A mechanism for preseismic steady rupture fronts observed in laboratory experiments

It has been shown that the onset of frictional instability is characterized by a transition from stable, quasi-static rupture growth to unstable, inertially-controlled high-speed rupture. In particular, slow rupture fronts propagating at a steady speed V_(slow) of the order of 5% of the S-wave speed have been observed prior to the onset of dynamic rupture in recent fault-friction laboratory experiments. However, the precise mechanism governing this V_(slow) stage is unknown. Here we reproduce this phenomenon in numerical simulations of earthquake sequences that incorporate laboratory-derived rate-and-state friction laws. Our simulations show that the V_(slow) stage originates from a stress concentration inherited from the coalescence of interseismic slow creep fronts. Its occurrence is limited to a narrow range of the parameter space but is found in simulations with two commonly-used state-variable evolution laws in the rate-and-state formulation. The sensitivity of the speed V_(slow) to the model parameters suggests that the propagation speed V_(slow) reported in laboratory experiments may also be sensitive to parameters of friction and stress conditions. Our results imply that time and space dimensions associated with the propagation of V_(slow) on natural faults can be as much as a few seconds and several hundred meters, respectively. Hence the detection of such preseismic signals may be possible with near-field high-resolution observations

Properties of Dynamic Earthquake Ruptures With Heterogeneous Stress Drop

Earthquake rupture is a notoriously complex process, at all observable scales. We introduce a simplified semi-dynamic crack model to investigate the connection between the statistical properties of stress and those of macroscopic source parameters such as rupture size, seismic moment, apparent stress drop and radiated energy. Rupture initiation is treated consistently with nucleation on a linear slip-weakening fault, whereas rupture propagation and arrest are treated according to the Griffith criterion. The available stress drop is prescribed as a spatially correlated random field and is shown to potentially sustain a broad range of magnitudes. By decreasing the amplitude of the stress heterogeneities or increasing their correlation length the distribution of earthquake sizes presents a transition from Gutenberg- Richter to characteristic earthquake behavior. This transition is studied through a mean-field analysis. The bifurcation to characteristic earthquake behavior is sharp, reminiscent of a first-order phase transition. A lower roll-off magnitude observed in the Gutenberg-Richter regime is shown to depend on the correlation length of the available stress drop, rather than being a direct signature of the nucleation process. More generally, we highlight the possible role of the stress correlation length scale on deviations from earthquake source self-similarity. The present reduced model is a building block towards understanding the effect of structural and dynamic fault heterogeneities on the scaling of source parameters and on basic properties of seismicity

Spectral-element simulations of long-term fault slip: Effect of low-rigidity layers on earthquake-cycle dynamics

We develop a spectral element method for the simulation of long-term histories of spontaneous seismic and aseismic slip on faults subjected to tectonic loading. Our approach reproduces all stages of earthquake cycles: nucleation and propagation of earthquake rupture, postseismic slip and interseismic creep. We apply the developed methodology to study the effects of low-rigidity layers on the dynamics of the earthquake cycle in 2-D. We consider two cases: small (M ~ 1) earthquakes on a fault surrounded by a damaged fault zone and large (M ~ 7) earthquakes on a vertical strike-slip fault that cuts through shallow low-rigidity layers. Our results indicate how the source properties of repeating earthquakes are affected by the presence of a damaged fault zone with low rigidity. Compared to faults in homogeneous media, we find (1) reduction in the earthquake nucleation size, (2) amplification of slip rates during dynamic rupture propagation, (3) larger recurrence interval, and (4) smaller amount of aseismic slip. Based on linear stability analysis, we derive a theoretical estimate of the nucleation size as a function of the width and rigidity reduction of the fault zone layer, which is in good agreement with simulated nucleation sizes. We further examine the effects of vertically-stratified layers (e.g., sedimentary basins) on the nature of shallow coseismic slip deficit. Our results suggest that low-rigidity shallow layers alone do not lead to coseismic slip deficit. While the low-rigidity layers result in lower interseismic stress accumulation, they also cause dynamic amplification of slip rates, with the net effect on slip being nearly zero

Spectral-element modeling of spontaneous earthquake rupture on rate and state faults: Effect of velocity-strengthening friction at shallow depths

We develop a spectral-element methodology (SEM) for simulating dynamic rupture on rate and state faults and use it to study how the rupture is affected by a shallow fault region of steady-state velocity-strengthening friction. Our comparison of the developed SEM and a spectral boundary-integral method (BIM) for an anti-plane (two-dimensional) test problem shows that the two methods produce virtually identical solutions for the finest resolution we use and that the convergence with grid reduction of the developed SEM methodology is comparable to that of BIM. We also use the test problem to compare numerical resolution required for different state evolution laws and for linear slip-weakening friction. Using our three-dimensional implementation of the methodology, we find that a shallow velocity-strengthening fault region can significantly alter dynamic rupture and ground motion. The velocity-strengthening region suppresses supershear propagation at the free surface occurring in the absence of such region, which could explain the lack of universally observed supershear rupture near the free surface. In addition, the velocity-strengthening region promotes faster fall-off of slip velocity behind the rupture front and decreases final slip throughout the entire fault, causing a smaller average stress drop. The slip decrease is largest in the shallow parts of the fault, resulting in the depth profile of slip qualitatively consistent with observations of shallow co-seismic slip deficit. The shallow velocity-strengthening region also reduces the amplification of strong ground motion due to a low-velocity bulk structure

Seismic Radiation From Simple Models of Earthquakes

We review some basic features of shear wave generation and energy balance for a 2D anti plane rupture. We first study the energy balance for a flat fault, and for a fault that contains a single localized kink. We determine an exact expression for the partition between strain energy flow released from the elastic medium surrounding the fault, radiated energy flow and energy release rate. This balance depends only on the rupture speed and the residual stress intensity factor. When the fault contains a kink, the energy available for fracture is reduced so that the rupture speed is reduced. When rupture speed changes abruptly, the radiated energy flow also changes abruptly. As rupture propagates across the kink, a shear wave is emitted that has a displacement spectral content that decreases like ω^(-2) at high frequencies. We then use spectral elements to model the propagation of an antiplane crack with a slip-weakening friction law. Since the rupture front in this case has a finite length scale, the wave emitted by the kink is smoothed at very high frequencies but its general behavior is similar to that predicted by the simple sharp crack model. A model of a crack that has several kinks and wanders around a mean rupture directions, shows that kinks reduce the rupture speed along the average rupture direction of the fault. Contrary to flat fault models, a fault with kinks produces high frequency waves that are emitted every time the rupture front turns at a kink. Finally, we discuss the applicability of the present results to a 3D rupture model

Downscaling of fracture energy during brittle creep experiments

We present mode 1 brittle creep fracture experiments along fracture surfaces that contain strength heterogeneities. Our observations provide a link between smooth macroscopic time-dependent failure and intermittent microscopic stress-dependent processes. We find the large-scale response of slow-propagating subcritical cracks to be well described by an Arrhenius law that relates the fracture speed to the energy release rate. At the microscopic scale, high-resolution optical imaging of the transparent material used (PMMA) allows detailed description of the fracture front. This reveals a local competition between subcritical and critical propagation (pseudo stick-slip front advances) independently of loading rates. Moreover, we show that the local geometry of the crack front is self-affine and the local crack front velocity is power law distributed. We estimate the local fracture energy distribution by combining high-resolution measurements of the crack front geometry and an elastic line fracture model. We show that the average local fracture energy is significantly larger than the value derived from a macroscopic energy balance. This suggests that homogenization of the fracture energy is not straightforward and should be taken cautiously. Finally, we discuss the implications of our results in the context of fault mechanics

Insights on earthquake triggering processes from early aftershocks of repeating microearthquakes

Characterizing the evolution of seismicity rate of early aftershocks can yield important information about earthquake nucleation and triggering. However, this task is challenging because early aftershock seismic signals are obscured by those of the mainshock. Previous studies of early aftershocks employed high-pass filtering and template matching but had limited performance and completeness at very short times. Here we take advantage of repeating events previously identified on the San Andreas Fault at Parkfield and apply empirical Green's function deconvolution techniques. Both Landweber and sparse deconvolution methods reveal the occurrence of aftershocks as early as few tenths of a second after the mainshock. These events occur close to their mainshock, within one to two rupture lengths away. The aftershock rate derived from this enhanced catalog is consistent with Omori's law, with no flattening of the aftershock rate down to the shortest resolvable timescale ∼0.3 s. The early aftershock rate decay determined here matches seamlessly the decay at later times derived from the original earthquake catalog, yielding a continuous aftershock decay over timescales spanning nearly 8 orders of magnitude. Aftershocks of repeating microearthquakes may hence be governed by the same mechanisms from the earliest time resolved here, up to the end of the aftershock sequence. Our results suggest that these early aftershocks are triggered by relatively large stress perturbations, possibly induced by aseismic afterslip with very short characteristic time. Consistent with previous observations on bimaterial faults, the relative location of early aftershocks shows asymmetry along strike, persistent over long periods

A New Strategy to Compare Inverted Rupture Models Exploiting the Eigenstructure of the Inverse Problem

Finite-fault-slip inversions provide crucial information on earthquake rupture phenomena. Many slip-inversion methods exist and differ in how the rupture model is parameterized and which regularizations or constraints are applied (e.g., Ide, 2007, and references therein). Some methods are utilized even routinely for large earthquakes and published online (e.g., the U.S. Geological Survey website http://earthquake.usgs.gov/, last accessed August 2015). However, the slip-inversion results obtained by various authors for the same event may differ (e.g., Clévédé et al., 2004). There is currently no consensus about which slip-inversion method is preferable, and there are concerns about the reliability of the inferred source models due to the nonuniqueness or ill conditioning of the inverse problem (Hartzell et al., 2007; Zahradník and Gallovič, 2010; Gallovič and Zahradník, 2011; Shao and Ji, 2012). Therefore, slip inversion is still a subject of active research

A phase coherence approach to identifying co-located earthquakes and tremor

We present and use a phase coherence approach to identify seismic signals that have similar path effects but different source time functions: co-located earthquakes and tremor. The method used is a phase coherence-based implementation of empirical matched field processing, modified to suit tremor analysis. It works by comparing the frequency-domain phases of waveforms generated by two sources recorded at multiple stations. We first cross-correlate the records of the two sources at a single station. If the sources are co-located, this cross-correlation eliminates the phases of the Green’s function. It leaves the relative phases of the source time functions, which should be the same across all stations so long as the spatial extent of the sources are small compared with the seismic wavelength. We therefore search for cross-correlation phases that are consistent across stations as an indication of co-located sources. We also introduce a method to obtain relative locations between the two sources, based on back-projection of interstation phase coherence. We apply this technique to analyse two tremor-like signals that are thought to be composed of a number of earthquakes. First, we analyse a 20 s long seismic precursor to a M 3.9 earthquake in central Alaska. The analysis locates the precursor to within 2 km of the mainshock, and it identifies several bursts of energy—potentially foreshocks or groups of foreshocks—within the precursor. Second, we examine several minutes of volcanic tremor prior to an eruption at Redoubt Volcano. We confirm that the tremor source is located close to repeating earthquakes identified earlier in the tremor sequence. The amplitude of the tremor diminishes about 30 s before the eruption, but the phase coherence results suggest that the tremor may persist at some level through this final interval

Interplay of seismic and aseismic deformations during earthquake swarms: An experimental approach

Observations of earthquake swarms and slow propagating ruptures on related faults suggest a close relation between the two phenomena. Earthquakes are the signature of fast unstable ruptures initiated on localized asperities while slow aseismic deformations are experienced on large stable segments of the fault plane. The spatial proximity and the temporal coincidence of both fault mechanical responses highlight the variability of fault rheology. However, the mechanism relating earthquakes and aseismic processes is still elusive due to the difficulty of imaging these phenomena of large spatiotemporal variability at depth. Here we present laboratory experiments that explore, in great detail, the deformation processes of heterogeneous interfaces in the brittle-creep regime. We track the evolution of an interfacial crack over 7 orders of magnitude in time and 5 orders of magnitude in space using optical and acoustic sensors. We explore the response of the system to slow transient loads and show that slow deformation episodes are systematically accompanied by acoustic emissions due to local fracture energy disorder. Features of acoustic emission activities and deformation rate distributions of our experimental system are similar to those in natural faults. On the basis of an activation energy model, we link our results to the Rate and State friction model and suggest an active role of local creep deformation in driving the seismic activity of earthquake swarms