The deep extension of the San Andreas Fault is believed to be creeping, but the recent observations of tectonic tremors from these depths indicate a complex deformation style1. In particular, an isolated tremor source near Parkfield has been producing a sequence of low-frequency earthquakes2 that indicates an uncommon mechanism of stress accumulation and release. The tremor pattern regularly oscillated between three and six days from mid-2003 until it was disrupted by the 2004 magnitude 6.0 Parkfield earthquake. After that event, the tremor source ruptured only about every three days, but over the next two years it gradually returned to its initial alternating recurrence pattern. The mechanism that drives this recurrence pattern is unknown. Here we use physics-based models to show that the same tremor asperity—the region from which the low-frequency earthquakes radiate—can regularly slip in slow and fast ruptures, naturally resulting in recurrence intervals alternating between three and six days. This unusual slip behaviour occurs when the tremor asperity size is close to the critical nucleation size of earthquakes. We also show that changes in pore pressure following the Parkfield earthquake can explain the sudden change and gradual recovery of the recurrence intervals. Our findings suggest a framework for fault deformation in which the same asperity can release tectonic stress through both slow and fast ruptures.
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We thank D. R. Shelly for sharing his tremor data and J.-P. Avouac for his comments on an earlier version of the manuscript. This work comprises Earth Observatory of Singapore contribution no. 115. S.B. is funded by the National Research Foundation Singapore under its Singapore NRF Fellowship scheme (National Research Fellow Award no. NRF-NRFF2013-04), by the Earth Observatory of Singapore, by the National Research Foundation Singapore and by the Singapore Ministry of Education under the Research Centres of Excellence initiative.
The authors declare no competing financial interests.
Extended data figures and tables
Extended Data Figure 1 Numerical model of the Parkfield tremors.
a, Schematic diagram of the model geometry and frictional properties. A square velocity-weakening patch (yellow) is embedded in a large velocity-strengthening fault domain. R is the asperity size of the patch. The entire fault domain is driven by a plate rate of Vpl = 3 cm yr−1. h* (dotted circle) is the critical nucleation size of the velocity-weakening patch to generate elasto-dynamic slip. We use the ratio R/h* = 0.73. The model has R = 3 m, L = 5 μm and an effective confining pressure of = 50 MPa, but period-doubling recurrence intervals at three and six days can be obtained for various asperity sizes, as discussed in the text. b, The yellow square patch in a produces a succession of slow and fast ruptures. Fast ruptures may be detected in seismograms and may coincide with one of the LFEs. The model reproduces the period-doubling recurrence pattern of the Parkfield tremors before the 2004 Parkfield earthquake.
Extended Data Figure 2 Recurrence pattern and source characteristics of the period-doubling Parkfield tremors and numerical simulations with slip velocity.
a–d, Same as Fig. 2, but plotting slip velocity (instead of slip) in c and d.
Extended Data Figure 3 Simulations of period-doubling sequences of slow and fast ruptures along eight orders of magnitude.
All simulations assume the same rheological parameters except for the characteristic weakening distance L, which is used to adjust the ratio R/h* to within the period-doubling range. a, With R = 3 m and L = 5μm, we obtained slow and fast ruptures with an equivalent geodetic moment magnitude of Mw −1.9 and Mw −0.5. b, With R = 30 m and L = 0.05 mm, the range is Mw 0.07 and Mw 1.4. c, For R = 300 m and L = 0.5 mm, the range is Mw 2.1 and Mw 3.5. d, For R = 3 km and L = 5 mm, the range is Mw 3.9 and Mw 5.4. Square patches of velocity-weakening friction with different sizes may exhibit period doubling at almost all magnitudes. The blue and red lines show aseismic and seismic slip, respectively. VS and VW represent the extent of the velocity strengthening and velocity weakening regions, respectively. Increments refer to the time steps between consecutive profiles (larger for aseismic than for seismic slip).
Extended Data Figure 4 Potential of non-circular shaped asperities to produce complex sequences of slow and fast ruptures with period doubling.
a, c, Velocity-weakening (VW) patches with two different shapes. b, d, The corresponding history of the period separating each event (a and c respectively). For both simulations, we assume the same frictional parameters and confining pressure. Elliptical (and potentially other non-circular) patches can produce period doubling over a wider range of parameters than a circular asperity can. With the parameters considered, the non-circular asperities produce period doubling of recurrence time, but the circular patch does not. The parameters considered are 50 MPa, a = 10−2, L = 5 μm, and the velocity-weakening regions are characterized by (a − b) = −4 × 10−3, while the velocity-strengthening regions have (a − b) = +4 × 10−3. Slip events (seismic and aseismic) are singled out when the slip velocity threshold reaches the value Vth = 10−4 m s−1.
Extended Data Figure 5 Simulation of the recurrence intervals of the period-doubling Parkfield tremors in a larger slip patch with R = 33 m and = 5 MPa.
a, Numerical simulation of the Parkfield tremor activity incorporating the change in effective pore pressure (red profile) after the Parkfield earthquake (EQ; vertical dashed line). The coloured dots denote the maximum velocity of the slip events. The slip events are flagged when the slip velocity is above the threshold Vpl = 10−4 m s−1 anywhere along the fault. Fast ruptures are preceded by shorter recurrence intervals. A change of pore pressure of about 300 kPa, representing 6% of the effective confining pressure, is applied at the onset of the Parkfield earthquake, resulting in a rapid occurrence of slip events, followed by a sequence of multiplets (highlighted in the two boxes) with varying period-multiplying factors. The pressure perturbation is chosen by trial and error to create a two-year transient that is similar to the seismic observations. The top right inset shows the model geometry with an asperity size R of 33 m. b, Characterization of the dynamics of the slip events. Fast ruptures are preceded by shorter recurrence intervals. The effective pore-pressure perturbation following the Parkfield earthquake affects the dynamics of the sequence with a temporary interruption of period doubling followed by a gradual recovery. See Fig. 2 legend for details of methodology and presentation.
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Veedu, D., Barbot, S. The Parkfield tremors reveal slow and fast ruptures on the same asperity. Nature 532, 361–365 (2016). https://doi.org/10.1038/nature17190
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