# A Physics-based seismic hazard model: CyberShake

The CyberShake, one of the Southern California Earthquake Center’s (SCEC) projects, is a seismic hazard model that uses full-wave method to simulate ground motions in Southern California. Here the term “full-wave” means using numerical solutions to compute the exact wave equation, rather than approximations. Recent advances in computational technology and numerical methods allow us to accurately simulate wave propagations in 3D strongly heterogeneous media [10, 11], and opened up the possibility of simulation-based seismic hazard models [5],extracting more information from waveform recordings for seismic imaging [12-14] and earthquake source inversions [15, 6]. For seismic hazard model, these physics-based simulations consider factors that affect ground motion results, for example, source rupture and wave propagation effects in a 3D velocity structure and then provide more accurate ground motion estimations.

The Los Angeles region is one of the most populous cities in the United States. The city is in a basin region and near active fault systems, so a reliable seismic hazard model is important for the city. The CyberShake selected 250 sites and simulated potential earthquake ruptures in Los Angeles region to build a seismic hazard model [5]. The SCEC Community Velocity Model, Version 4 (CVM4) which has detailed basins and other structures is used as the 3D velocity model in simulations [16].

The potential earthquake ruptures within 200km and Mw larger than 6.0 in the Los Angeles region are selected from the Uniform California Earthquake Rupture Forecast, Version 2 (UCERF 2) for ground motion simulations in Cybershake [5]. The earthquake ruptures in UCERF2 only provide possible magnitudes in faults, without information of rupture process. To consider the earthquake rupture effects, each earthquake rupture selected from UCERF2 could convert to a kinematic rupture description for numerical simulations [5] based on Somerville et al.’s method [17].

In CyberShake, ground motion predictions are based on physics-based simulations rather than empirical attenuation relations. The qualified rupture sources are more than 10,000 in the Los Angeles region [5]. However, when the uncertainties of earthquake ruptures are considered, the number of earthquake rupture increases to more than 415,000. It will take a lot of computational resources and time to simulate all rupture models [5]. An efficient method is storing receiver Green’s tensors (RGTs) of selected sites in the model and applying reciprocity to generate synthetic seismograms of rupture models [18, 5]. The RGTs called strain Green’s tensors (SGTs) in CyberShake project [5]. Following Zhao et al. [18], the displacement field from a point source located at r ‘ with moment tensor Mij can be expressed as [19]

In CyberShake, the SGTs can therefore be computed through wave-propagation simulations of two orthogonal horizontal components with a unit impulsive force acting at the receiver location rR and pointing in the direction ˆek in each simulation and store the strain fields at all spatial grid points r’ and all time sample t. The synthetic seismogram at the receiver due to any point source located within the modeling domain can be obtained by retrieving the strain Green’s tensor at the source location from the SGT volume and then applying equation (6).

In CyberShake project, one of objectives is improving the Ground Motion Prediction Equations (GMPEs), which are widely used in seismic hazard analysis, by replacing empirical ground motion database with physics-based simulated ground motions. Some advantages in physics-based simulation results could be found by comparing hazard curves among different methods. The hazard curves derived from Boore and Atkinson’s [20] method and Campbell and Bozorgnia’s [8] method that consider basin effects in GMPEs are selected for comparisons. However, the earthquake rupture directivity effects are not considered in these methods.

Here, three hazard curves which show exceedance probability for spectral acceleration (SA) at 3 seconds period are used to discuss differences among results [Figure 2]. At the PAS site [Figure 2], a rock site, the hazard curves among the three methods are similar. At the STNI site [Figure 2], a basin site, the hazard curves of CyberShake and Campbell and Bozorgnia’s [Figure 2] method which consider basin amplification effects are similar, but the hazard curve of Boore and Atkinson’s [20] method is significantly lower than the other two curves.

However, at WNGC site, the hazard curve of CyberShake has higher hazard level than the other two. The WNGC site is at the region that channeling energy from earthquake ruptures in the southern San Andreas fault into Los Angeles basin, and the factors are included in physics-based simulations. The channeling phenomenon also can be found from other studies [21, 22]. The CyberShake seismic hazard map [Figure 3] is derived from the 250 sites used in simulations [5]. In the physics-based hazard map, some effects don’t include in attenuation relations, including, for example, earthquake rupture effects, basin amplification effects, and wave propagation phenomena in 3D complex structures.