We analyze the conditions for unstable slip of a fluid infiltrated fault using a rate and state dependent friction model including the effects of dilatancy and pore compaction. We postulate the existence of a steady state drained porosity of the fault gouge which depends on slip velocity as ϕss = ϕ0 + εln(v/v0) over the range considered, where v is sliding velocity and ε and v0 are constants. Porosity evolves toward steady state over the same distance scale, dc, as “state.” This constitutive model predicts changes in porosity upon step changes in sliding velocity that are consistent with the drained experiments of Marone et al. (1990). For undrained loading, the effect of dilatancy is to increase (strengthen) ∂τss/∂lnv by μssε/(σ – p)β where μss is steady state friction, σ and p are fault normal stress and pore pressure, and β is a combination of fluid and pore compressibilities. Assuming ε ∼ 1.7×10−4 from fitting the Marone et al. data, we find the “dilatancy strengthening” effect to be reasonably consistent with undrained tests conducted by Lockner and Byerlee (1994). Linearized perturbation analysis of a single degree of freedom model in steady sliding shows that unstable slip occurs if the spring stiffness is less than a critical value given by kcrit = (σ‐p)(b‐a)/dc ‐ εμssF(c*)/βdc where a and b are coefficients in the friction law and F(C*) is a function of the model hydraulic diffusivity c* (diffusivity/diffusion length2). In the limit c* →∞ F(c*) → 0, recovering the drained result of Ruina (1983). In the undrained limit, c* → 0, F(c*) → 1, so that for sufficiently large ε slip is always stable to small perturbations. Under undrained conditions (σ – p) must exceed εμss/β(b ‐ a) for instabilities to nucleate, even for arbitrarily reduced stiffness. This places constraints on how high the fault zone pore pressure can be, to rationalize the absence of a heat flow anomaly on the San Andreas fault, and still allow earthquakes to nucleate without concommitant fluid transport. For the dilatancy constitutive laws examined here, numerical simulations do not exhibit large interseismic increases in fault zone pore pressure. The simulations do, however, exhibit a wide range of interesting behavior including: sustained finite amplitude oscillations near steady state and repeating stick slip events in which the stress drop decreases with decreasing diffusivity, a result of dilatancy strengthening. For some parameter values we observe “aftershock” like events that follow the principal stick‐slip event. These aftershocks are noteworthy in that they involve rerupture of the surface due to the interaction of the dilatancy and slip weakening effects rather than to interaction with neighboring portions of the fault. This mechanism may explain aftershocks that appear to be located within zones of high mainshock slip, although poor resolution in mainshock slip distributions can not be ruled out.

[1] We present here a new InSAR persistent scatterer (PS) method for analyzing episodic crustal deformation in non-urban environments, with application to volcanic settings. Our method for identifying PS pixels in a series of interferograms is based primarily on phase characteristics and finds low-amplitude pixels with phase stability that are not identified by the existing amplitude-based algorithm. Our method also uses the spatial correlation of the phases rather than a well-defined phase history so that we can observe temporally-variable processes, e.g., volcanic deformation. The algorithm involves removing the residual topographic component of flattened interferogram phase for each PS, then unwrapping the PS phases both spatially and temporally. Our method finds scatterers with stable phase characteristics independent of amplitudes associated with man-made objects, and is applicable to areas where conventional InSAR fails due to complete decorrelation of the majority of scatterers, yet a few stable scatterers are present.

[1] While conventional interferometric synthetic aperture radar (InSAR) is a very effective technique for measuring crustal deformation, almost any interferogram includes large areas where the signals decorrelate and no measurement is possible. Persistent scatterer (PS) InSAR overcomes the decorrelation problem by identifying resolution elements whose echo is dominated by a single scatterer in a series of interferograms. Existing PS methods have been very successful in analysis of urban areas, where stable angular structures produce efficient reflectors that dominate background scattering. However, man-made structures are absent from most of the Earth's surface. Furthermore, existing methods identify PS pixels based on the similarity of their phase history to an assumed model for how deformation varies with time, whereas characterizing the temporal pattern of deformation is commonly one of the aims of any deformation study. We describe here a method for PS analysis, StaMPS, that uses spatial correlation of interferogram phase to find pixels with low-phase variance in all terrains, with or without buildings. Prior knowledge of temporal variations in the deformation rate is not required for their identification. We apply StaMPS to Volcán Alcedo, where conventional InSAR fails because of dense vegetation on the upper volcano flanks that causes most pixels to decorrelate with time. We detect two sources of deformation. The first we model as a contracting pipe-like body, which we interpret to be a crystallizing magma chamber. The second is downward and lateral motion on the inner slopes of the caldera, which we interpret as landsliding.Citation: Hooper, A., P. Segall, and H. Zebker (2007), Persistent scatterer interferometric synthetic aperture radar for crustal deformation analysis, with application to Volcán Alcedo, Galápagos,

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[1] The mechanics of slow slip events (SSE) in subduction zones remain unresolved. We suggest that SSE nucleate in areas of unstable friction under drained conditions, but as slip accelerates dilatancy reduces pore pressure p quenching instability. Competition between dilatant strengthening and thermal pressurization may control whether slip is slow or fast. We model SSE with 2-D elasticity, rate-state friction, and a dilatancy law where porosity evolves toward steady state ss over distance d c and ss = 0 + ln(v/v 0 ); v is slip speed. We consider two diffusion models. Membrane diffusion (MD) is approximated by −(p − p ∞ )/t f where p and p ∞ are shear zone and remote pore pressure and t f is a characteristic diffusion time. Homogeneous diffusion (HD) accurately models fault-normal flow with diffusivity c hyd . For MD, linearized analysis defines a boundary E = 1 − a/b between slow and fast slip, where E ≡ f 0 /bb(s − p ∞ ), f 0 , a, and b are friction parameters and b is compressibility. When E < 1 − a/b slip accelerates to instability for sufficiently large faults, whereas for E > 1 − a/b slip speeds remain quasi-static. For HD,defines dilatancy efficiency, where h is shear zone thickness and v ∞ is plate velocity. SSE are favored by large h and low effective stress. The ratio E p to thermal pressurization efficiency scales with 1/(s − p ∞ ), so high p ∞ favors SSE, consistent with seismic observations. For E p ∼ 10 −3 transient slip rates, repeat times, average slip, and stress drops are comparable to field observations. Model updip propagation speeds are comparable to those observed along-strike. Many simulations exhibit slow phases driven by steady downdip slip and faster phases that relax the accumulated stress. Model SSE accommodate only a fraction of plate motion; the remaining deficit must be accommodated during coseismic or postseismic slip.Citation: Segall, P., A. M. Rubin, A. M. Bradley, and J. R. Rice (2010), Dilatant strengthening as a mechanism for slow slip events,

Fault traces consist of numerous discrete segments, commonly arranged as echelon arrays. In some cases, discontinuities influence the distribution of slip and seismicity along faults. To analyze fault segments, we derive a two‐dimensional solution for any number of nonintersecting cracks arbitrarily located in a homogeneous elastic material. The solution includes the elastic interaction between cracks. Crack surfaces are assumed to stick or slip according to a linear friction law. For an array of echelon cracks the ratio of maximum slip to array length significantly underestimates the difference between the driving stress and frictional resistance. The ratio of maximum slip to crack length slightly overestimates this difference. Stress distributions near right‐ and left‐stepping echelon discontinuities differ in two important ways. For right lateral shear and left‐stepping cracks, normal tractions on the overlapped crack ends increase and inhibit frictional sliding, whereas for right‐stepping cracks, normal tractions decrease and facilitate sliding. The mean compressive stress between right‐stepping cracks also decreases and promotes the formation of secondary fractures, which tend to link the cracks and allow slip to be transferred through the discontinuity. For left‐stepping cracks the mean stress increases; secondary fracturing is more restricted and tends not to link the cracks. Earthquake swarms and aftershocks cluster near right steps along right lateral faults. Our results suggest that left steps store elastic strain energy and may be sites of large earthquakes. Opposite behavior results if the sense of shear is left lateral.

The standard model of injection‐induced seismicity considers changes in Coulomb strength due solely to changes in pore pressure. We consider two additional effects: full poroelastic coupling of stress and pore pressure, and time‐dependent earthquake nucleation. We model stress and pore pressure due to specified injection rate in a homogeneous, poroelastic medium. Stress and pore pressure are used to compute seismicity rate through the Dieterich (1994) model. For constant injection rate, the time to reach a critical seismicity rate scales with t ∼ r2/(cfc), where r is distance from the injector, c is hydraulic diffusivity, and fc is a factor that depends on mechanical properties, and weakly on r. The seismicity rate decays following a peak, consistent with some observations. During injection poroelastic coupling may increase or decrease the seismicity rate, depending on the orientation of the faults relative to the injector. If injection‐induced stresses inhibit slip, abrupt shut‐in can lead to locally sharp increases in seismicity rate; tapering the flux mitigates this effect. The maximum magnitude event has been observed to occur postinjection. We suggest the seismicity rate at a given magnitude depends on the nucleation rate, the size distribution of fault segments, and if the background shear stress is low, the time‐varying volume of perturbed crust. This leads to a rollover in frequency‐magnitude distribution for larger events, with a “corner” that increases with time. Larger events are absent at short times, but approach the background frequency with time; larger events occurring post shut‐in are thus not unexpected.