[1] The spontaneously propagating shear crack on a frictional interface has proven to be a useful idealization of a natural earthquake. The corresponding boundary value problems are nonlinear and usually require computationally intensive numerical methods for their solution. Assessing the convergence and accuracy of the numerical methods is challenging, as we lack appropriate analytical solutions for comparison. As a complement to other methods of assessment, we compare solutions obtained by two independent numerical methods, a finite difference method and a boundary integral (BI) method. The finite difference implementation, called DFM, uses a traction-at-split-node formulation of the fault discontinuity. The BI implementation employs spectral representation of the stress transfer functional. The three-dimensional (3-D) test problem involves spontaneous rupture spreading on a planar interface governed by linear slip-weakening friction that essentially defines a cohesive law. To get a priori understanding of the spatial resolution that would be required in this and similar problems, we review and combine some simple estimates of the cohesive zone sizes which correspond quite well to the sizes observed in simulations. We have assessed agreement between the methods in terms of the RMS differences in rupture time, final slip, and peak slip rate and related these to median and minimum measures of the cohesive zone resolution observed in the numerical solutions. The BI and DFM methods give virtually indistinguishable solutions to the 3-D spontaneous rupture test problem when their grid spacing Dx is small enough so that the solutions adequately resolve the cohesive zone, with at least three points for BI and at least five node points for DFM. Furthermore, grid-dependent differences in the results, for each of the two methods taken separately, decay as a power law in Dx, with the same convergence rate for each method, the calculations apparently converging to a common, grid interval invariant solution. This result provides strong evidence for the accuracy of both methods. In addition, the specific solution presented here, by virtue of being demonstrably grid-independent and consistent between two very different numerical methods, may prove useful for testing new numerical methods for spontaneous rupture problems.Citation: Day, S. M., L. A. Dalguer, N. Lapusta, and Y. Liu (2005), Comparison of finite difference and boundary integral solutions to three-dimensional spontaneous rupture,

We use a two‐dimensional finite difference computer program to study the effect of fault steps on dynamic ruptures. Our results indicate that a strike‐slip earthquake is unlikely to jump a fault step wider than 5 km, in correlation with field observations of moderate to great‐sized earthquakes. We also find that dynamically propagating ruptures can jump both compressional and dilational fault steps, although wider dilational fault steps can be jumped. Dilational steps tend to delay the rupture for a longer time than compressional steps do. This delay leads to a slower apparent rupture velocity in the vicinity of dilational steps. These “dry” cases assumed hydrostatic or greater pore‐pressures but did not include the effects of changing pore pressures. In an additional study, we simulated the dynamic effects of a fault rupture on ‘undrained’ pore fluids to test Sibson's (1985, 1986) suggestion that “wet” dilational steps are a barrier to rupture propagation. Our numerical results validate Sibson's hypothesis by demonstrating that the effect of the rupture on the ‘undrained’ pore fluids is to inhibit the rupture from jumping dilational stepovers. The basis of our result differs from Sibson's hypothesis in that our model is purely elastic and does not necessitate the opening of extension fractures between the fault segments.

We describe Version 2 of the three-dimensional (3D) seismic velocity model of southern California developed by the Southern California Earthquake Center and designed to serve as a reference model for multidisciplinary research activities in the area. The model consists of detailed, rule-based representations of the major southern California basins (Los Angeles basin, Ventura basin, San Gabriel Valley, San Fernando Valley, Chino basin, San Bernardino Valley, and the Salton Trough), embedded in a 3D crust over a variable depth Moho. Outside of the basins, the model crust is based on regional tomographic results. The model Moho is represented by a surface with the depths determined by the receiver function technique. Shallow basin sediment velocities are constrained by geotechnical data. The model is implemented in a computer code that generates any specified 3D mesh of seismic velocity and density values. This parameterization is convenient to store, transfer, and update as new information and verification results become available.

Children with cerebral palsy who have very low weights have more major medical conditions and are at increased risk of death. The weight-for-age charts presented here may assist in the early detection of nutritional issues or other health risks in these children.

This study examined growth of children and adolescents with cerebral palsy (CP) who received services from the California Department of Developmental Services from 1987 to 2002. In all, 141 961 measurements of height and weight were taken from 24920 patients with CP (14103 males, 10817 females). Centiles of weight and height were determined by age, sex, and five levels of functional ability ranging from fully ambulatory to unable to walk, crawl, or feed self, and fed via gastrostomy tube. Resulting charts of height and weight centiles were compared with Centers for Disease Control and Prevention weight and height charts for the general population of the US. Centiles of height and weight of patients with CP were close to those of the general population for the highest functioning groups with CP, but lagged substantially for other groups. Presence of a feeding tube was associated with greater height and weight in the lowest functioning groups, with centiles for weight being 2 to 5kg higher for those with gastrostomy tubes. The charts may assist in early identification of nutritional or metabolic difficulties beyond what might be expected for patients with similar functional disabilities.