**3. 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]

$$
\mu\_k(\mathbf{r}\_\prime t; \mathbf{r}') = M\_{ij} \partial\_j \, ^\prime G\_{ki}(\mathbf{r}\_\prime t; \mathbf{r}'), \tag{1}
$$

where ' *<sup>j</sup>* denotes the source-coordinate gradient with respect to **r**' and the Green's tensor ( , ; ') *G t ki* **r r** relates a unit impulsive force acting at location **r**' in direction eˆ*<sup>i</sup>* to the displacement response at location **r** in direction eˆ *<sup>k</sup>* . Taking into account the symmetry of the moment tensor, we also have

$$
\hbar \mu\_k(\mathbf{r}, t; \mathbf{r}') = \frac{1}{2} \left[ \hat{\boldsymbol{\mathcal{O}}}\_j \left[ \mathbf{G}\_{ki}(\mathbf{r}, t; \mathbf{r}') + \hat{\boldsymbol{\mathcal{O}}}\_i \left[ \mathbf{G}\_{kj}(\mathbf{r}, t; \mathbf{r}') \right] \right] \mathbf{M}\_{ij} \tag{2}
$$

Applying reciprocity of the Green's tensor

$$G\_{kl}(\mathbf{r}, t; \mathbf{r}') = G\_{il}(\mathbf{r}', t; \mathbf{r}), \tag{3}$$

equation (2) can be written as

134 Earthquake Engineering

are controlled by the major faults in California.

more accurate ground motion estimations.

velocity model in simulations [16].

based on Somerville et al.'s method [17].

expressed as [19]

**3. A Physics-based seismic hazard model: CyberShake** 

Hazard curves, exceedance probability as a function of ground motion, are derived from source models and attenuation relations of grids. The final seismic hazard maps are made by interpolating annual exceedance probabilities form hazard curves in the model. On the California 1 Hz spectral acceleration (SA) hazard map [Figure 1], high hazard level regions

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

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

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]

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

$$
\hbar \mu\_k(\mathbf{r}, t; \mathbf{r}') = \frac{1}{2} \left[ \hat{\boldsymbol{\mathcal{O}}}\_j \left[ \mathbf{G}\_{ik}(\mathbf{r}', t; \mathbf{r}) + \hat{\boldsymbol{\mathcal{O}}}\_i \left[ \mathbf{G}\_{jk}(\mathbf{r}', t; \mathbf{r}) \right] \right] \mathbf{M}\_{ij} \tag{4}
$$

For a given receiver location **r** = **r**R, the receiver Green tensor (RGT or SGT) is a 3rd-order tensor defined as the spatial-temporal strain field

$$H\_{jik}(\mathbf{r}',t;\mathbf{r}\_{\mathbb{R}}) = \frac{1}{2} \Big[ \hat{\boldsymbol{\mathcal{O}}}\_{j}{}^{\prime} \mathbf{G}\_{ik}(\mathbf{r}',t;\mathbf{r}\_{\mathbb{R}}) + \hat{\boldsymbol{\mathcal{O}}}\_{i}{}^{\prime} \mathbf{G}\_{jk}(\mathbf{r}',t;\mathbf{r}\_{\mathbb{R}}) \Big]. \tag{5}$$

Using this definition, the displacement recorded at receiver location **r**R due to a source at **r**<sup>S</sup> with moment tensor **M** can be expressed as

$$\mathbf{u}\_k(\mathbf{r}\_{\mathbb{R}}, t; \mathbf{r}\_{\mathbb{S}}) = M\_{\vec{\eta}} H\_{\vec{\eta}k}(\mathbf{r}\_{\mathbb{S}}, t; \mathbf{r}\_{\mathbb{R}}) \text{ or } \mathbf{u}(\mathbf{r}\_{\mathbb{R}}, t; \mathbf{r}\_{\mathbb{S}}) = \mathbf{M} : \mathbf{H}(\mathbf{r}\_{\mathbb{S}}, t; \mathbf{r}\_{\mathbb{R}}), \tag{6}$$

and the synthetic seismogram due to a source at **r**S with the basis moment tensor **M***m* can be expressed as

$$\mathbf{g}\_m(\mathbf{r}\_{\mathbb{R}}, t; \mathbf{r}\_{\mathbb{S}}) = \mathbf{M}\_m : \mathbf{H}(\mathbf{r}\_{\mathbb{S}}, t; \mathbf{r}\_{\mathbb{R}}). \tag{7}$$

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 **r**R and pointing in the direction eˆ *<sup>k</sup>* 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.

Full-Wave Ground Motion Forecast for Southern California 137

**Figure 3.** The CyberShake hazard map for Los Angeles region of 3 seconds period spectral acceleration

There are many differences between the hazard maps of USGS and CyberShake, including, procedures of making hazard maps, required computational resources and results [3, 5]. The USGS National Seismic Hazard maps in California region are derived form source models based on seismological data, geological surveys and earthquake rupture models, and the Next Generation Attenuation (NGA) database [8, 9]. The CyberShake hazard map is constructed by physics-based simulations in the 3D velocity model for all potential earthquake ruptures with Mw ≥ 6.0 near Los Angeles region [5]. The computational resources requirements for generating USGS hazard maps do not mention in the 2008 report of seismic hazard maps update, but the hazard maps should be able to done without a super computer. To generate the CyberShake hazard map, lots of wave propagation simulations are required to build a database for generating synthetic seismograms of potential earthquake ruptures [5]. The computational resource of physics-based seismic hazard maps is much higher than the computational requirement of USGS hazard maps. However, the advances in computer sciences make the computational requirements affordable for CyberShake, also accurate estimations of ground motions are important for a city with a large population. The seismic hazard levels are quit different in the Los Angeles region between two hazard maps. In the USGS hazard map [Figure 1], the high hazard level regions are almost along the fault zones and hazard values decrease as the distance between a site and fault zones increases. In the Los Angeles basin region, the hazard level is about the same in the USGS hazard map [Figure 1]. In the CyberShake hazard map, the hazard values along the San Andreas fault are high, but the width of high hazard zones is narrower. In addition, the CyberShake hazard map in the Los Angeles basin has more details [5]. This probably reflects the source and structure effects

**4. Comparisons between USGS and CyberShake hazard maps** 

(SA) for 2% exceedance probability in 50 years. Adopted from [5].

in ground motion predictions.

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.

**Figure 2.** Hazard curves derived form three different methods at three sites, PAS, STNI and WNGC, in Los Angeles region. The red lines represent the results of using Campbell and Bozorgnia's [8] method; the orange lines represent the results of Boore and Atkinson's [20] method; the black lines represent the results of CyberShake. Adopted from [5].

**Figure 3.** The CyberShake hazard map for Los Angeles region of 3 seconds period spectral acceleration (SA) for 2% exceedance probability in 50 years. Adopted from [5].

#### **4. Comparisons between USGS and CyberShake hazard maps**

136 Earthquake Engineering

considered in these methods.

results of CyberShake. Adopted from [5].

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

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

**Figure 2.** Hazard curves derived form three different methods at three sites, PAS, STNI and WNGC, in Los Angeles region. The red lines represent the results of using Campbell and Bozorgnia's [8] method; the orange lines represent the results of Boore and Atkinson's [20] method; the black lines represent the

effects, and wave propagation phenomena in 3D complex structures.

There are many differences between the hazard maps of USGS and CyberShake, including, procedures of making hazard maps, required computational resources and results [3, 5]. The USGS National Seismic Hazard maps in California region are derived form source models based on seismological data, geological surveys and earthquake rupture models, and the Next Generation Attenuation (NGA) database [8, 9]. The CyberShake hazard map is constructed by physics-based simulations in the 3D velocity model for all potential earthquake ruptures with Mw ≥ 6.0 near Los Angeles region [5]. The computational resources requirements for generating USGS hazard maps do not mention in the 2008 report of seismic hazard maps update, but the hazard maps should be able to done without a super computer. To generate the CyberShake hazard map, lots of wave propagation simulations are required to build a database for generating synthetic seismograms of potential earthquake ruptures [5]. The computational resource of physics-based seismic hazard maps is much higher than the computational requirement of USGS hazard maps. However, the advances in computer sciences make the computational requirements affordable for CyberShake, also accurate estimations of ground motions are important for a city with a large population. The seismic hazard levels are quit different in the Los Angeles region between two hazard maps. In the USGS hazard map [Figure 1], the high hazard level regions are almost along the fault zones and hazard values decrease as the distance between a site and fault zones increases. In the Los Angeles basin region, the hazard level is about the same in the USGS hazard map [Figure 1]. In the CyberShake hazard map, the hazard values along the San Andreas fault are high, but the width of high hazard zones is narrower. In addition, the CyberShake hazard map in the Los Angeles basin has more details [5]. This probably reflects the source and structure effects in ground motion predictions.
