This paper reviews rock friction and the frictional properties of earthquake faults. The basis for rate- and state-dependent friction laws is reviewed. The friction state variable is discussed, including its interpretation as a measure of average asperity contact time and porosity within granular fault gouge. Data are summarized showing that friction evolves even during truly stationary contact, and the connection between modern friction laws and the concept of “static” friction is discussed. Measurements of frictional healing, as evidenced by increasing static friction during quasistationary contact, are reviewed, as are their implications for fault healing. Shear localization in fault gouge is discussed, and the relationship between microstructures and friction is reviewed. These data indicate differences in the behavior of bare rock surfaces as compared to shear within granular fault gouge that can be attributed to dilation within fault gouge. Physical models for the characteristic friction distance are discussed and related to the problem of scaling this parameter to seismic faults. Earthquake afterslip, its relation to laboratory friction data, and the inverse correlation between afterslip and shallow coseismic slip are discussed in the context of a model for afterslip. Recent observations of the absence of afterslip are predicted by the model.

/pdf/laboratory-derived-friction-laws-and-their-application-to-44s35v6won.pdf

Laboratory-derived friction laws and their application to seismic faulting

A study on the influence of the plasticity index (PI) on the cyclic stress‐strain parameters of saturated soils needed for site‐response evaluations and seismic microzonation is presented. Ready‐to‐use charts are included, showing the effect of PI on the location of the modulus reduction curve G/Gmax versus cyclic shear strain γc, and on the material damping ratio λ versus γc curve. The charts are based on experimental data from 16 publications encompassing normally and overconsolidated clays (OCR=1-15), as well as sands. It is shown that PI is the main factor controlling G/Gmax and λ for a wide variety of soils; if for a given γc PI increases, G/Gmax rises and λ is reduced. Similar evidence is presented showing the influence of PI on the rate of modulus degradation with the number of cycles in normally consolidated clays. It is concluded that soils with higher plasticity tend to have a more linear cyclic stress‐strain response at small strains and to degrade less at larger γc than soils with a lower PI. ...

Effect of Soil Plasticity on Cyclic Response


 The spectral ratio between horizontal and vertical components (H/V ratio) of microtremors measured at the ground surface has been used to estimate fundamental periods and amplification factors of a site, although this technique lacks theoretical background. The aim of this article is to formulate the H/V technique in terms of the characteristics of Rayleigh and Love waves, and to contribute to improve the technique. The improvement includes use of not only peaks but also troughs in the H/V ratio for reliable estimation of the period and use of a newly proposed smoothing function for better estimation of the amplification factor. The formulation leads to a simple formula for the amplification factor expressed with the H/V ratio. With microtremor data measured at 546 junior high schools in 23 wards of Tokyo, the improved technique is applied to mapping site periods and amplification factors in the area.

Ground Motion Characteristics Estimated from Spectral Ratio between Horizontal and Verticcl Components of Mietremors.

Many aspects of earthquake mechanics remain an enigma as we enter the closing years of the twentieth century. One potential bright spot is the realization that simple calculations of stress changes may explain some earthquake interactions, just as previous and on going studies of stress changes have begun to explain human-induced seismicity. This paper, which introduces the special section “Stress Triggers, Stress Shadows, and Implications for Seismic Hazard,” reviews many published works and presents a compilation of quantitative earthquake interaction studies from a stress change perspective. This synthesis supplies some clues about certain aspects of earthquake mechanics. It also demonstrates that much work remains before we can understand the complete story of how earthquakes work.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JB01576

Introduction to Special Section: Stress Triggers, Stress Shadows, and Implications for Seismic Hazard

Evidence for and implications of self-healing pulses of slip in earthquake rupture

The network of strong motion accelerographs in Mexico includes instruments that were installed, under an international cooperative research program, in sites selected for the high potenial of a large earthquake. The 19 September 1985 earthquake (magnitude 8.1) occurred in a seismic gap where an earthquake was expected. As a result, there is an excellent descripton of the ground motions that caused the disaster.

https://science.sciencemag.org/content/sci/233/4768/1043.full.pdf

Strong Ground Motion from the Michoacan, Mexico, Earthquake

The proximity and similarity of the 1992, magnitude 7.3 Landers and 1999, magnitude 7.1 Hector Mine earthquakes in California permit testing of earthquake triggering hypotheses not previously possible. The Hector Mine earthquake confirmed inferences that transient, oscillatory ‘dynamic’ deformations radiated as seismic waves can trigger seismicity rate increases, as proposed for the Landers earthquake1,2,3,4,5,6. Here we quantify the spatial and temporal patterns of the seismicity rate changes7. The seismicity rate increase was to the north for the Landers earthquake and primarily to the south for the Hector Mine earthquake. We suggest that rupture directivity results in elevated dynamic deformations north and south of the Landers and Hector Mine faults, respectively, as evident in the asymmetry of the recorded seismic velocity fields. Both dynamic and static stress changes seem important for triggering in the near field with dynamic stress changes dominating at greater distances. Peak seismic velocities recorded for each earthquake suggest the existence of, and place bounds on, dynamic triggering thresholds. These thresholds vary from a few tenths to a few MPa in most places, depend on local conditions, and exceed inferred static thresholds by more than an order of magnitude. At some sites, the onset of triggering was delayed until after the dynamic deformations subsided. Physical mechanisms consistent with all these observations may be similar to those that give rise to liquefaction or cyclic fatigue.

Earthquake triggering by seismic waves following the Landers and Hector Mine earthquakes

It is thought that small 'static' stress changes due to permanent fault displacement can alter the likelihood of, or trigger, earthquakes on nearby faults. Many studies of triggering in the near-field, particularly of aftershocks, rely on these static changes as the triggering agent and consider them only in terms of equivalent changes in the applied load on the fault. Here we report a comparison of the aftershock pattern of the moment magnitude Mw = 7.3 Landers earthquake, not only with static stress changes but also with transient, oscillatory stress changes transmitted as seismic waves (that is, 'dynamic' stresses). Dynamic stresses do not permanently change the applied load and thus can trigger earthquakes only by altering the mechanical state or properties of the fault zone. These dynamically weakened faults may fail after the seismic waves have passed by, and might even cause earthquakes that would not otherwise have occurred. We find similar asymmetries in the aftershock and dynamic stress patterns, the latter being due to rupture propagation, whereas the static stress changes lack this asymmetry. Previous studies have shown that dynamic stresses can promote failure at remote distances, but here we show that they can also do so nearby.

Triggering of earthquake aftershocks by dynamic stresses.

The 3 November 2002 moment magnitude 7.9 Denali fault earthquake generated large, permanent surface displacements in Alaska and large-amplitude surface waves throughout western North America. We find good agreement between strong ground-motion records integrated to displacement and 1-hertz Global Positioning System (GPS) position estimates collected ∼140 kilometers from the earthquake epicenter. One-hertz GPS receivers also detected seismic surface waves 750 to 3800 kilometers from the epicenter, whereas these waves saturated many of the seismicinstruments in the same region. High-frequency GPS increases the dynamic range and frequency bandwidth of ground-motion observations, providing another tool for studying earthquake processes.

https://science.sciencemag.org/content/sci/300/5624/1421.full.pdf

Using 1-Hz GPS data to measure deformations caused by the denali fault earthquake

Observational evidence for both static and transient near-field and far-field triggered seismicity are explained in terms of a frictional instability model, based on a single degree of freedom spring-slider system and rate- and state-dependent frictional constitutive equations. In this study a triggered earthquake is one whose failure time has been advanced by Δt (clock advance) due to a stress perturbation. Triggering stress perturbations considered include square-wave transients and step functions, analogous to seismic waves and coseismic static stress changes, respectively. Perturbations are superimposed on a constant background stressing rate which represents the tectonic stressing rate. The normal stress is assumed to be constant. Approximate, closed-form solutions of the rate-and-state equations are derived for these triggering and background loads, building on the work of Dieterich [1992, 1994]. These solutions can be used to simulate the effects of static and transient stresses as a function of amplitude, onset time t0, and in the case of square waves, duration. The accuracies of the approximate closed-form solutions are also evaluated with respect to the full numerical solution and t0. The approximate solutions underpredict the full solutions, although the difference decreases as t0 approaches the end of the earthquake cycle. The relationship between Δt and t0 differs for transient and static loads: a static stress step imposed late in the cycle causes less clock advance than an equal step imposed earlier, whereas a later applied transient causes greater clock advance than an equal one imposed earlier. For equal Δt, transient amplitudes must be greater than static loads by factors of several tens to hundreds depending on t0. We show that the rate-and-state model requires that the total slip at failure is a constant, regardless of the loading history. Thus a static load applied early in the cycle, or a transient applied at any time, reduces the stress at the initiation of failure, whereas static loads that are applied sufficiently late raise it. Rate-and-state friction predictions differ markedly from those based on Coulomb failure stress changes (ΔCFS) in which Δt equals the amplitude of the static stress change divided by the background stressing rate. The ΔCFS model assumes a stress failure threshold, while the rate-and-state equations require a slip failure threshold. The complete rate-and-state equations predict larger Δt than the ΔCFS model does for static stress steps at small t0, and smaller Δt than the ΔCFS model for stress steps at large t0. The ΔCFS model predicts nonzero Δt only for transient loads that raise the stress to failure stress levels during the transient. In contrast, the rate-and-state model predicts nonzero Δt for smaller loads, and triggered failure may occur well after the transient is finished. We consider heuristically the effects of triggering on a population of faults, as these effects might be evident in seismicity data. Triggering is manifest as an initial increase in seismicity rate that may be followed by a quiescence or by a return to the background rate. Available seismicity data are insufficient to discriminate whether triggered earthquakes are “new” or clock advanced. However, if triggering indeed results from advancing the failure time of inevitable earthquakes, then our modeling suggests that a quiescence always follows transient triggering and that the duration of increased seismicity also cannot exceed the duration of a triggering transient load. Quiescence follows static triggering only if the population of available faults is finite.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JB01125

Paul Bodin

Papers

Strong Ground Motion from the Michoacan, Mexico, Earthquake

Earthquake triggering by seismic waves following the Landers and Hector Mine earthquakes

Triggering of earthquake aftershocks by dynamic stresses.

Using 1-Hz GPS data to measure deformations caused by the denali fault earthquake

Earthquake triggering by transient and static deformations