stops the fracture. The dilatation determines the volume of the fluid injected
MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 21 407 408 409 410 411 412 413 414 into the dry region. Thus the dilatation may control the area of failure and hence the magnitude of the resulting slip event. The problem of correlating amplitude of the stress and triggering can be addressed by considering a distribution of fault stresses. Some faults might be near and the others far from failure. Small strains will only affect the faults near-failure while larger strains will affect both the ones far- and near-failure. The nearly exponential dependence of signal amplitude of dilatation implies an exponential distribution of failure stress, i.e., if the shear stresses on faults are distributed such that for stresses σ less than the critical stress 415 σ c ( ) σ c σ n(σ) = C 1 exp C 2 σ c (9) 416 417 418 419 where n(σ) is the number of faults with stress σ and C 1 and C 2 are constants, then the number of faults triggered by a change in effective stress σ ( V/V ) is found by integrating equation (9) from σ c σ to σ c. The result is [ ( ) σ c σ N( σ) = C 1 exp C 2 C 2 σ c ] 1 (10) 420 421 422 423 424 where N( σ) is the total number of failures triggered by the imposed stress. Alternatively, N( σ) represents the relative fault area in a particular stress state. The observed tremor is the superposition of all the failure signals, so the more faults that fail, the higher the amplitude of the resulting tremor. C 2 /σ c = 4.7 10 4, 3.9 10 4, 3.7 10 4, 1.0 10 4,
X - 22 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 and 4.6 10 4 Pa 1 for KWBH, IKWH, HRKH, URSH, and NUKH, respectively, in Figure 10. For IKWH the average of triggering amplitudes against background noise is too poor to obtain some relationships. This distribution approach is similar to that taken by Dieterich [1994] and results in a similar distribution of failure strengths. To relate this model to the rate-state paradigm, we can identify σ c /C 2 with Aσ, where A is the usual rate-state parameter and σ is the background stress. Dieterich [1994] derives seismicity rate change as a function of shear stress change divided by Aσ and the effective stress changes described here produce the similar effect. The combined value of Aσ of about 10 4 Pa is similar to that inferred from crustal triggering studies [e.g., Toda and Stein, 2003], but the much greater depth of the triggering poses a problem. If A is a nearly constant material property of order 10 3, then the background effective stress must be nearly two orders of magnitude below the lithostatic pressure at 30 km. Such a scenario would require extraordinarily high fluid pressures, so fluids would still be a key to the triggering process. Once the strain energy has been released, triggering sequence is not expected at the same region unless some strain energies remain. The variable strength of the tremor as a result of identical dilatation in Figures 9 12, may indicate the possibility that each deep low-frequency events have slightly different hypocenters. There may be many strong and weak (or large and small) asperity regions, where the large and small strain energies, respectively, are to be released relatively slowly. The smaller dilatation is capable of moving smaller amount of fluid and triggering events, while the larger dilatation is capable of moving larger amount of fluid, providing high and various opportunities for the fluid to contact with both high- and low-strain-preexisting regions to cause much larger events.
MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 23 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 This possibly is one of the reasons to explain large variance for large dilatations in Figure 10. In the proposed model, the low-frequency nature of the seismic signals is controlled by the slip process rather than the fluid flow. The frequency of shear failure events with a given seismic moment is determined by the stress drop and rupture velocity. If either quantity is unusually low, the seismograms will appear low-frequency for their amplitude. From spectra in Figure 4, it is difficult to estimate the corner frequency, but original waveforms show the tremors of 1 Hz on which high frequency (< 15 Hz) waves superimposed. Using these observations, we could not conclude which factor contributes to the generation of low-frequency waves. Another clue to the origin of the low-frequency signals is that deep low-frequency events and the similar episodic tremor-and-slip (ETS) event found in Cascadia subduction, where the feature of tremor is similar to the deep low-frequency events, have been observed accompanied with the slow slip events [Obara et al., 2004; Rogers and Dragert, 2003], suggesting that the phenomenon occurs at the aseismic-seismic transition. In the ratestate framework, the transition is where the slip is stable, A B. If rupture velocities or stress drops are low in this transitional region, the slip events would radiate unusually long-period waves for their magnitudes. There are observations of deep low-frequency events related to slower strain changes [e.g., Obara et al., 2004; Miyazawa and Mori, 2005; Obara and Hirose, 2006]. Kao et al. [2006] propose that episodic tremor-and-slip evens are excited by the procedure that dilatational strain field changes due to slow slip on the plate boundary cause fluid migration and trigger the events. This observation relating quasi-static deformation to tremor
X - 24 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR 471 472 reinforces our connection of the triggered tremor to strain, rather than acceleration. We observed significant triggering when the strain changes are at least on the order of 10 8. 3.2. Triggering from the 2005 Sumatra event (Mw 8.7) 473 474 475 476 477 478 479 480 481 482 483 On March 28, 2005, another large (Mw 8.7) earthquake occurred off northern Sumatra, south-east region of the 2004 Sumatra event. Figure 13 shows the root-mean-square envelopes (2 16 Hz) at KWBH and Rayleigh wave envelopes (0.01 1 Hz) at TSA, for recent three large earthquakes (M>8); the 2003 Tokachi-oki earthquake (Mw 8.1), the 2004 Sumatra event, and the 2005 Sumatra event. In the 2003 event, Rayleigh wave amplitude is related to the signals with the three large peaks corresponding to strong signals (450 600 sec). Moreover, they occurred during large dilatations with a period of 20 sec just as in the case of the 2004 event. Triggering from the 2005 event is very weak. The relationships between the signal amplitude and volumetric strain are consistent with the variance in Figure 10. The inference is that the deep low-frequency events would be potentially triggered by any large short-period Rayleigh waves trapped in the crust. 4. Conclusions 484 485 486 487 488 489 490 Pulsating triggering of deep low-frequency tremors were observed in western Japan during arrivals of the Rayleigh waves from the 2004 Sumatra-Andaman earthquake. The triggering is coincident with the large dilatation at the source region at a depth of 30 km. The dilatation is related to the triggered signal amplitude. Short-period (15 30 sec) Rayleigh waves with vertical expansion and radial compression, triggered the events much more strongly than the first arrival long-period (> 40 sec) ones. Quantitative analyses of the relationship between amplitudes of triggered events and volumetric changes revealed
MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 25 491 492 493 494 495 496 497 498 499 500 that there was the exponential relationship between the dilatation and the mean amplitude of signals from deep low-frequency events. Since triggering is related with dilatation, but not with shear components, the fluid supplied by the dehydration from the subducting slab should contribute to the excitation. Larger triggering strains can likely produce a fluid-related process that produces larger events. The friction of the fault is weakened by the fluid injection due to dilatational changes in the heterogeneous structure. The results can constrain the mechanism of the deep low-frequency events. In order to reveal the clear source mechanism, we should continue to monitor such triggering as well as usual seismicity monitoring, since the investigation of event triggering is potentially one of the new useful ways to make the unknown source clear. 501 502 503 504 Acknowledgments. Discussion with Jim Mori and Hiroo Kanamori helped develop this study. We thank National Research Institute for Earth Science and Disaster Prevention (NIED) for Hi-net and F-net data and Japan Meteorological Agency (JMA) for the earthquake catalogue. We use hypodd [Waldhauser, 2001] for the event relocation. References 505 506 507 508 509 510 511 Brodsky, E. E. and S. G. Prejean (2005), New constraints on mechanisms of remotely triggered seismicity at Long Valley Caldera, J. Geophys. Res., 110, B04302, doi:10.1029/2004jb003211. Dieterich, J. (1994), A constitutive law for rate of earthquake production and its application to earthquake clustering, J. Geophys. Res., 99, 2601-2618. Kao, H., S.-J. Shan, H. Dragert, G. Rogers, J. F. Cassidy, K. Wang, T. S. James, and K. Ramachandran (2006), Spatialtemporal patterns of seismic tremors in northern Casca-
X - 26 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 dia, J. Geophys. Res., 111, B03309, doi:10.1029/2005jb003727. Katsumata, A., and N. Kamaya (2003), Low-frequency continuous tremor around the Moho discontinuity away from volcanoes in the southwest Japan, Geophys. Res. Lett., 30, 1020, doi:10.1029/2002gl015981. Lay, T., and T. C. Wallace (1995), Modern Global Seismology, 521 pp., Elsevier, New York. Miyazawa, M., and J. Mori (2005), Detection of triggered deep low-frequency events from the 2003 Tokachi-oki earthquake, Geophys. Res. Lett., 32, L10307, doi:10.1029/2005gl022539. Miyazawa, M., and J. Mori (2006), Evidence suggesting fluid flow beneath Japan due to periodic seismic triggering from the 2004 Sumatra-Andaman earthquake, Geophys. Res. Lett., 33, L05303, doi:10.1029/2005gl025087. Obara, K. (2002), Nonvolcanic deep tremor associated with subduction in southwest Japan, Science, 296, 1679-1981, doi:10.1126/science.1070378. Obara, K., and H. Hirose (2006), Non-volcanic deep low-frequency tremors accompanying slow slips in the southwest Japan subduction zone, Tectonophysics, 417, 33-51. Obara, K., H. Hirose, F. Yamamizu, and K. Kasahara (2004), Episodic slow slip events accompanied by non-volcanic tremors in southwest Japan subduction zone, Geophys. Res. Lett. 31, L23602. doi:10.1029/2004gl020848. Omori, S., K. Komabayashi, and S. Maruyama (2004), Dehydration and earthquakes in the subducting slab: empirical link in intermediate and deep seismic zones, Phys. Earth Planet. Inter., 146, 297-311, doi:10.1016/j.pepi.2003.08.014.
MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 27 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 Rogers, G., and H. Dragert (2003), Episodic tremor and slip on Cascadia subduction zone: The chatter of silent slip, Science, 300, 1942-1943. Seno, T., and T. Yamasaki (2003), Low-frequency tremors, intraslab and interplate earthquakes in southwest Japan-from a viewpoint of slab dehydration, Geophys. Res. Lett., 30, 2171, doi:10.1029/2003gl018349. Shelly, D. R., G. C. Beroza, S. Ide, and S. Nakamula (2006), Low-frequency earthquakes in Shikoku, Japan, and their relationship to episodic tremor and slip, Nature, 442, 188-191, doi:10.1038/nature04931. Snow, D. (1969), Anisotropic Permeability of Fractured Media: Water Resources Research, 5, no. 6, 1273-1289. Special issue of Bull. Seism. Soc. Am. (2004), 94(6B) Toda, S., and R. Stein (2003), Toggling of seismicity by the 1997 Kagoshima earthquake couplet: A demonstration of time-dependent stress transfer, J. Geophys. Res., 108(B12), 2567, doi:10.1029/2003jb002527. Toriumi, M., and M. Inui (2001), Pressure-temperature-water production rate paths in the subduction metamorphism, Bull. Earthq. Res. Inst. Univ. Tokyo, 76, 367-376. Waldhauser, F., and W. L. Ellsworth (2000), A double-difference earthquake location algorithm: method and application to the northern Hayward fault, California, Bull. Seis. Soc. Am., 90, 1353-1368. Waldhauser, F. (2001), hypodd A program to compute double-difference hypocenter locations, U.S. Geol. Surv. Open File Rep. 01-113. West, M., J. Sanchez, and S. McNutt (2005), Periodically triggered seismicity at Mount Wrangell, Alaska, after the Sumatra earthquake, Science, 308, 1144-1146,
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MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR X - 29 (a) KWBH vertical (2-16 Hz) velocity [µm/s] 2 1 0-1 -2 radial (2-16 Hz) transverse (2-16 Hz) 500 1000 1500 2000 time [s] (b) TSA vertical (0.01-1 Hz) P Rayleigh velocity [m/s] radial (0.01-1 Hz) S 0.01 0.00-0.01 transverse (0.01-1 Hz) Love 500 1000 1500 2000 time [s] Figure 1. Observed velocity waveforms from the 2004 Sumatra-Andaman earthquake; (a) filtered with a pass-band from 2 to 16 Hz at a bore-hole high sensitive station KWBH and (b) filtered with a pass-band from 0.01 to 1 Hz at a broad-band station TSA. Zero is the origin time of the Sumatra earthquake (26 December 2004, 00:58:53 UT). Three traces indicate the vertical, radial and transverse components from the top to the bottom. The two station locations are shown in Figure 3.
X - 30 MIYAZAWA AND BRODSKY: FLUID RELATED DEEP-LOW FREQUENCY TREMOR (a) E W 1 µm/s 20 s (b) + - 1 10-7 Large dilatation (c) 5 kpa Figure 2. Example of the relationship between triggered deep low-frequency events and strains in the source region. (a) Time series of vertical seismic activity observed at KWBH (1887 1962 sec, in Figure 1). The time is corrected in order to compare to the bottom trace. (b) Volumetric dilatation caused by the arriving Rayleigh waves obtained by using equations (5) and (6). (c) Stress changes on the lateral plane. Black and white arrows indicate expansion and compression, respectively.