Hugo Perfettini

Frictional response induced by time-dependent fluctuations of the normal loading

We study the effect of time-variable normal stress perturbations on a creeping fault which satisfies a velocity-weakening rate- and state-dependent friction law and is slipping at constant speed. We use the spring-block model and include the effect of inertia. To account for the variable normal stress, we use the description introduced by Linker and Dieterich [1992], which links normal stress fluctuations to changes of the state variable. We consider periodic perturbations of the normal stress in time (as caused, for instance, by tides) and compare the behavior for two commonly used friction laws (the “slip” and the “ageing” laws). Their mechanical response is shown to be significantly different for normal stress fluctuations. It could be used to probe these two laws during laboratory friction experiments. We show that there is a resonance phenomenon, involving strong amplification of the shear and velocity response of the interface, when the spring stiffness is modestly above its critical value (or when, at a given stiffness, the normal stress is modestly below its critical value). We show that such an amplification is also observed when periodic fluctuations of the shear loading are considered, making the resonance phenomenon a general feature of the response of a near-critical creeping surface to periodic fluctuations of the external loading. Analytical solutions are based on a linear expansion for low amplitude of normal or shear stress variations and are in very good agreement with numerical solutions. A method to find the evolution of friction in the case of an arbitrary perturbation of the normal stress is also presented. The results show that a creeping fault may be destabilized and enter a stick-slip regime owing to small normal stress oscillations. This may also account for a mechanism for the generation of “creep bursts.” However, these phenomena require very specific parameter ranges to excite the resonance, which may not be met very generally in nature. This study illustrates the importance of the normal stress fluctuations on stable sliding and suggests further friction laboratory experiments.

Stress transfer by the 1988-1989 M=5.3 and 5.4 Lake Elsman foreshocks to the Loma Prieta fault: Unclamping at the site of peak mainshock slip

We study the stress transferred by the June 27, 1988, M = 5.3 and August 8, 1989, M = 5.4 Lake Elsman earthquakes, the largest events to strike within 15 km of the future Loma Prieta rupture zone during 74 years before the 1989 M = 6.9 Loma Prieta earthquake. We find that the first Lake Elsman event brought the rupture plane of the second event 0.3–1.6 bars (0.03–0.16 MPa) closer to Coulomb failure but that the Lake Elsman events did not bring the future Loma Prieta hypocentral zone closer to failure. Instead, the Lake Elsman earthquakes are calculated to have reduced the normal stress on (or “undamped”) the Loma Prieta rupture surface by 0.5–1.0 bar (0.05–0.10 MPa) at the site where the greatest slip subsequently occurred in the Loma Prieta earthquake. This association between the sites of peak unclamping and slip suggests that the Lake Elsman events did indeed influence the Loma Prieta rupture process. Unclamping the fault would have locally lowered the resistance to sliding. Such an effect could have been enhanced if the lowered normal stress permitted fluid infusion into the undamped part of the fault. Although less well recorded, the ML = 5.0 1964 and ML = 5.3 1967 Corralitos events struck within 10 km of the southwest end of the future Loma Prieta rupture. No similar relationship between the normal stress change and subsequent Loma Prieta slip is observed, although the high-slip patch southwest of the Loma Prieta epicenter corresponds roughly to the site of calculated Coulomb stress increase for a low coefficient of friction. The Lake Elsman-Loma Prieta result is similar to that for the 1987 M = 6.2 Elmore Ranch and M = 6.7 Superstition Hills earthquakes, suggesting that foreshocks might influence the distribution of mainshock slip rather than the site of mainshock nucleation.

Periodic loading on a creeping fault : Implications for tides

We study the eect of time varying normal and shear stress perturbations on a creeping fault and in which inertia is neglected. When interpreted in terms of earth- quaketriggeringbyearthtides,ourresultssuggestthattidal triggeringmayexistbutbeverydiculttodetect. Weusea spring-block model with a rate-and state dependentfriction law, loaded at constant velocity, and in which inertia is ne- glected. Whenaperiodicstressisapplied,aresonanceexists which can destabilize sliding (i.e. earthquakes). However, when frictional parameters slightly vary along the fault, the observed phase lag between the response of the fault and the perturbating stresses close to resonance shows a broad and uncorrelated scattering. It is now well accepted that faults are not subjected to spatially uniform stress. Correlations between Coulomb stress changes induced by previous earthquakes and after- shocks locations have been widely reported in the literature (King et al., 1994). These spatial variations in stress are ac- companied by temporal changes of thestate of stress on the fault. The latter may occur because of seismic waves gener- ated by surrounding earthquakes (Gomberg et al., 1998) and also by periodic (and non-transient) changes of stress. The most important periodic fluctuations of the stresses acting onafaultareduetoearthtides(createdbythegravitational attractionofthesunandthemoon)andthesevariationsare oforder0:001to0:004MPa(Vidale et al.,1998). Waterlevel changes inreservoirs also create periodic variations in stress but the time scales are of the order of a year (seasonalfluc- tuations). Periodic loading in shear as well as in normal stress may highly influence failure. Considering periodic fluctu- ations of the normal stress in a spring-block model, Perfet- tini (2000) showed that such perturbations can destabilize sliding. In this case, the fault enters a stick-slip regime, and earthquake-like events are observed. This eect is en- hanced close to the stability boundary, i.e. when the sti- ness of the spring is close to the critical stiness kc ,a nd when the period of the normal stress oscillations is close to a period Tc .B othkc and Tc are dened further in the text. The model proposed by Perfettini (2000) is extended heretoperiodicperturbationsof thenormalaswellasshear load, leadingtoqualitativelysimilar observations. Thesere- sultssuggestthattidesmaypromoteruptureprovidingthat the eective stiness k of the fault is close to kc and that Tc is close to the period T of the external perturbations.

Slow Crack Propagation and Slip Correlations

The propagation of an interfacial crack through a weak plane of a transparent Plexiglas block is studied experimentally. The toughness is controlled artificially by a sand blasting procedure, and fluctuates locally in space like uncorrelated random noise. The block is fractured in mode I at low speed (10 7 10 4 m/s). The crack front is observed optically with a microscope and a high resolution digital camera. During the propagation, the front is pinned by micro-regions of high toughness and becomes rough. Roughness of the crack front is analyzed in terms of self-affinity. The in-plane roughness exponent is shown to be 0:63 0:05. Experimental results are compared to a numerical model. The model reproduces the self-affine behavior of the crack front, i.e., long-range correlations of the roughness. Analogies between mode I and mode III are presented in order to discuss implications of the experimental results for creeping faults. Accordingly, correlations of the slip pattern are shown to exist over scales substantially larger than the asperity sizes.

Slip correlations on a creeping fault

Using a quasi-static three dimensional fault model which accounts for long range elastic interactions, we examine the influence of spatial heterogeneities of frictional strength on the slip distribution along a creeping fault. Slip fluctuates spatially because of pinning on local asperities. We show that three regimes of slip correlations exist. The first regime results in a uniform slip as in an homogeneous medium. On the contrary, slip in the second regime highly fluctuates and is controlled by heterogeneities of frictional strength. The third regime is intermediate and develops areas of high slip that are much bigger than the local asperity size (self-affine properties of the slip distribution). This particular regime illustrates the possible misinterpretation of low frequency slip data (e.g. interferometric and GPS data) in terms of structural or compositional properties along the fault.

Shear and normal load perturbations on a two-dimensional continuous fault: 2. Dynamic triggering: DYNAMIC TRIGGERING ON A CONTINUOUS FAULT

[1] We study the consequences of temporal stress perturbations on earthquake nucleation in a continuous fault model. Using a two-dimensional (2-D) quasi-dynamic model of a strikeslip fault governed by a rate-and-state friction law with depth variable properties, we show that dynamic triggering (due to stress pulses or wave packets), although allowed by our results, is an exception rather than a rule and should be limited to understressed areas such as areas of high pore pressures or to faults at the very end of their earthquake cycle. When periodic stress perturbations are sensitive, the response of the fault is frequency-independent for periods lower than a period T 0 but strongly depends on the frequency for periods larger than T . We demonstrate that the crossover period T 0 is equal to the time left until the earthquake instability. According to our model, high frequencies are demonstrated to have a higher triggering potential than low ones, which makes tidal triggering very unlikely before the end of the cycle due to the very low amplitudes of the stress perturbations involved.