Michael K. Sachs

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 …

Simulating Gravity Changes in Topologically Realistic Driven Earthquake Fault Systems: First Results

Currently, GPS and InSAR measurements are used to monitor deformation produced by slip on earthquake faults. It has been suggested that another method to accomplish many of the same objectives would be through satellite-based gravity measurements. The Gravity Recovery and Climate Experiment (GRACE) mission has shown that it is possible to make detailed gravity measurements from space for climate dynamics and other purposes. To build the groundwork for a more advanced satellite-based gravity survey, we must estimate the level of accuracy needed for precise estimation of fault slip in earthquakes. We turn to numerical simulations of earthquake fault systems and use these to estimate gravity changes. The current generation of Virtual California (VC) simulates faults of any orientation, dip, and rake. In this work, we discuss these computations and the implications they have for accuracies needed for a dedicated gravity monitoring mission. Preliminary results are in agreement with previous results calculated from an older and simpler version of VC. Computed gravity changes are in the range of tens of μGal over distances up to a few hundred kilometers, near the detection threshold for GRACE.

Virtual Quake: Statistics, Co-seismic Deformations and Gravity Changes for Driven Earthquake Fault Systems

With the ever increasing number of geodetic monitoring satellites, it is vital to have a variety of geophysical simulations produce synthetic datasets. Furthermore, just as hurricane forecasts are derived from the consensus among multiple atmospheric models, earthquake forecasts cannot be derived from a single comprehensive model. Here we present the functionality of Virtual Quake (formerly known as Virtual California), a numerical simulator that can generate sample co-seismic deformations, gravity changes, and InSAR interferograms in addition to producing probabilities for earthquake scenarios.Virtual Quake is now hosted by the Computational Infrastructure for Geodynamics. It is available for download and comes with a user manual. The manual includes a description of the simulator physics, instructions for generating fault models from scratch, and a guide to deploying the simulator in a parallel computing environment. http://geodynamics.org/cig/software/vq/.

Evaluating the RELM Test Results

We consider implications of the Regional Earthquake Likelihood Models (RELM) test results with regard to earthquake forecasting. Prospective forecasts were solicited for earthquakes in California during the period 2006–2010. During this period 31 earthquakes occurred in the test region with . We consider five forecasts that were submitted for the test. We compare the forecasts utilizing forecast verification methodology developed in the atmospheric sciences, specifically for tornadoes. We utilize a “skill score” based on the forecast scores of occurrence of the test earthquakes. A perfect forecast would have , and a random (no skill) forecast would have . The best forecasts (largest value of ) for the 31 earthquakes had values of to . The best mean forecast for all earthquakes was . The best forecasts are about an order of magnitude better than random forecasts. We discuss the earthquakes, the forecasts, and alternative methods of evaluation of the performance of RELM forecasts. We also discuss the relative merits of alarm-based versus probability-based forecasts.

Parametrizing Physics-Based Earthquake Simulations

Utilizing earthquake source parameter scaling relations, we formulate an extensible slip weakening friction law for quasi-static earthquake simulations. This algorithm is based on the method used to generate fault strengths for a recent earthquake simulator comparison study of the California fault system. Here we focus on the application of this algorithm in the Virtual Quake earthquake simulator. As a case study we probe the effects of the friction law’s parameters on simulated earthquake rates for the UCERF3 California fault model, and present the resulting conditional probabilities for California earthquake scenarios. The new friction model significantly extends the moment magnitude range over which simulated earthquake rates match observed rates in California, as well as substantially improving the agreement between simulated and observed scaling relations for mean slip and total rupture area.