A document by Chao Song. Click on the document to view its contents.

The empirical constitutive modeling framework of Rate- and State-dependent Friction (RSF) is commonly used to describe the time-dependent frictional response of fault gouge to perturbations from steady sliding. In a previous study (Ferdowsi & Rubin, 2020), we found that a granular-physics-based model of a fault shear zone, with time-independent properties at the contact scale, reproduces the phenomenology of laboratory rock and gouge friction experiments in velocity-step and slide-hold protocols. A few slide-hold-slide simulations further suggested that the granular model might outperform current empirical RSF laws in describing laboratory data. Here, we explore the behavior of the same Discrete Element Method model in slide-hold and slide-hold-slide protocols over a wide range of sliding velocities, hold durations, and system stiffnesses, and provide additional support for this view. We find that, similar to laboratory data, the rate of stress decay during slide-hold simulations is in general agreement with the “Slip law” version of the RSF equations, using parameter values determined independently from velocity-step tests. During reslides following long hold times, the model, similar to lab data, produces a nearly constant rate of frictional healing with log hold time, with that rate being in the range of ~0.5-1 times the RSF “state evolution” parameter b. We also find that, as in laboratory experiments, the granular layer undergoes log-time compaction during holds. This is consistent with the traditional understanding of state evolution under the Aging law, even though the associated stress decay is similar to that predicted by the Slip and not the Aging law.

Nearly all frictional interfaces strengthen as the logarithm of time when sliding at ultra-low speeds. Observations of also logarithmic-in-time growth of interfacial contact area under such conditions has led to constitutive models which assume that this frictional strengthening results from purely time-dependent, and slip-insensitive, contact area growth. The main laboratory support for such strengthening has traditionally been derived from increases in friction during ‘load-point hold’ experiments, wherein a sliding interface is allowed to gradually self-relax down to sub-nanometric slip rates. In contrast , following step decreases in the shear loading rate, friction is widely reported to increase over a characteristic slip scale, independent of the magnitude of the slip-rate decrease-a signature of slip-dependent strengthening. To investigate this apparent contradiction, we subjected granite samples to a series of step decreases in shear rate of up to 3.5 orders of magnitude, and load-point holds of up to 10,000 s, such that both protocols accessed the phenomenologi-cal regime traditionally inferred to demonstrate time-dependent fric-tional strengthening. When modeling the resultant data, which probe interfacial slip rates ranging from 3 μm/s to less than 10^-5 μm/s, we found that constitutive models where low slip-rate friction evolution mimics log-time contact area growth require parameters that differ by orders of magnitude across the different experiments. In contrast, an alternative constitutive model in which friction evolves only with interfacial slip fits most of the data well with nearly identical parameters. This leads to the surprising conclusion that frictional strengthening is dominantly slip dependent even at sub-nanometric slip rates.

Rate‐ and State‐dependent Friction (RSF) equations are commonly used to describe the time‐dependent frictional response of fault gouge to perturbations in sliding velocity. Among the better‐known versions are the Aging and Slip laws for the evolution of state. Although the Slip law is more successful, neither can predict all the robust features of lab data. RSF laws are also empirical, and their micromechanical origin is a matter of much debate. Here we use a granular‐physics‐based model to explore the extent to which RSF behavior, as observed in rock and gouge friction experiments, can be explained by the response of a granular gouge layer with time‐independent properties at the contact scale. We examine slip histories for which abundant lab data are available, and find that the granular model (1) mimics the Slip law for those loading protocols where the Slip law accurately models laboratory data (velocity‐step and slide‐hold tests), and (2) deviates from the Slip law under conditions where the Slip law fails to match laboratory data (the reslide portions of slide‐hold‐slide tests), in the proper sense to better match those data. The simulations also indicate that state is sometimes decoupled from porosity in a way that is inconsistent with traditional interpretations of “state” in RSF. Finally, if the “granular temperature” of the gouge is suitably normalized by the confining pressure, it produces an estimate of the direct velocity effect (the RSF parameter a) that is consistent with our simulations, and in the ballpark of lab data.

Although tremor is believed to consist of myriad Low-frequency Earthquakes (LFEs), it also contains longer-period signals of unknown origin. We investigate the source of some of the longer-period signals by locating tremor windows independently in relatively high-frequency (’HF’, 1.25–6.5 Hz, containing typical LFEs) and low-frequency (’LF’, 0.5–1.25 Hz) bands. We hypothesize that if tremor consists entirely of LFEs, such that the lower-frequency signals come from the non-uniform timing of higher-frequency ($\sim$2 Hz) LFEs, then contemporaneous LF and HF signals should be nearly co-located. Here we search for a systematic offset between the locations of contemporaneous LF and HF detections during rapid tremor migrations (RTMs). This first requires correcting for apparent offsets in location that arise simply from filtering in different passbands. To guard against possible errors in our empirical filtering effect corrections, we focus on a region of the subduction interface beneath southern Vancouver Island that hosts migrations propagating in nearly opposing directions. We find that the LF energy appears to occur roughly 500 m farther behind the propagating fronts of RTMs than the HF energy, whether those fronts propagate to the ENE or to the WSW. This separation is small compared to the location error of individual LF detections, but the result seems robust owing to the large number of detections. If this result stands, it suggests that tremor consists of more than just a collection of LFEs, with longer-period energy being generated farther behind the migrating fronts of RTMs, where slip speeds are presumably lower.

The broadband stacks (templates) of velocity seismograms of nearly co-located low-frequency earthquakes (LFEs) detected using a 1-8 Hz passband beneath southern Vancouver Island tend to exhibit a simple dipolar shape with a characteristic duration of ~0.3-0.5 s, which is also found to be nearly independent of the seismic moment. An important question left unanswered is whether the duration is due to the nature of the source, is set by attenuation near the source region, or is just a bias introduced by the narrow passband used to detect LFEs. In tremor catalogs detected using a relatively low-frequency passband, 0.5-1.25 Hz, we have found some tremor windows that contain relatively isolated dipole arrivals similar to LFEs. A few of these have a duration apparently longer than that of the LFE templates. Notably, the same location on the fault also seems capable of generating signals with a shorter duration at other times. Figure 1 shows seismograms, at 3 stations, of one such example in the vicinity of LFE family 001 of Bostock et al. (2012), in which the main arrival has a duration of ~1 s, whereas another signal 3 s earlier with a duration of only ~0.4 s comes from roughly the same location (same move-out between the stations). This significant variability in duration at approximately the same location suggests that the long-duration events owe their duration to source processes and not attenuation, provided that attenuation does not vary on extremely short time and space scales during the episodic tremor and slip episode. The relative isolation in time also makes the longer duration less likely to result from the temporal clustering of multiple typical LFEs. We will undertake a more systematic search of our longer- and shorter-period tremor catalogs to assess this possibility. Addressing this question will shed more light on the factors that control the apparent duration of LFEs. Figure 1 The top panel shows the long-duration tremor signal in a relatively lower-frequency band, 0.5-1.25 Hz, whereas the second panel from the top is the same 32-s segment in a higher-frequency band, 1.25-6.5 Hz. The third panel shows the trace in a broader passband, 0.5-6.5 Hz. The bottom panel shows the stacked LFE templates of the same family filtered through 0.5-6.5 Hz.