Dynamical system analysis and forecasting of deformation produced by an earthquake fault

We present a method of constructing low-dimensional nonlinear models describing the main dynamical features of a discrete 2D cellular fault zone, with many degrees of freedom, embedded in a 3D elastic solid. A given fault system is characterized by a set of parameters that describe the dynamics, rheology, property disorder, and fault geometry. Depending on the location in the system parameter space we show that the coarse dynamics of the fault can be confined to an attractor whose dimension is significantly smaller than the space in which the dynamics takes place. Our strategy of system reduction is to search for a few coherent structures that dominate the dynamics and to capture the interaction between these coherent structures. The identification of the basic interacting structures is obtained by applying the Proper Orthogonal Decomposition (POD) to the surface deformations fields that accompany strike-slip faulting accumulated over equal time intervals. We use a feed-forward artificial neural network (ANN) architecture for the identification of the system dynamics projected onto the subspace (model space) spanned by the most energetic coherent structures. The ANN is trained using a standard back-propagation algorithm to predict (map) the values of the observed model state at a future time given the observed model state at the present time. This ANN provides an approximate, large scale, dynamical model for the fault.Comment: 30 pages, 12 figure

Gutenberg Richter and Characteristic Earthquake Behavior in Simple Mean-Field Models of Heterogeneous Faults

The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in the mean field version of a model for a segmented fault system in a three-dimensional elastic solid. The studies focus on the interplay between the roles of disorder, dynamical effects, and driving mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of dynamical weakening (or ``overshoot'') effects (epsilon) and the normal distance (L) of the driving forces from the fault. In general, small epsilon and small L are found to produce Gutenberg-Richter type power law statistics with an exponential cutoff, while large epsilon and large L lead to a distribution of small events combined with characteristic system-size events. In a certain parameter regime the behavior is bistable, with transitions back and forth from one phase to the other on time scales determined by the fault size and other model parameters. The implications for realistic earthquake statistics are discussed.Comment: 21 pages, RevTex, 6 figures (ps, eps

An algorithm for automated identification of fault zone trapped waves

We develop an algorithm for automatic identification of fault zone trapped waves in data recorded by seismic fault zone arrays. Automatic S picks are used to identify time windows in the seismograms for subsequent search for trapped waves. The algorithm calculates five features in each seismogram recorded by each station: predominant period, 1 s duration energy (representative of trapped waves), relative peak strength, arrival delay and 6 s duration energy (representative of the entire seismogram). These features are used collectively to identify stations in the array with seismograms that are statistical outliers. Applying the algorithm to large data sets allows for distinguishing genuine trapped waves from occasional localized site amplification in seismograms of other stations. The method is verified on a test data set recorded across the rupture zone of the 1992 Landers earthquake, for which trapped waves were previously identified manually, and is then applied to a larger data set with several thousand events recorded across the San Jacinto fault zone. The developed technique provides an important tool for systematic objective processing of large seismic waveform data sets recorded near fault zones

An earthquake detection algorithm with pseudo-probabilities of multiple indicators

We develop an automatic earthquake detection algorithm combining information from numerous indicator variables in a non-parametric framework. The method is shown to perform well with multiple ratios of moving short- and long-time averages having ranges of time intervals and frequency bands. The results from each indicator are transformed to a pseudo-probability time-series (PPTS) in the range [0, 1]. The various PPTS of the different indicators are multiplied to form a single joint PPTS that is used for detections. Since all information is combined, redundancy among the different indicators produces robust peaks in the output. This allows the trigger threshold applied to the joint PPTS to be significantly lower than for any one detector, leading to substantially more detected earthquakes. Application of the algorithm to a small data set recorded during a 7-d window by 13 stations near the San Jacinto fault zone detects 3.13 times as many earthquakes as listed in the Southern California Seismic Network catalogue. The method provides a convenient statistical platform for including other indicators, and may utilize different sets of indicators to detect other information such as specific seismic phases or tremor

Cracks, pulses and macroscopic asymmetry of dynamic rupture on a bimaterial interface with velocity-weakening friction

We study in-plane ruptures on a bimaterial fault governed by a velocity-weakening friction with a regularized normal stress response. Numerical simulations and analytical estimates provide characterization of the ranges of velocity-weakening scales, nucleation lengths and background stresses for which ruptures behave as cracks or pulses, decaying or sustained, bilateral or unilateral. With strongly velocity-weakening friction, ruptures occur under a wide range of conditions as large-scale pulses with a preferred propagation direction, that of slip of the more compliant material. Such ruptures have macroscopic asymmetry manifested by significantly larger seismic potency and propagation distance in the preferred direction, and clearly quantified by the directivity ratio derived from the second order moments of the spatio-temporal distribution of slip rate. The macroscopic rupture asymmetry of the large-scale pulses stems from the difference in the criticality conditions for self-sustained propagation in each rupture direction, induced by the asymmetric normal stress changes operating in bimaterial interfaces. In contrast, crack-like ruptures show macroscopic asymmetry under restrictive conditions. The discussed mechanism is robust with respect to regularization parameters, ranges of stress heterogeneities and a proxy for off-fault yielding and should operate similarly for crustal-scale rupture pulses even in the absence of velocity-weakening. Small-scale pulses, driven by the bimaterial normal stress reduction at the scale of the process zone, can detach from the rupture front of the large-scale pulses that propagate in the preferred direction. However, their occurrence depends on the relaxation scale in the regularization of the normal stress response and their development can be hindered by off-fault yieldin

Cracks, pulses and macroscopic asymmetry of dynamic rupture on a bimaterial interface with velocity-weakening friction

We study in-plane ruptures on a bimaterial fault governed by a velocity-weakening friction with a regularized normal stress response. Numerical simulations and analytical estimates provide characterization of the ranges of velocity-weakening scales, nucleation lengths and background stresses for which ruptures behave as cracks or pulses, decaying or sustained, bilateral or unilateral. With strongly velocity-weakening friction, ruptures occur under a wide range of conditions as large-scale pulses with a preferred propagation direction, that of slip of the more compliant material. Such ruptures have macroscopic asymmetry manifested by significantly larger seismic potency and propagation distance in the preferred direction, and clearly quantified by the directivity ratio derived from the second order moments of the spatio-temporal distribution of slip rate. The macroscopic rupture asymmetry of the large-scale pulses stems from the difference in the criticality conditions for self-sustained propagation in each rupture direction, induced by the asymmetric normal stress changes operating in bimaterial interfaces. In contrast, crack-like ruptures show macroscopic asymmetry under restrictive conditions. The discussed mechanism is robust with respect to regularization parameters, ranges of stress heterogeneities and a proxy for off-fault yielding and should operate similarly for crustal-scale rupture pulses even in the absence of velocity-weakening. Small-scale pulses, driven by the bimaterial normal stress reduction at the scale of the process zone, can detach from the rupture front of the large-scale pulses that propagate in the preferred direction. However, their occurrence depends on the relaxation scale in the regularization of the normal stress response and their development can be hindered by off-fault yielding

Spatio-temporal variations of double-couple aftershock mechanisms and possible volumetric earthquake strain

We analyze spatio‐temporal patterns in rotation angles of double‐couple–constrained mechanisms of aftershocks of the 1992 Landers earthquake. The rotation angles provide information on the distribution of source geometries in different regions of space and time with respect to the mainshock focal mechanism. The results indicate that the mechanisms of the early aftershocks are more scattered and less aligned with the mainshock than those of the long‐term events. This is most pronounced around the northern end of the Landers rupture, least pronounced around the central section, and intermediate around the southern end of the rupture. The relatively large scatter and misalignment of the mean rotation angles of the early focal mechanisms around the edges of the Landers rupture suggest possible volumetric earthquake strain in these regions. The results may reflect isotropic source terms produced by dynamic generation of rock damage. Synthetic tests indicate that the observed differences in the rotation distributions of the early and long‐term events around the end regions of the Landers rupture can result from neglecting in the inversion process isotropic components that are 0.03–0.15 of the total event moments

Statistics of Earthquakes in Simple Models of Heterogeneous Faults

Simple models for ruptures along a heterogeneous earthquake fault zone are studied, focussing on the interplay between the roles of disorder and dynamical effects. A class of models are found to operate naturally at a critical point whose properties yield power law scaling of earthquake statistics. Various dynamical effects can change the behavior to a distribution of small events combined with characteristic system size events. The studies employ various analytic methods as well as simulations.Comment: 4 pages, RevTex, 3 figures (eps-files), uses eps

Statistical properties of seismicity of fault zones at different evolutionary stages

We perform a systematic parameter space study of the seismic response of a large fault with different levels of heterogeneity, using a 3-D elastic framework within the continuum limit. The fault is governed by rate-and-state friction and simulations are performed for model realizations with frictional and large scale properties characterized by different ranges of size scales. We use a number of seismicity and stress functions to characterize different types of seismic responses and test the correlation between hypocenter locations and the employed distributions of model parameters. The simulated hypocenters are found to correlate significantly with small L values of the rate-and-state friction. The final sizes of earthquakes are correlated with physical properties at their nucleation sites. The obtained stacked scaling relations are overall self-similar and have good correspondence with properties of natural earthquakes

Fault-Zone Waves Observed at the Southern Joshua Tree Earthquake Rupture Zone

Waveform and spectral characteristics of several aftershocks of the M 6.1 22 April 1992 Joshua Tree earthquake recorded at stations just north of the Indio Hills in the Coachella Valley can be interpreted in terms of waves propagating within narrow, low-velocity, high-attenuation, vertical zones. Evidence for our interpretation consists of: (1) emergent P arrivals prior to and opposite in polarity to the impulsive direct phase; these arrivals can be modeled as headwaves indicative of a transfault velocity contrast; (2) spectral peaks in the S wave train that can be interpreted as internally reflected, low-velocity fault-zone wave energy; and (3) spatial selectivity of event-station pairs at which these data are observed, suggesting a long, narrow geologic structure. The observed waveforms are modeled using the analytical solution of Ben-Zion and Aki (1990) for a plane-parallel layered fault-zone structure. Synthetic waveform fits to the observed data indicate the presence of NS-trending vertical fault-zone layers characterized by a thickness of 50 to 100 m, a velocity decrease of 10 to 15% relative to the surrounding rock, and a P-wave quality factor in the range 25 to 50