Faculty and Collaborators: Yehuda Ben-Zion (USC), Steve Day (SDSU), Ruth Harris (USGS), Leon Knopoff (UCLA), Andy Michael (USGS), Jim Rice (Harvard), Charlie Sammis (USC), Didier Sornette (UCLA)

Postdocs: Mark Abinante (UCLA), Kim Olsen (UCSB), Moritz Heimpel (UCLA), Matt Lee (UCLA)

Students: David Bowman (USC), Dawei Guo (UCLA), J. Landoni (UCLA), Nadia Lapusta (Harvard), Shoshana Levin (USC), Cheng-Ping Li (USC), Yun-Feng Liu (USC), Xiao-Xi Ni (UCLA)

I. Source Dynamics

The basic building block for studies of both synthetic seismicity and of source motions for the purposes of understanding ground motions, is and always has been the fracture of earth materials. If the model of fracture is inappropriate, we will get inappropriate results. A decade ago we were using extraordinarily simple models of fracture; specifically, our models were those in which the static friction was instantaneously dropped to the sliding friction and thereby became the triggering agent for slip motions. Now we know that the decrease in friction cannot be instantaneous, and that it must take place by a gradual weakening of the material at the edge of a crack. The laboratory evidence bearing on models of weakening in the dynamic regime has been almost non-existent, and we have been obliged to use plausible models obtained from low strain-rate, i.e. quasistatic, measurements. During the past year we have made significant progress on understanding the influence and importance of the weakening process.

Rice and Lapusta have shown that crack growth in a weakening regime characterized by the rate-state rule, develops a series of slip pulses that develop as a sequence of instabilities. If the velocity is reduced too much, it builds up once again in a new outburst; it is not known as yet whether this result is specific to the rate-state law or if it is a generic feature of weakening relations in the dynamics of fracture.

Knopoff and Landoni have shown analytically that the ad hoc assumption of either a linear slip weakening law or a linear velocity weakening law in the vicinity of a crack edge is non-physical. These assumptions lead to solutions that exhibit stress waves that travel with infinite wave speeds through the elastic medium astride the fault, or even generate waves that converge toward the fault. Their conclusion is that one cannot simply adopt a strength-weakening relation for dynamic crack propagation merely because it is convenient or because it seems plausible. They speculate that other quasistatic models for weakening will also turn out to be nonphysical. They further speculate that the specification of the strength-weakening relation in the dynamic regime of crack propagation is going to involve dynamics and hence inertia, in the weakening process.

Lee has shown in quasistatic models that the statistics of aftershocks is strongly dependent on the rate of decay of strength of an asperity expressed as a function of the load stress. Thus the aftershock statistics of the Omori law and the Gutenberg-Richter relation may limit the class of models of non-linear strength decay in the weakening regime.

Olsen has found that the slip-weakening distance is a critical quantity for growth of ruptures. A failed asperity imbedded in a crack stress field will not develop into a large rupture if the slip-weakening distance is too small. He and colleagues find that a critical slip-weakening distance of 0.5 m is needed to allow the Landers earthquake to grow.

Guo is developing a numerical program that implements a Green's function calculation of 3-D fractures. This is a welcome alternative to the 3-D fracture model of Olsen which makes use of a finite-difference scheme. Both programs make use of friction laws that imply weakening: Olsen's program uses a linear slip-weakening law for small slips and a velocity-weakening law at large slips.

Both Nielsen + Olsen and Ni + Knopoff have identified lattice oscillations in dynamical fractures that arise in calculations by finite difference schemes to study crack propagation. The basic reason is that the growth of a crack into an inhomogeneous region will excite stress waves that trigger local, high-frequency oscillations of a lattice mass in its own local potential of the near-neighbor springs implied in the finite difference procedure. (These problems do not appear in Green's function formulations.) To alleviate this problem both groups introduce a local evolving (weakening) friction, rather than one that changes abruptly: Nielsen and Olsen's friction depends on slip velocity, and that of Ni and Knopoff depends on viscoelastic dissipation.

II. Seismicity on Fault Networks

A second major thrust has been to study the evolution of seismicity on a complex network of faults, and indeed to study the evolution of these faults themselves. The treatment of earthquakes in these problems is quasistatic. We also have been evaluating the importance of rough geometry of faults on the properties of the seismicity of model faults.

Ben-Zion and colleagues have studied fault evolution in an elastic-brittle seismogenic layer that is viscoelastically coupled to a substrate. The form of the fault system that develops is strongly dependent on the healing rates after fractures. If the healing rate is rapid, a network of disordered faults is obtained, while if the rate is slow, the fault systems are more regular.

Heimpel has considered an elastic-plastic seismogenic zone, with a simple throughgoing fault with two strike-slip segments parallel to the regional stress field, connected by a transverse segment at two "big bends", modeled on the San Andreas Fault (SAF) in Southern California. As slip evolves on the model SAF over long times, secondary zones of high slip begin to develop and extend and grow from one big bend that is similar to a Landers fault complex, and its image at the other bend (see Figure 4). If earthquakes are introduced into the above model, the transverse segment ruptures infrequently in comparison with the strike-slip sections. Now the fault structure off the main fault becomes more complex; in addition to the above features, the models exhibit orthogonal, complementary left-lateral features. The fault system is much more heterogeneous.

Li and Ben-Zion have found that the stress correlation lengths fluctuate with time on a spatially heterogeneous fault. The correlation lengths are small after a large event and increase in the early times after a large event. After some time, the correlations saturate until the next big event; there are some fluctuations in the latter episode.

Abinante has studied the energy-to-moment ratio for dynamic fractures on a heterogeneous fault. Energy is given by an integral of stress drop times displacement over the rupture surface. Its approximation by the product of average slip times average stress drop times area is particularly inappropriate for an asperity model of fracture since large slips may take place in low stress-drop regions. The ratio of strain energy to seismic moment can differ by as much as a factor of 3 from expectations for a classical barrier model of fracture.


[Thrust 1] [Thrust 2] [Thrust 3] [Thrust 4]

Back to Executive Summary