Tidal Modulation of Nonvolcanic Tremor

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Science  11 Jan 2008:
Vol. 319, Issue 5860, pp. 186-189
DOI: 10.1126/science.1150558


Episodes of nonvolcanic tremor and accompanying slow slip recently have been observed in the subduction zones of Japan and Cascadia. In Cascadia, such episodes typically last a few weeks and differ from “normal” earthquakes in their source location and moment-duration scaling. The three most recent episodes in the Puget Sound/southern Vancouver Island portion of the Cascadia subduction zone were exceptionally well recorded. In each episode, we saw clear pulsing of tremor activity with periods of 12.4 and 24 to 25 hours, the same as the principal lunar and lunisolar tides. This indicates that the small stresses associated with the solid-earth and ocean tides influence the genesis of tremor much more effectively than they do the genesis of normal earthquakes. Because the lithostatic stresses are 105 times larger than those associated with the tides, we argue that tremor occurs on very weak faults.

Shortly after the discovery of both nonvolcanic tremor (1) and recurring slow-slip events (2, 3), Rogers and Dragert determined that these two phenomena occur coincident with each other at regular intervals in the Cascadia subduction zone (4). They termed this phenomenon episodic tremor and slip (ETS). Soon thereafter, ETS was also observed in the Nankai Trough in Japan (5). ETS falls into a newly identified class of geophysical phenomena that are distinct from “normal” earthquakes. For these slow-slip phenomena, seismic moment scales with event duration (6), whereas for earthquakes, moment scales with the cube of event duration (7). The relative locations of nonvolcanic tremor and earthquakes also indicate that they are different processes. In Cascadia, tremor appears to fill volumes of crust that have little or no seismicity (8), whereas on the San Andreas Fault, tremor is found below crustal seismicity (9). Precise locations of low-frequency earthquakes in Japan, which have been shown to make up a substantial part of nonvolcanic tremor (10), place them well above the only nearby seismicity (11).

ETS has been interpreted by many as intermittent accelerated slip located between the locked and freely slipping portions of subduction megathrust faults, possibly mediated by pressure fluctuations of fluids rising from the subducting slab (46, 10, 11). However, a wide range of other physical mechanisms for ETS remains on the table. Here we spotlight a striking difference from normal earthquakes: The amplitude of trem- or strongly correlates with tidal stresses. Many have sought a correlation between earthquakes and the stress fluctuations induced by the tides, but only those examining the most favorable conditions for triggering (1217) see any correlation of earthquakes with the tides. Careful studies of large earthquake data sets find no such correlation (1821).

The ETS episodes in the portion of the Cascadia subduction zone near Puget Sound and southern Vancouver Island have a periodicity of approximately 14 months, with each episode lasting 2 to 3 weeks. The last three major ETS episodes in this region were in July 2004, September 2005, and January 2007. Although each event had its own characteristics, they all covered approximately the same region from southern Puget Sound to southern Vancouver Island (Fig. 1). Before each of these events, we deployed focused seismic arrays to better locate and characterize ETS. Each array recorded one ETS event. The arrays had 5 to 11 stations and their apertures ranged from 0.6 to 2.0 km. In this study, we used five of these arrays (Fig. 1) to filter out noise and to closely examine how the amplitude of tremor varies with time (22). This allowed us investigate whether nonvolcanic tremor has a tidal periodicity. Two additional arrays that were deployed (LO in 2004 and BD in 2007) and two individual stations (SE-1 and PA-15) were not used because they were dominated by cultural noise.

Fig. 1.

Map of the study region. Seismic arrays used to record tremor (triangles), the approximate source region of Puget Sound/southern Vancouver Island ETS episodes (shaded region), and isodepths of the plate interface between the Juan de Fuca and North American plates (lines) are indicated on the map.

The amplitude of the tremor varied over time and from array to array (Fig. 2). The recorded amplitude of the tremor depended on both the strength of the tremor and the proximity of the array to the migrating tremor source. For example, it is evident that the 2007 ETS episode migrated from the south to the north, because early in the ETS event, the amplitudes were larger at the southern array PL than at array BS. A few days later, amplitudes were largest at array BS (Fig. 2C).

Fig. 2.

Tremor amplitudes for ETS episodes in 2004 (A), 2005 (B), and 2007 (C). Each line represents the amplitude of a stack of envelope amplitudes for a single array, each of which recorded a single ETS episode. These stacks were low-pass filtered at a period of 1 hour to distill signals at the frequencies we are interested in. Earthquakes and glitches were removed before stacking. Before computing the envelope, seismograms were band-pass filtered between 1 and 8 Hz. The shaded regions represent a 13-day period during each ETS episode when tremor was strongest at the arrays we were using. The ETS episodes for these events lasted longer than the 13-day windows highlighted; we focused on the periods when recordings of tremor were strongest, when the ETS sources were passing near the arrays. These shaded regions are the regions used to analyze the periodicity of tremor. The dashed-boxed regions represent a 13-day window in which there was no substantial tremor and were used to characterize the noise. Amplitude was normalized at each array by maximum amplitude.

When examining the amplitude of the tremor for the 2004 and 2007 ETS episodes, one can clearly identify a twice-a-day pulsing of tremor activity, and there are suggestions of such a periodicity in the 2005 episode (Fig. 2 and fig. S1). Once-a-day periods are also visible in several of the time series. The likely signals from tidal stresses would be roughly once- and twice-a-day signals from the gravitational influence of the Sun and Moon. As with all seismic data, we also have to contend with cultural noise that has a daily cycle and often a week/weekend cycle. These signals are visible, for example, in the nontremor interval at the PA array (Fig. 2).

To present a more quantitative evaluation of the periodicity of the tremor, we took a 13-day window of the tremor and computed its spectrum (22). The approximately twice-daily periodicity visible in the amplitude time series for each array (Fig. 2) is even more clear when we examine the spectra during ETS episodes (Fig. 3). At all five arrays, there is a strong peak in the spectral amplitude at 12.4 hours, the period of the principal lunar tide. This is in contrast with the characterization of the noise at these same arrays, many of which have a much weaker peak at periods of approximately 12 hours. The strongest tidal forcing is at a period of 12.4 hours, so, given its presence in all three ETS episodes, its absence at other times, and the lack of alternative sources, we can confidently identify the 12.4-hour peaks as due to tidal stresses. The strong 12.4-hour periodicity of the tremor amplitudes is evident when one compares the tremor amplitudes to a sinusoid with 12.4-hour periodicity (fig. S1). Many peaks in the tremor amplitude line up with peaks in an aligned 12.4hour–period sinusoid.

Fig. 3.

Spectra of the 13-day windows of tremor (A and B) and noise (C and D). Shaded regions in (A) and (C) represent the region that is shown in a zoom in (B) and (D). (D) has been rescaled by a factor of 5. Amplitudes in each panel have been normalized so that the area under each curve in (A) is equal. The variation in amplitudes of the noise [(C) and (D)] indicates the variation in the signal-to-noise ratios at individual arrays; that is, arrays with higher amplitudes of noise have lower signal-to-noise ratios. Dashed vertical lines indicate the strong tidal periods of 12, 12.4, and 24 hours.

To quantify the influence of the 12.4-hour lunar tide on the tremor, we examined the relationship between tremor amplitude and its phasing in a best-fit 12.4-hour periodic model (Fig. 4). To do this, we converted time into a phase angle, given a function with a 12.4-hour periodicity. This means that we can now express tremor amplitude as a function of phase instead of time. For each degree of phase, we computed the mean amplitude of the tremor over all ∼25 times that particular phase angle repeated in the 13-day window. We then stacked these curves for all five arrays deployed to get an overall sense of how the tides influenced the amplitude of tremor. Using this calculation, we find that tremor amplitude varies smoothly as a function of phase in a sinusoidal fashion. Tremor amplitude varies strongly with phase; the variance of the amplitude is 33.4% from the mean. This is in strong contrast with the results from same methodology applied to the noise. The noise shows no significant amplitude variation with phase, having a variance of 3.3% from the mean.

Fig. 4.

Amplitude versus phase for a 12.4-hour tidal cycle. In this figure, we compare the variation of the amplitude of tremor during the 13-day ETS windows (solid line) and the 13-day noise windows (dotted line) according to phase in the best-fitting 12.4-hour–period tidal cycle. Phase for each array was determined by cross-correlating a 12.4-hour–period cosine function with the tremor and noise amplitude functions. The amplitude for each degree at each array was averaged over the 25 to 26 times that phase occurred in the 13-day window examined. The amplitudes at the five arrays were averaged for both noise and tremor and were then normalized so that the mean of each curve is 1.

During the ETS episodes, we also identified a strong peak in the spectra at a range of periods from 24 to 25 hours, the period of the lunisolar and lunar declination tides (Fig. 3). This peak is more difficult to interpret than those at 12.4 hours, because this is the period at which we would expect to identify cultural noise. In fact, we expect that the rather strong source at a period of 24 hours during periods without ETS is a result of cultural noise (Fig. 3C). Fortunately, we have no reason to believe that the cultural noise that we observe at our sites should be variable from any one period of time to another. Therefore, the much larger spectral amplitudes at periods of 24 to 25 hours during ETS than when ETS is not occurring indicate that tremor is being strongly forced at a daily periodicity in addition to the twice-daily periodicity discussed earlier. We also note that the peaks in tremor amplitude that have an ∼24-hour periodicity do not correlate with daylight hours, when cultural noise is at a maximum. This lends further support to our argument that the 24-hour periodicity of the tremor is real. Because of the complication of having two sources of energy that are periodic at 24 hours and do not have the same phasing, we elected not to examine the relationship between amplitude and phase at these periods, because the noise and tremor would interfere with each other.

We have conducted exploratory modeling of the ocean tidal stresses, finding peak-to-peak values of 15 KPa on the Cascadia subduction interface at depth. Solid-earth tides are also likely to be important, inducing stresses on the order of 5 KPa (13). A direct correlation of tremor with the phase of stressing proved beyond the scope of this study. Such correlation would require tidal stress calculations that account for the complexities of tremor as a moving source (4), variability in the orientation and even polarity of tidal stresses across the source region, and variability with depth for the appropriate loading geometry. We did compare tremor amplitude and tidal heights (fig. S2), because the normal stress effect of water loading is simple: An increment in water increases normal stress with a diminishing effect with depth. We found that tremor is stronger at periods of high water and therefore periods of increased normal stress. This is in line with the findings of Shelly et al. (23), who argue that the increment in water height above the subducting slab will slightly decouple the subduction zone and thus allow for increased tremor. An alternate explanation is to consider that the increase in water height above the overriding plate (and the tremor) is increasing friction on the already slipping subduction zone, causing the slow-slip event to radiate more energy. There are undoubtedly other viable explanations for this correlation, but they require knowledge of the shear stresses associated with ocean loading or the earth tides, which will both have a constant phase relative to the ocean tides and the tremor.

Other recent studies have shown twice-daily tidal periodicities in ETS tremor in Japan (23, 24). To explain the propensity for tremor at certain periods of time, they suggest that solid-earth tides (24) and ocean tides (23) increase the Coulomb failure stress on the plate interface. We do not yet know whether the Coulomb model can explain our observations.

We have shown that tidal modulation at both daily and twice-daily frequencies is a pervasive feature of all three recent episodes in the best-instrumented tremor source region in Cascadia. The stresses associated with these tides are on the order of 15 KPa, approximately 105 times smaller than the lithostatic stresses at the depth where tremor radiates. Although it seems improbable that such small stress changes would have such a dramatic effect, there is supporting evidence that small stress changes can influence the genesis of nonvolcanic tremor. A recent study (25) has shown that nonvolcanic tremor was triggered in Cascadia by the surface waves of the moment magnitude 7.8 Denali earthquake, which imparted shear stress changes of ∼40 Kpa. Similar observations of teleseismic earthquakes triggering tremor have also been made in California (26) and Japan (2729).

Our observation that tremor is strongly modulated by the tides shows that the physical processes underpinning nonvolcanic tremor are substantially different from those governing earthquakes, which are not typically affected by the tides. ETS appears to represent slow ongoing failure, and thus any increment in stress should affect the failure rate, regardless of the stress state. We believe that this failure is occurring on very weak faults, because small stresses will have a much larger effect on a low-stress fault than a high-stress one. These faults could be very low-friction or, similarly, occur in the presence of near-lithostatic pore pressures.

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