Tremor-tide Correlations and Near Lithostatic Pore Pressures on the Deep San Andreas Fault

Amanda Thomas, Robert Nadeau, and Roland Bürgmann


Early studies of non-volcanic tremor (NVT) attempted to relate the tremor signal and flow processes of fluids introduced from metamorphic dehydration in the subducting crust, but more recent evidence from subduction zone tremor in Japan and Cascadia indicates that tremor is directly associated with shear failure (Shelly et al., 2006). The presence of fluids and the significant impact small stress perturbations, such as tidal forcing, have on tremor activity implies low effective normal stresses are present in the tremor source region (Gomberg et al., 2008; Miyazawa and Brodsky, 2008; Peng et al., 2008a; Rubinstein et al., 2007).

Following the initial discovery in Japan and Cascadia, two additional tremor varieties were discovered in different tectonic environments: widespread triggered tremor, activated by dynamic stress changes associated with the passage of teleseismic surface waves (Gomberg et al., 2008; Rubinstein et al., 2007), and continuous tremor located deep on the San Andreas fault, near the 2004 Parkfield mainshock (Nadeau and Dolenc, 2005). The Parkfield tremor demonstrates several notable dissimilarities when compared to tremor in Cascadia and Japan, including continuous occurrence, changes in activity levels due to nearby intermediate-size earthquakes, and absence of an accompanying geodetic signature (Nadeau and Dolenc, 2005; Smith, 2009). In this study, we investigate the influence of tidal loading conditions on non-volcanic tremor on the San Andreas fault in order to determine if the Parkfield tremor is modulated by tides, resolve which tidal stresses affect tremor, and explore implications about the source region conditions.

Methods and Preliminary Results

We develop our analysis in parallel for the tremor catalog and two earthquake catalogs. We consider a regional catalog of events within .5$^{\circ}$of Cholame, and a repeating micro-earthquake catalog located along the creeping segment of the San Andreas fault (Nadeau and McEvilly, 2004). We compute the extensional and shear strains induced in the lithosphere by the solid earth and ocean tides (Agnew, 1997). Assuming 2-D plane strain and linear elasticity, with an elastic modulus of 30 GPa and Poisson ratio of .25, we then convert the strains to stresses and resolve those stresses onto the fault normal and parallel (shear) directions on the San Andreas fault (N45$^{\circ}$W). For each catalog, the normal, shear, and Coulomb stresses and stress rates are computed for the start time of each event (Figure 2.2).

Figure 2.2: Example one-day tremor time series with superimposed tidal signals. Black is RMS envelope of tremor activity in Cholame. Red, blue, and green curves are the tidally induced fault-normal stress (FNS), right-lateral shear stress (RLSS), and Coulomb stress (CS) for $\mu$=0.4. Yellow stars mark tremor start times. Some short spikes in the RMS envelope are micro-earthquakes. Inset map shows tremor locations in red, regular earthquakes in blue, and the repeating earthquake catalog in green. Background earthquake activity is shown in black. White star indicates epicenter of the 2004 Parkfield earthquake.
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To investigate the influence of both the stress magnitude and rate on tremor occurrence, we divide the tremor into ``quadrants'' depending on the sign of the loading condition under which they occur. The tidal signal consists of a superposition of multiple harmonic functions, thus the amount of time that the tides induce a given load is not equal for all loading conditions. If tremor and tides are uncorrelated, the number of tremors that occur under a particular tidal loading condition will be directly proportional to the amount of time that condition exists. We use a chi-square test to establish the existence of a correlation using the null hypothesis that tremor start times are randomly distributed with respect to tidal influence. For the tremor catalog, the level of correlation of the normal, shear, and Coulomb stresses exceed the 99% significance level, while the correlation levels for the other catalogs are statistically insignificant. The lack of correlation in the earthquake catalogs is not surprising given the size of the catalogs and results from previous efforts to establish a significant tidal triggering of earthquakes in California (Beeler and Lockner, 2003; Lockner and Beeler, 1999).

Figure 2.3: Percentage of excess events (i.e. above long term average) during times of positive $\Delta$CS parallel to the San Andreas fault vs. effective coefficient of friction. Values for the tremor, regular, and repeating event catalogs are shown as red circles, blue squares, and green triangles respectively. Standard deviations (2$\sigma$) were computed using a bootstrap procedure on each friction value of each catalog. Maximum 2$\sigma$ errors over all possible friction values are 5.66%, 5.80%, and 4.66% for the tremor, regular, and repeating catalogs respectively. The inset diagram displays the positive percent excess tremor for FNS (black) and RLSS (grey) relative to the fault orientation.
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We further explore this apparent correlation by comparing tremor start times with the loading conditions they occur under. Correlation between tremor occurrence and tidal stressing rate is insignificant for all components. Induced shear stresses ($\Delta$RLSS) demonstrate the most compelling correlation of the three magnitude comparisons, with distinct increases in tremor activity that correspond to positive (right-lateral) shear stresses parallel to the San Andreas fault and equally apparent decreases when values are negative. Additionally, the tremor surpluses and deficits become more pronounced as $\Delta$RLSS increases to peak values of $\pm$ 150 Pa. Though normal stresses changes ($\Delta$FNS) are much larger, they only exhibit a weak correlation at large, positive (tensile) values of greater than 1000 Pa. Coulomb stresses ($\Delta$CS=$\Delta$RLSS+$\mu$$\Delta$FNS, $\mu$=0.4) exhibit less correlation than the shear stress alone.

Assuming tremor is caused by a frictional Coulomb failure process, the optimal friction coefficient is the value that maximizes the number of events that occur during times of encouraged failure stress (Figure 2.3). Tremors show a marked increase for friction values near zero with a peak above 30% excess for $\mu$=0. Percent excess for both the regular and repeating earthquake catalogs does not exceed 5%. This demonstrates that tidally induced shear stresses parallel to the San Andreas fault, while of much smaller magnitude than normal stress changes, have the most robust correlation with non-volcanic tremor near Parkfield. Since the stress perturbations are so small relative to the overburden stresses at these depths, this finding is indicative of very low effective normal stresses or near-lithostatic pore pressures at depth. Finally, going back to the initial assumption of the strike of the San Andreas fault in our stress calculations, we perform the same analysis to determine the percent excess tremor with respect to any vertical fault orientation (Figure 2.3, inset). The peak percent excess occurs at N44$^{\circ}$W, nearly parallel to the strike of the San Andreas fault.


Supported by the USGS through awards 06HQGR0167, 07HQAG0014, and 08HQGR0100, by the NSF through awards EAR-0537641, EAR-0544730, and the GRFP.


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