Annual Report

Implementation of background seismicity in the physics-based earthquake simulator RSQSim

Principal investigator: Keith Richards-Dinger Department of Earth Sciences University of California, Riverside

Other investigators included graduate student Kayla Kroll and researcher Heming Xu.

Introduction

Typically synthetic seismic catalogs from earthquake simulators only include those earthquakes that occur on the explicitly modeled faults in the fault system used by the simulator. However, a large fraction of natural seismicity (including most aftershocks of large events) occurs on pervasive unmodeled small-scale faults. The work under this proposal was aimed at allowing RSQSim to model these events as well in order to 1) facilitate comparison with real seismicity catalogs; 2) allow more complete exploration of the effects of geometrical complexity, fault constitutive properties, and other model input parameters on the spatial-temporal clustering of earthquakes; 3) provide direct simulator-based estimates of seismic hazard from these “off-fault” events (which correspond closely to UCERF2’s background seismicity).

Method

We based our simulation of the background seismicity on the rate-state seismicity rate formulation of Dieterich [1994] in a manner similar to Smith and Dieterich [2010]. In the Dieterich [1994] formulation, the seismicity rate R(t) is determined by a state variable �(�):

�(�) = ! !!!(!) where r is the constant seismicity rate that would occur at a constant (Coulomb) stressing rate of �!, and �(�) evolves with time and stress as

�� = �� − ��� /(��), where � is normal stress and a is the rate coefficient from the rate-and-state constitutive law.

We divide the area of interest into 2 km x 2 km cells and estimate the background rate r in each cell from the smoothed observed seismicity. In each cell we consider planes of orientated optimally in: 1) the (tensor) stressing rate from the far-field plate motion alone and 2) the sum of the far-field plate motion stressing rate tensor and that due to the long-term average motion of the explicitly-modeled faults in RSQSim. The reference stressing rate �! is given by the projection of the far-field plate motion stressing rate tensor on each plane in each cell. The stressing rate history on each plane in each cell is made up of constant stressing (at a rate �!) punctuated by instantaneous stress steps at the time of each explicit RSQSim earthquake. The magnitudes of the stress steps are calculated using Okada [1992] or Gimbutas et al. [2012] and the slip on each RSQSim fault element. Given the rate on each plane in each cell from the above calculation, we then use that rate to simulate the seismicity as a non-stationary Poisson process to generate times of the events and draw the magnitudes from a Gutenberg-Richter distribution.

Results

The first example shows the background seismicity following a M7.5 event on the San Jacinto Fault and uses a simple spatially uniform background seismicity rather than one calculated from observed seismicity. In addition this background rate is unrealistically high (or, equivalently, represents seismicity down to an unrealistically low magnitude of completeness). The slip distribution in this event is shown in Figure 1 and a map view of the subsequent background seismicity for several time periods in Figure 2.

Fig. 1: Slip distribution for an RSQSim event of magnitude 7.5 on the San Jacinto Fault. Cool to warm colors indicate increasing amounts of slip. The maximum slip is 5.3 m.

Fig. 2: Background seismicity following the RSQSim event of Figure 1 for several different time periods. See caution in text about the background rate.

There are very few aftershocks along or near most of the rupture surface. The aftershocks are concentrated at and beyond the ends of the rupture and at areas of geometric complexity. Real mainshocks typically do have aftershocks along or near much of their rupture surface. We believe that the addition of realistic (possibly stochastic) roughness on the explicitly-modeled RSQSim faults will produce more realistic aftershock behavior along and near the main rupture surface.

Our second example is more realistic as it uses a background rate estimated from that observed for the Yuha Desert from 1981 until just before the M7.2 El Mayor-Cucapah earthquake of 4 April 2010. We supplement the primary UCERF3 fault geometry for southern California (~14,000, 1 km2 triangular elements) with secondary faults in the Yuha Desert (~26,000, 0.04 km2 rectangular elements based on observations of triggered slip and aftershock lineations – Kroll et al. [2013]) and simulate 64,000 years of RSQSim seismicity. In that 64,000-year catalog there are 38 events of M > 7 on the Laguna Salada fault. We use these events as a proxy for the El Mayor-Cucapah event (as the faults which ruptured in the actual El Mayor-Cucapah event are not in the UCERF3 fault models) and calculate background seismicity in the Yuha Desert following each of these events to compare with the observed Yuha Desert aftershocks of El Mayor-Cucapah.

Fig. 3: Left) Observed aftershocks following the magnitude Mw=7.2, 04/04/2010 El Mayor- Cucapah earthquake. Aftershocks between El Mayor-Cucapah and the 06/14/2010 M5.9 Ocotillo aftershock are in blue and earthquakes following Ocotillo are shown in red. Simulated on-fault and background aftershocks of an M7.2 RSQSim event on the Laguna Salada Fault. Aftershocks between the Laguna Salada event and an (explicit RSQSim) M5.9 aftershock in blue and those after the M5.9 in red.

We show one example in Figure 3. The explicitly-modeled (on-fault) aftershocks of this particular Laguna Salada event happened to include a large aftershock similar to the actual 14 June 2010 M5.9 Ocotillo event (though slightly later relative to the Laguna Salada event than the Ocotillo was relative to EMC). There some striking similarities between the observed and simulated aftershocks: a) the overall locations and numbers of the pre-M5.9 aftershocks (although the simulated locations are overall more diffuse and do not extend quite as far to the NW as the observed ones); b) the activation of the far NW after the M5.9 (although again the simulations are more diffuse); c) the shutdown of the region directly east of the M5.9 epicenter.

Future work will include the addition of small-scale fault roughness to the RSQSim faults to generate more realistic rates of aftershocks near the mainshock rupture surface and experimentation with other orientations of planes in the grid cells.

References

Dieterich, J. A constitutive law for rate of earthquake production and its application to earthquake clustering, J. Geophys. Research, v. 99, p. 2601-2618, 1994.

Gimbutas, Z., Greengard, L., Barall, M., & Tullis, T. E. On the calculation of displacement, stress, and strain induced by triangular dislocations. Bulletin of the Seismological Society of America, 102(6), 2776-2780, 2012.

Kroll, K. A., Cochran, E. S., Richards-Dinger, K. B., & Sumy, D. F., Aftershocks of the 2010 Mw 7.2 El Mayor-Cucapah earthquake reveal complex faulting in the Yuha Desert, California. Journal of Geophysical Research: Solid Earth, 118(12), 6146-6164, 2013.

Smith and Dieterich, 2010. Aftershock Sequences Modeled with 3-D Stress Heterogeneity and Rate- State Seismicity Equations: Implications for Crustal Stress Estimation, Pure and Applied Geophysics, v 167, n 8-9, 1067-1085, DOI: 10.1007/s00024-010-0093-1.

Okada Y., 1992, Internal deformation due to shear and tensile faults in a half-space, Bull Seismol Soc Am, 82:1018–1040