The elastic modulus, percolation, and disaggregation of strongly interacting, intersecting antiplane cracks.

We study the modulus of a medium containing a varying density of nonintersecting and intersecting antiplane cracks. The modulus of nonintersecting, strongly interacting, 2D antiplane cracks obeys a mean-field theory for which the mean field on a crack inserted in a random ensemble is the applied stress. The result of a self-consistent calculation in the nonintersecting case predicts zero modulus at finite packing, which is physically impossible. Differential self-consistent theories avoid the zero modulus problem, but give results that are more compliant than those of both mean-field theory and computer simulations. For problems in which antiplane cracks are allowed to intersect and form crack clusters or larger effective cracks, percolation at finite packing is expected when the shear modulus vanishes. At low packing factor, the modulus follows the dilute, mean-field curve, but with increased packing, mutual interactions cause the modulus to be less than the mean-field result and to vanish at the percolation threshold. The "nodes-links-blobs" model predicts a power-law approach to the percolation threshold at a critical packing factor of p(c) = 4.426. We conclude that a power-law variation of modulus with packing, with exponent 1.3 drawn tangentially to the mean-field nonintersecting relation and passing through the percolation threshold, can be expected to be a good approximation. The approximation is shown to be consistent with simulations of intersecting rectangular cracks at all packing densities through to the percolation value for this geometry, p(c) = 0.4072.

The magnitude distribution of declustered earthquakes in Southern California.

The binned distribution densities of magnitudes in both the complete and the declustered catalogs of earthquakes in the Southern California region have two significantly different branches with crossover magnitude near M = 4.8. In the case of declustered earthquakes, the b-values on the two branches differ significantly from each other by a factor of about two. The absence of self-similarity across a broad range of magnitudes in the distribution of declustered earthquakes is an argument against the application of an assumption of scale-independence to models of main-shock earthquake occurrence, and in turn to the use of such models to justify the assertion that earthquakes are unpredictable. The presumption of scale-independence for complete local earthquake catalogs is attributable, not to a universal process of self-organization leading to future large earthquakes, but to the universality of the process that produces aftershocks, which dominate complete catalogs.

Northridge earthquake damage caused by geologic focusing of seismic waves

Despite being located 21 kilometers from the epicenter of the 1994 Northridge earthquake (magnitude 6.7), the city of Santa Monica experienced anomalously concentrated damage with Mercalli intensity IX, an intensity as large as that experienced in the vicinity of the epicenter. Seismic records from aftershocks suggest that the damage resulted from the focusing of seismic waves by several underground acoustic lenses at depths of about 3 kilometers, formed by the faults that bound the northwestern edge of the Los Angeles basin. The amplification was greatest for high-frequency waves and was less powerful at lower frequencies, which is consistent with focusing theory and finite-difference simulations.

A selective phenomenology of the seismicity of Southern California.

Predictions of earthquakes that are based on observations of precursory seismicity cannot depend on the average properties of the seismicity, such as the Gutenberg-Richter (G-R) distribution. Instead it must depend on the fluctuations in seismicity. We summarize the observational data of the fluctuations of seismicity in space, in time, and in a coupled space-time regime over the past 60 yr in Southern California, to provide a basis for determining whether these fluctuations are correlated with the times and locations of future strong earthquakes in an appropriate time- and space-scale. The simple extrapolation of the G-R distribution must lead to an overestimate of the risk due to large earthquakes. There may be two classes of earthquakes: the small earthquakes that satisfy the G-R law and the larger and large ones. Most observations of fluctuations of seismicity are of the rate of occurrence of smaller earthquakes. Large earthquakes are observed to be preceded by significant quiescence on the faults on which they occur and by an intensification of activity at distance. It is likely that the fluctuations are due to the nature of fractures on individual faults of the network of faults. There are significant inhomogeneities on these faults, which we assume will have an important influence on the nature of self-organization of seismicity. The principal source of the inhomogeneity on the large scale is the influence of geometry--i.e., of the nonplanarity of faults and the system of faults.

The organization of seismicity on fault networks.

Although models of homogeneous faults develop seismicity that has a Gutenberg-Richter distribution, this is only a transient state that is followed by events that are strongly influenced by the nature of the boundaries. Models with geometrical inhomogeneities of fracture thresholds can limit the sizes of earthquakes but now favor the characteristic earthquake model for large earthquakes. The character of the seismicity is extremely sensitive to distributions of inhomogeneities, suggesting that statistical rules for large earthquakes in one region may not be applicable to large earthquakes in another region. Model simulations on simple networks of faults with inhomogeneities of threshold develop episodes of lacunarity on all members of the network. There is no validity to the popular assumption that the average rate of slip on individual faults is a constant. Intermediate term precursory activity such as local quiescence and increases in intermediate-magnitude activity at long range are simulated well by the assumption that strong weakening of faults by injection of fluids and weakening of asperities on inhomogeneous models of fault networks is the dominant process; the heat flow paradox, the orientation of the stress field, and the low average stress drop in some earthquakes are understood in terms of the asperity model of inhomogeneous faulting.

Intermediate - term prediction of occurence times of strong earthquakes

Pattern recognition procedures for infrecuent events are adapted to the problem of identifyng patterns of clustering of small-and intermediate-scale seismicity before large earthquakes. Identification procedures derived from analysis of large California and Nevada earthquakes yield a high success rate when applied to other parts of the world

Statistical short-term earthquake prediction.

A statistical procedure, derived from a theoretical model of fracture growth, is used to identify a foreshock sequence while it is in progress. As a predictor, the procedure reduces the average uncertainty in the rate of occurrence for a future strong earthquake by a factor of more than 1000 when compared with the Poisson rate of occurrence. About one-third of all main shocks with local magnitude greater than or equal to 4.0 in central California can be predicted in this way, starting from a 7-year database that has a lower magnitude cut off of 1.5. The time scale of such predictions is of the order of a few hours to a few days for foreshocks in the magnitude range from 2.0 to 5.0.

Fracture dynamics of fusion of two anti-plane cracks.

The problem of the fracture dynamics of two two-dimensional coplanar anti-plane shear cracks is considered. Both cracks extend under a critical stress-intensity fracture criterion. The two cracks are initiated at different locations and times. A solution developed by Kostrov [Kostrov, B. V. (1966) J. Appl. Math. Mech. 30, 1241-1248] for isolated cracks is used to determine the tearing loci of the cracks up to the time at which the individual cracks begin to interact. In the interaction interval prior to the fusion of the two cracks, both the stresses and the fracture tip loci are determined sequentially by applying the solution to Abel's equation twice iteratively. This method can be used to solve problems of the fusion of any number of coplanar cracks.

Earthquake prediction: modeling the anomalous vp/vs source region.

Soviet observations of anomalously low values of the ratio of the compressional wave velocity to the shear wave velocity (V(p)/ V(s)) in a restricted volume around the locus of a future earthquake are duplicated by models based on the dilatancy hypothesis. In nature the cracks that cause the dilation may be oriented, leading to anisotropic seismic wave propagation in the anomalous region. The models show that vertical cracks are most effective in producing the observed effects, but that a slightly higher density of randomly oriented cracks will yield similar effects. The premonitory observations at Blue Mountain Lake, New York, are also duplicated by the models. These models demonstrate that V(p)/V(s) measured at the surface is not that of the anomalous zone, but is related to it by a transfer function, involving the shape and velocity gradient of the zone boundary.

Variations of Rayleigh Wave Phase Velocities across the Pacific Ocean.

Rayleigh wave phase velocities on paths crossing the Pacific Ocean show variations which are well correlated with some "average" lithospheric age of the region traversed. The seismic velocities in the upper mantle are highest in the oldest parts of the Pacific and lowest in the youngest parts.

Variations of Upper Mantle Structure under the Pacific Ocean.

The inversion of Rayleigh wave dispersion data for the Pacific Ocean shows that lithospheric thickness increases systematically with age. The lid to the low-velocity channel is very thin or absent near the ridge crest; the low-velocity channel may be absent in the oldest parts of the ocean.

Drift of continental rafts with asymmetric heating.

A laboratory model of a lithospheric raft is propelled through a viscous asthenospheric layer with constant velocity of scaled magnitude appropriate to continental drift. The propulsion is due to differential heat concentration in the model oceanic and continental crusts.