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

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

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

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

Imaging the deep structure of the San Andreas Fault south of Hollister with joint analysis of fault zone head and direct P arrivals

Author Posting. © Blackwell, 2007. This article is posted here by permission of Blackwell for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 169 (2007): 1028–1042, doi:10.1111/j.1365-246X.2006.03319.x.We perform a joint inversion of arrival time data generated by direct P and fault zone (FZ) head waves in the San Andreas Fault south of Hollister, CA, to obtain a high-resolution local velocity structure. The incorporation of head waves allows us to obtain a sharp image of the overall velocity contrast across the fault as a function of depth, while the use of near-fault data allows us to resolve internal variations in the FZ structure. The data consist of over 9800 direct P and over 2700 head wave arrival times from 450 events at up to 54 stations of a dense temporary seismic array and the permanent northern California seismic network in the area. One set of inversions is performed upon the whole data set, and five inversion sets are performed on various data subsets in an effort to resolve details of the FZ structure. The results imply a strong contrast of P-wave velocities across the fault of ~50 per cent in the shallow section, and lower contrasts of 10–20 per cent below 3 km, with the southwest being the side with faster velocities. The presence of a shallow low velocity zone around the fault, which could corresponds to the damage structures imaged in trapped wave studies, is detected by inversions using subsets of the data made up of only stations close to the fault. The faster southwest side of the fault shows the development of a shallow low velocity FZ layer in inversions using instruments closer and closer to the fault (<5 and <2 km). Such a feature is not present in results of inversions using only stations at greater distances from the fault. On the slower northeast side of the fault, the presence of a low velocity shallow layer is only detected in the inversions using the stations within 2 km of the fault. We interpret this asymmetry across the fault as a possible indication of a preferred propagation direction of earthquake ruptures in the region. Using events from different portions of the fault, the head wave inversions also resolve small-scale features of the fault visible in the surface geology and relocated seismicity

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 earthquake

Universal mean moment rate profiles of earthquake ruptures

Earthquake phenomenology exhibits a number of power law distributions including the Gutenberg-Richter frequency-size statistics and the Omori law for aftershock decay rates. In search for a basic model that renders correct predictions on long spatio-temporal scales, we discuss results associated with a heterogeneous fault with long range stress-transfer interactions. To better understand earthquake dynamics we focus on faults with Gutenberg-Richter like earthquake statistics and develop two universal scaling functions as a stronger test of the theory against observations than mere scaling exponents that have large error bars. Universal shape profiles contain crucial information on the underlying dynamics in a variety of systems. As in magnetic systems, we find that our analysis for earthquakes provides a good overall agreement between theory and observations, but with a potential discrepancy in one particular universal scaling function for moment-rates. The results reveal interesting connections between the physics of vastly different systems with avalanche noise.Comment: 13 pages, 5 figure

Damage and seismic velocity structure of pulverized rocks near the San Andreas Fault

A combination of seismic refraction tomography, laboratory ultrasonic velocity measurements, and microstructural observations was used to study the shallow velocity structure of a strand of the San Andreas fault (SAF) just south of Littlerock, California. The examined site has a strongly asymmetric damage structure with respect to the SAF core. The conglomerates to the southwest show little to no damage, whereas a ~100 m wide damage zone exists to the northeast with a ~50 m wide zone of pulverized granite adjacent to the fault core. Seismic P‐wave velocities of the damaged and pulverized granite were investigated over a range of scales. In situ seismic velocity imaging was performed on three overlapping profiles normal to the SAF with lengths of 350 m, 50 m, and 25 m. In the laboratory, ultrasonic velocities were measured on centimeter‐ to decimeter‐sized samples taken along the in situ profiles. The samples were also investigated microstructurally. Micro‐scale fracture damage intensifies with increasing proximity to the fault core, allowing a subdivision of the damage zone into several sections. Laboratory‐derived velocities in each section display varying degrees of anisotropy, and combined with microfracture analysis suggest an evolving damage fabric. Pulverized rocks close to the fault exhibit a preferred fault‐parallel orientation of microfractures, resulting in the lowest P‐wave velocity orientated in fault‐perpendicular direction. Closest to the fault, pulverized rocks exhibit a gouge‐like fabric that is transitional to the fault core. Comparison of absolute velocities shows a scaling effect from field to laboratory for the intact rocks. A similar scaling effect is absent for the pulverized rocks, suggesting that they are dominated by micro‐scale damage. Fault‐parallel damage fabrics are consistent with existing models for pulverized‐rock generation that predict strong dynamic reductions in fault‐normal stress. Our observations provide important constraints for theoretical models and imaging fault damage properties at depth using remote methods

Horizontal polarization of ground motion in the Hayward fault zone

We investigate shear wave polarization in the Hayward fault zone near Niles Canyon, Fremont, CA. Waveforms of 12 earthquakes recorded by a seven-accelerometer seismic array around the fault are analysed to clarify directional site effects in the fault damage zone. The analysis is performed in the frequency domain through H/V spectral ratios with horizontal components rotated from 0◦ to 180◦, and in the time domain using the eigenvectors and eigenvalues of the covariance matrix method employing three component records. The near-fault ground motion tends to be polarized in the horizontal plane. At two on-fault stations where the local strike is N160◦, ground motion polarization is oriented N88 ± 19◦ and N83 ± 32◦, respectively. At a third on-fault station, the motion is more complex with horizontal polarization varying in different frequency bands. However, a polarization of N86 ± 7◦, similar to the results at the other two on-fault stations, is found in the frequency band 6–8 Hz. The predominantly high-angle polarization from the fault strike at the Hayward Fault is consistent with similar results at the Parkfield section of the San Andreas Fault and the Val d’Agri area (a Quaternary extensional basin) in Italy. In all these cases, comparisons of the observed polarization directions with models of fracture orientation based on the fault movement indicate that the dominant horizontal polarization is near-orthogonal to the orientation of the expected predominant cracking direction. The results help to develop improved connections between fault mechanics and near-fault ground motion