Periodic Earthquake Rate Variations on the San Andreas Fault

Robert M. Nadeau

Slip Rates from Micro-quakes

A characteristically repeating micro-earthquake sequence (CS) is a sequence of small earthquakes (M $\sim<$ 3.5) whose seismograms, locations and magnitudes are nearly identical. Each earthquake in the sequence represents a repeated rupture of the same patch of fault, and the times between the ruptures (i.e., their recurrence intervals) are, in general, inversely proportional to the average tectonic loading rate on the fault (Nadeau and McEvilly, 1999; Bürgmann et al., 2000; Igarashi et al., 2003). Their unique properties allow CS to be used to infer fault slip rates at depth on faults, and this capability has been proven to be particularly useful in regions where geodetic measurments are limited in spatial coverage and frequency.

Repeating Quake Analysis

Along much of the 175 km stretch of the San Andreas Fault (SAF) separating the rupture zones of California's two great earthquakes (i.e., the $\sim$ M8 1906 San Francisco and 1857 Fort Tejon events), geodetic measurments have been done relatively infrequently in campaign mode. Along this stretch, however, over 500 CS have been identified with events occurring between 1984 and 1999 (inclusive). And, analysis of these sequences reveal: 1) that the recurrence intervals within any given CS vary significantly, 2) that among different CS on a given fault segment the recurrence variations are coherent through time and 3) that in many cases the coherent variations recurred quasi-periodically (Nadeau and McEvilly, 2004).

Correlation with Larger Earthquakes

Recurrence variation information was used to construct a profile of deep fault slip rate histories along the 175 km study zone for the 1984-1999 study period (Nadeau and McEvilly, 2004). The profile reveals that along the northwestern-most 80 km segment of the study zone (Figure 12.1), deep fault slip rates commonly vary by over 100% and their variation patterns (i.e., pulse patterns) recurr with a periodicity of $\sim$ 3 years. Shown at the right in Figure 12.1 is a comparison of this large-scale periodic deep slip pattern with the occurrence times of M3.5 to M7.1 earthquakes (i.e., magnitudes larger than those of the CS events) and with the occurrence times of three known slow slip events in the area (Linde et al., 1996; Gwyther et al., 2000). The comparison reveals a significant correlation between the onset periods of the repeating deep slip signals and the occurrence rates of the larger events.

To the resolution of the characteristic microearthquake slip rate data, the M7.1 Loma Prieta mainshock occurred coincident with the onset of the P2 timed pulse (Figure 12.1, right). The times of the next two largest non-aftershock events in the area and study period (i.e., M5.4 San Juan Bautista mainshock in 1998 and a M4.7 event in 1986) are also coincident with the onset of pulses P5 and P1, respectively, and the P3, P4, and P5 pulse onsets correspond closely to the times of the three slow slip events in the area whose aseismic moment magnitudes were estimated to be $\sim$ 5$M_{w}$ (Linde et al., 1996; Gwyther et al., 2000).

Excluding Loma Prieta aftershocks, 45 earthquakes with M $>$ 3.5 occurred in region during the 1984-1999 study period, and a general correlation is also observed between the occurrence times of these events and the 1-year onset periods of the pulses (i.e. the time interval where pulse slip velocities transition from low to high values). Thirty-three of the 45 events were found to occur during the onset periods, this represents an occurrence rate that is 6 times larger than the rate observed during the non-onset periods. When Loma Prieta aftershocks are included into the analysis the onset period rate increased to 7 times that of the non-onset period rate (Figure 12.1, right).


Earthquake triggering induced by velocity weakening effects (Dietrich, 1986; Scholz, 1990) associated with increasing fault slip velocities may provide an explanation for the increased rates of the larger earthquakes during the pulse onsets. It is also possible that the increased rates occur quasi-periodically due to some other mechanism, such as the accelerated accumulation fo failure during quasi-periodic tectonic loading.

Continued monitoring of the M $>$ 3.5 earthquake activity occurring since the 1984-1999 analysis period along the 80 km SAF segment shows that the quasi-periodic occurrence rate pattern for larger quakes is continuing and that the timing of the rate increases remains consistent with the projected pulse onset times based on the 1984-1999 pusling statistics (Figure 12.1, right-top). As a consequence analysis of the post-1999 CS seismicity has now been initiated in order to confirm the continuance of the deep slip rate pulsing that the larger magnitude seismicity patterns suggest may be taking place.

Regardless of the outcome of this subsequent analysis, however, the the ongoing quasi-periodic patterns of the larger earthquake rates holds the potential for refinement of time-dependent earthquake forecasts models for this area (WGCEP, 1999; Matthews et al., 2002) to time scales comparable to the average pulse cycle duration of $\sim$ 3 years that is observed.


Thanks are given to Roland Bürgmann and Mark H. Murray for stimulating conversations and inciteful comments regarding this work. This research was supported by the U.S. Geological Survey through awards 02HQGR0067 and 03HQGR0065 and by the National Science Foundation through award 9814605.


Bürgmann, R., D. Schmidt, R.M. Nadeau, M. d'Alessio, E. Fielding, D. Manaker, T.V. McEvilly, and M.H. Murray, Earthquake Potential along the Northern Hayward Fault, California, Science, 289, 1178-1182, 2000.

Dieterich, J.H., A model for the nucleation of earthquake slip, in Earthquake Source Mechanics, S. Das, J. Boatwright, and C.H. Scholz (Editors), American Geophyusical Monograph 37, American Geophysical Union, Washington, D.C., 37-47, 1986.

Gwyther, R.L., C.H. Thurber, M.T. Gladwin, and M. Mee, Seismic and Aseismic Observations of the 12th August 1998 San Juan Bautista, California, M5.3 Earthquake, in Proceedings of the 3rd Conference on tectonic problems of the San Andreas Fault system, G. Bokelmann and R. Kovach, Eds., Stanford California School of Earth Sciences, Stanford University, 2000.

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Nadeau, R.M., and T.V. McEvilly, Fault slip rates at depth from recurrence intervals of repeating microearthquakes. Science, 285, 718-721, 1999.

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Working Group on California earthquake Probabilities (WGCEP). Earthquake probabilities in the San Francisco Bay Region: 2000 to 2030-a summary of findings, U.S. Geol. Surv. Open-File Rept. 99-517, 36 pp., 1999.

Figure 12.1: (Left) Background Seismicity (gray points) and CS locations (black circles) in depth section and map view along the northwestern 80 km segment. Horizontal scales are exaggerated by x2. White stars are locations of the two largest non-aftershock events (M5.4 and M4.7) occurring in the region and study period. Squares labeled SJB and HOL are the cities of San Juan Bautista and Hollister, CA. Calaveras and Paicines-San Benito fault seismicity are labeled CF and PBF, respectively. CS locations in map view outline the trend of the SAF. The 1989, M7.1 Loma prieta earthquake occurred adjacent to the northwest of this 80 km segment. (Right, center) Profile of the 1984-1999 (inclusive) deep slip rate history for the segment inferred from the CS data. Rates (in color) are given in percent difference from the 1984-1999 average rate and color intensity are 95% confidence bounds. Open circles are along fault positions and times of the M $>$ 3.5 earthquakes occurring in the region and study period. Sizes of these circles are keyed to there relative magnitudes. Verticle black line indicates the time of the Loma Prieta earthquake. (Right, bottom) Deep slip rates as a function of time for a representative 15 km sub-segment showing the P1 through P5 pulses discussed in the text. Verticle scale is in cm/yr. (Right, top) Occurrence times and magnitudes of the M $>$ 3.5 earthquakes occurring in the study zone and for the period between 1984 and 2004.73 (inclusive). The times of the Loma Prieta and two largest non-aftershock events are labeled at the top. Horizontal green bars are the pulse onset periods discussed in the text. Horizontal red bars are the projected pulse onset times based on the 1984-1999 CS slip patterns. Gray extensions of the red bars show uncertainties in these projections based on the variance of the 1984-1999 pulse recurrence intervals. Analysis of the CS data for deep slip estimation has yet to be carried out for the 2000-2004.73 time period, but the ongoing pattern of occurrence of M $>$ 3.5 earthquakes suggests that the quasi-periodic deep slip pattern may also continue.
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