Michael Barall

Generic Earthquake Simulator

Many of the papers in this topical issue concern earthquake simulators and their results. The goals and history of the project leading to this work are described in the preface to this topical issue. Earthquake simulators are computer programs that use physics of stress transfer and frictional resistance to describe earthquake sequences. Some are capable of generating long earthquake histories on many faults. They necessarily adopt a variety of simplifications to make computation feasible. The amount of detail computed within individual earthquakes depends on the simulator. None of those capable of generating long histories includes elastodynamics, but some make approximations of it. Nevertheless, seismic waves are not computed in any of the many‐fault simulators focused on here. The faults are typically approximated by many rectangular elements, although the future use of triangles would allow more accurate representation of curved fault surfaces. This paper briefly describes the features that are common to all of the earthquake simulators discussed in this topical issue of SRL . Following it are four papers (Pollitz, 2012; Richards‐Dinger and Dieterich, 2012; Sachs et al. , 2012; Ward, 2012) authored by each of the groups, which present features of their simulator that go beyond this generic description. Results from using these simulators are not presented in those papers but are contained within a subsequent paper (Tullis et al. , 2012) that compares the results of using these five simulators on an all‐California fault model, allcal2. A detailed description of this fault model can be found at http://scec.usc.edu/research/eqsims/, and the formats used for input and output by our group are described by Barall (2012). ### Fault Geometry and Slip Rates UCERF …

A Comparison among Observations and Earthquake Simulator Results for the allcal2 California Fault Model

Online Material: Supplemental figures of space‐time and frequency‐magnitude relations, scaling plots, mean and covariance plots of interevent times, probability distribution functions of recurrence intervals, and earthquake density plots. In order to understand earthquake hazards we would ideally have a statistical description of earthquakes for tens of thousands of years. Unfortunately the ∼100‐year instrumental, several 100‐year historical, and few 1000‐year paleoseismological records are woefully inadequate to provide a statistically significant record. Physics‐based earthquake simulators can generate arbitrarily long histories of earthquakes; thus they can provide a statistically meaningful history of simulated earthquakes. The question is, how realistic are these simulated histories? This purpose of this paper is to begin to answer that question. We compare the results between different simulators and with information that is known from the limited instrumental, historic, and paleoseismological data. As expected, the results from all the simulators show that the observational record is too short to properly represent the system behavior; therefore, although tests of the simulators against the limited observations are necessary, they are not a sufficient test of the simulators’ realism. The simulators appear to pass this necessary test. In addition, the physics‐based simulators show similar behavior even though there are large differences in the methodology. This suggests that they represent realistic behavior. Different assumptions concerning the constitutive properties of the faults do result in enhanced capabilities of some simulators. However, it appears that the similar behavior of the different simulators may result from the fault‐system geometry, slip rates, and assumed strength drops, along with the shared physics of stress transfer. This paper describes the results of running four earthquake simulators that are described elsewhere in …

Data Transfer File Formats for Earthquake Simulators

Online Material: Specifications for the standard earthquake simulator input and output files. An earthquake simulator is a computer program that simulates a long sequence of earthquakes, which may range from tens of thousands of years up to millions of years. Different simulator codes have different input requirements, but in general the inputs to a simulator program include the fault system geometry, fault slip rates, rake angles, friction parameters, initial stress state, and elastic parameters. The output from a simulator program is a list of events, each of which is characterized by time, location, magnitude, rupture area, mean slip, stress change, and, optionally, a map that shows the distribution of slip over the fault surface. It is challenging to demonstrate that an earthquake simulator program is reliable, in the sense that it produces a simulated history whose statistical properties are similar to the properties of real earthquake sequences. The Southern California Earthquake Center (SCEC) Earthquake Simulator Comparison Project addresses this challenge by comparing the results from five different earthquake simulators with each other and, to the extent possible, with what is known about real earthquakes (Tullis et al. , 2012a). The five simulators are independently developed, so agreement among the simulators can provide some confidence in their reliability. To carry out the comparison, it is necessary for each simulator code to receive precisely the same inputs. It is also necessary for each simulator code to generate output in the same format, so that output from all the codes can be analyzed by the same set of statistical tools. We have achieved this by designing standard file formats for transferring data into and out of simulator codes. Although the standard files are formatted as ASCII text and are human‐readable, they are intended primarily for transferring data from one computer program to another. …

On the calculation of displacement, stress, and strain induced by triangular dislocations

Abstract Integral equation‐based methods in elasticity require the calculation of integrals that involve a singular (or weakly singular) matrix Green’s function and a traction or displacement vector field defined on a surface. A variety of numerical methods based on analytic quadratures have been developed for such calculations, using either rectangular or triangular surface patches. Unfortunately, without correction, these analytic rules are subject to numerical instabilities in certain parameter regimes. In this paper, we present a stable, semi‐analytic collection of quadrature rules that can be applied to both infinite medium and half‐space simulations. We describe our underlying approach and illustrate its performance with numerical examples. Online Material: Fortran routines.

A Suite of Exercises for Verifying Dynamic Earthquake Rupture Codes

We describe a set of benchmark exercises that are designed to test if computer codes that simulate dynamic earthquake rupture are working as intended. These types of computer codes are often used to understand how earthquakes operate, and they produce simulation results that include earthquake size, amounts of fault slip, and the patterns of ground shaking and crustal deformation. The benchmark exercises examine a range of features that scientists incorporate in their dynamic earthquake rupture simulations. These include implementations of simple or complex fault geometry, off‐fault rock response to an earthquake, stress conditions, and a variety of formulations for fault friction. Many of the benchmarks were designed to investigate scientific problems at the forefronts of earthquake physics and strong ground motions research. The exercises are freely available on our website for use by the scientific community.

The Performance of Triangular Fault Elements in Earthquake Simulators

It has recently become practical to use triangular fault elements in earthquake simulators instead of the usual rectangular fault elements. A simulator spends most of its time computing how slip on some fault elements affects the stresses on other fault elements. We explore whether rectangles or triangles yield more accurate stress values on curved fault surfaces. One might expect triangles to perform better, because triangles can follow the shape of a curved surface, whereas rectangles leave gaps and overlaps between adjacent fault elements. Our test results show that, contrary to expectations, rectangles overall perform as well as or better than triangles when computing stresses on curved fault surfaces. We also find that one triangulation may perform significantly better than another triangulation.