The studies below are supported by the NSF Division of Earth Sciences, the U. S. Geological Survey, National Earthquake Hazards Reduction Program, and the Southern California Earthquake Center (through cooperative agreements with the NSF and USGS).

Earthquakes in Disordered Fault Systems

Models of evolutionary seismicity are useful because they allow us to investigate complex spatio-temporal patterns of earthquakes, using theoretical frameworks having controlled, simplified conditions. We have studied the evolution of stress and slip along a heterogeneous fault in a 3D elastic matrix. Our results indicate that the seismicity is strongly dependent on the range of sizes which characterize the heterogeneities. A narrow range of sizes leads to more large earthquakes than would be predicted by a power law extrapolation of the low magnitude seismicity (i.e., the characteristic earthquake distribution), and to a quasi-periodic temporal distribution of large events (as in, e.g., the seismic gap hypothesis). On the other hand, a wide range of sizes leads to power law frequency-size statistics over a broad magnitude range (i.e., the Gutenberg-Richter statistics), and to a random or clustered temporal distribution of large earthquakes. Our current working hypothesis is that immature faults are characterized by strongly disordered, non-planar fault zones having a broad spatial distribution of heterogeneities. Progressive slip tends to regularize the disorder and localize it to an approximately planar fault-zone, thereby narrowing the range of sizes of the heterogeneities. The continuing studies in this topic aim to understand better the key attributes of a fault which govern its seismicity patterns, and to substantiate the results with observations.

Computer simulations indicate that small earthquakes prepare the fault for the occurrence of a large event by smoothing the long wavelength component of the stress field. The pattern is reversed during large scale ruptures of the big events which re-roughen the long wavelength stress field on the fault. In the language of critical phenomena, the smoothing of long wavelength components of stress corresponds to the build-up of long range correlation of stress in the system as the fault approaches a critical stress transition associated with the occurrence of a large earthquake. An important question is whether the evolving stress process is associated with precursory features of the seismicity. We are addressing this issue in studies of the next three topics.

Coupled Evolution of Earthquakes and Faults

Most models of evolutionary seismicity are confined to studies of seismic activity along a single or a few fault systems. Recently, we have developed, together with Vladimir Lyakhovsky and Amotz Agnon from the Hebrew Univ. of Jerusalem, Israel, a model incorporating deformation- and time-dependent damage rheology in a structure consisting of a layered elastic/viscoelastic half-space. The formulation accounts for 3D stress transfer during failure episodes. The assumed damage rheology is based on thermodynamic principles and is compatible with observed nonlinear aspects of deformation. The model allows us to simulate long histories of crustal deformation, and to study the simultaneous self-organization of regional earthquakes and faults, in an internally consistent framework. Comparisons of model predictions to observed lab data, and initial simulation results of large spatio-temporal patterns are promising.

The continuing studies in this topic aim to understand interrelations between different modes of deformation, structural properties of faults, and rheological properties of the crust. Specific investigation topics include properties of foreshock and aftershock sequences; strain partitioning in the upper crust between seismic and aseismic deformations; activity switching among faults and other fluctuations of seismicity in space and time, and evolution of geometrical properties of fault systems with cumulative slip.

Analysis of Earthquake Catalogs

We have used, together with Mariana Eneva from the Univ. of Toronto, Canada, pattern recognition techniques to search synthetic earthquake catalogs generated by our heterogeneous fault models for informative patterns of seismicity. The analysis employs inter-event distance and time statistics, correlation dimension, ratios of numbers of events in different magnitude ranges, statistics of repeating small events, and other derivative parameters. The goals are to identify potential precursory information of earthquake catalogs, to quantify the predictive utility of the various examined parameters, and to establish causal relations between different features of seismicity and physical and geometrical properties of faults. The use of synthetic earthquake catalogs has several important advantageous over the use of observed data. The synthetic catalogs are free of errors and they can be made as long as needed to obtain good statistical samples. In addition, the model physical processes, although simplified compared to reality (this being the essence of any model) are completely known, and the parameters governing the synthetic seismicity can be varied at will. The results obtained so far highlight the complexity of the information contained in the synthetic earthquake catalogs; strong universal precursory signals have not been found. Nevertheless, the analysis indicates that the examined parameters have various larger-than-random degrees of time associations with large events, and they thus have some potential for intermediate-term earthquake prediction, especially when used in combinations. Continuing work in this direction will extend our effort to clarify the predictive information content of earthquake catalogs. Special emphasis will be given to rigorous quantification of issues related to space-time fluctuations of seismicity.

Dynamic Slip on a Fault Governed by Rate and State Friction

The origin of spatio-temporal complexities of earthquakes is a subject of ongoing controversy in the seismological and physics communities. While various studies suggest that seismic complexities are explainable in a way consistent with observations of fault segmentation and other heterogeneities, arguments linking complexities solely to inertial dynamics are also made. We have developed recently, together with Jim Rice and other colleagues from Harvard Univ., a code for simulating earthquake cycles along a 2D vertical strike-slip fault in an elastic half-space, using a framework incorporating rate- and state-dependent friction and fully inertial elastodynamics. The elastodynamic calculations are based on spectral representations of variables, and a new algorithm providing a unified computational framework for calculations of long deformational histories containing short periods of rapid instabilities. The results account for stable sliding, nucleation phases of instabilities, dynamic rupture, and wave phenomena. The model has natural boundary, (evolving) initial, loading, and arrest conditions, and it thus provides a proper framework for simulations over many earthquake cycles that can deliver definitive results on the capacity of inertial-dynamics to generate complexity on a smooth fault.

The analysis done so far does not support the conclusion that dynamics alone could provide a sufficient generic mechanism for sustained generation of complexities. The continuing work in this topic will attempt to resolve persisting controversy over the origin of spatio-temporal complexity of seismic response; study properties of nucleation phases of slip instabilities, i.e., transitions from quasi-static creep to dynamic rupture; establish conditions for the existence of short duration slip pulses; study histories of stress build-up and release on faults (including stress-drop distributions during large dynamic events) in simulations extending over several earthquake cycles; and examine interactions of dynamic ruptures with moderate amount of geometric or rheological fault zone heterogeneities.

Dynamic Rupture in Laterally Heterogeneous Structures

Fault zones consist of materials with varying physical properties and they often contain surfaces of material discontinuity. Wear products of the faulting process, such as gouge and breccia, form fault zones that are more compliant than the country rock. Large displacements on mature faults juxtapose different rock bodies. Despite the above, and the fact that most large earthquakes occur along mature fault systems having prominent material interfaces, properties of rupture propagation along material interfaces, and associated dynamic phenomena, are not well understood.

Together with Joe Andrews from the U.S. Geological Survey, we have conducted 2D numerical simulations of dynamic rupture along a planar material interface governed by simple friction. The results show remarkable dynamic phenomena including self-sustaining propagation of narrow slip pulse without loss of energy to friction, and spontaneous break up of the propagating pulse to a number of smaller pulses. The latter provides a potential dynamic mechanism for increasing stress and slip complexity at the source, while generating in the process high frequency waves. The self-sustaining propagation of the slip pulse arises from interaction between normal and tangential deformation that exist only with a material contrast. Rupture propagation occurs only in one direction, that of slip in the more compliant medium. This effect may generate a statistically significant bias of ground shaking near major faults due to preferred directions of rupture propagation and associated directivity effects.

Particle velocities at a given time in a 2D model of two elastic media separated by a fault at y=0. The thick red line along the fault marks the current extent of slip pulse propagating to the right. Differential dynamic normal motion near the rupture tip leads to dilatation which allows the slip pulse to propagate. (From Andrews and Ben-Zion, JGR, 1997.)

The initial simulations point to dynamic ruptures in laterally heterogeneous faults as a possible mechanism for providing a unifying explanation for long standing controversies, such as the heat flow paradox, the origin of short rise times in earthquake slip, dynamic contributions to spatio-temporal slip complexities, and earthquake source contribution to high frequency radiation. Recently, we examined the range of values of elastic parameters, friction coefficient, and strength heterogeneities allowing for the existence of the wrinkle-like pulse. The strength of the wrinkle-like pulse increases with S-wave velocity contrast up to a maximum at about 35% contrast. Beyond such a velocity contrast the strength of the pulse decreases. However, the wrinkle-like pulse can still propagate in a self-sustaining manner for larger velocity contrasts. For a fixed velocity contrast, the strength has little dependence on density contrast or Poisson's ratio, but pulse strength increases rapidly with increasing coefficient of friction. In all cases of self-sustaining rupture, the pulse becomes narrower and higher with propagation distance along the interface. Stress/strength heterogeneities with small correlation length have little effect on the pulse, while long wavelength heterogeneities reduce the efficiency of the pulse. The high mechanical efficiency of the wrinkle-like pulse suggests that earthquake ruptures may favor such mode of failure when possible.

Fault-Zone Waveform tomography

The complexity of the earthquake process advocates detailed monitoring within active fault zones with special attention to basic fault-zone heterogeneities. We are working toward developing rigorous fault-zone waveform tomography. This involve using seismic guided (head and trapped) waves specific to structures containing coherent material interfaces. Synthetic waveform fits of such phases can potentially provide an imaging tool of fault-zone structure with an unmatched resolution. An accurate determination of fault-zone properties provides a basis for studies on the earthquake source as well as the deformational field it generates.

Analytical free surface seismograms in a structure consisting of a fault zone (FZ) layer (width 50 m; shear wave velocity 2.0 km/s; attenuation coefficient 30) between two quarter-spaces (shear wave velocities 3.2 km/s and 3.0 km/s; attenuation coefficients 1000). Numbers on traces give receiver offset from the FZ in units of FZ width. Propagation length is 10 km. D, H and T denote direct wave, head wave, and trapped waves.