**2. USGS National Seismic Hazard Maps**

In the United States, the USGS incorporates different geophysics and geological information to continually update the National Seismic Hazard Maps for log-term ground motion forecasts[4, 3]. In USGS hazard maps, source models, including seismicity models and faults source models, and attenuation relations are two main components[3]. The Southern California is included in the western U.S. hazard maps, so here we take western U.S. as an example for explaining the procedures of hazard maps of USGS.

To estimate potential seismicity, we need to consider earthquake recurrence in or near the locations of past earthquakes occurred and the possibility of earthquake occurrences in areas never have earthquakes. First, the gridded-seismicity models are based on earthquake catalogs and historical earthquakes. The seismicity rates in each grid (0.1° longitude by 0.1° latitude) are based on the number of earthquake in it [3]. To smooth the seismicity rates, a 2D Gaussian function is applied to the model[3]. In most of areas the correlation distance is 50 kilometers, but in high seismicity regions the correlation distances parallel to the seismicity trends is 75 kilometers and normal to the seismicity trend is 10 kilometers to avoid effecting the seismicity estimations near the fault zones[3]. The uniform background seismicity models are used to estimate the possibilities of random earthquakes in aseismic regions [3]. The western U.S. region is separated into few sub-regions and the uniform background seismicity rate in each sub-region is based on the annual seismicity rates of earthquakes with Mw ≥ 4 since 1963 [3]. Now, there are two seismicity rate estimations in each grid cell. If the uniform background seismicity rate is larger than the griddedseismicity rate in a grid, the final seismicity rate is the sum of 67% gridded-seismicity rate and 33% of uniform background seismicity rate in that grid; otherwise, the final seismicity rate just equals to the gridded-seismicity rate in the grid [3].

Existing fault zones have relative high possibilities of occurring destructive earthquakes. The fault source models are based on geological fault studies, geodesy and seismological date to estimate geometries, maximum magnitudes and recurrence periods for fault zones [3, 7]. To obtain fault geometries, the geological surveys and earthquake location distributions are used for estimating fault areas. The maximum magnitudes in fault zones could be inferred from relationships between fault areas and magnitudes or historical magnitudes [3, 7]. The Gutenberg-Richter magnitude-frequency distribution and the characteristic rate on a fault, ratio of the slip rate to the slip of the characteristic earthquake of the fault, are used in earthquake recurrence estimations [3]. In California region, USGS gives 67% on the characteristic rate and 33% on the Gutenberg-Richter [3]. The Uniform California Earthquake Rupture Forecast, Version 2 (UCERF 2) [7] presented in 2007 Working Group on California Earthquake Probabilities (WGCEP) is used as the fault source model in California region. In seismic hazard maps, fault sources only consider type-A faults that have information on fault geometries, slip rates and earthquake data and type-B faults that only have information on fault geometries and slip rates[3].

132 Earthquake Engineering

will provide more accurate and detailed estimations.

**2. USGS National Seismic Hazard Maps** 

example for explaining the procedures of hazard maps of USGS.

rate just equals to the gridded-seismicity rate in the grid [3].

2]. The ElarmS uses the signal of the first arrived primary waves to estimate magnitudes, locations and then estimate peak ground motions of earthquakes [1, 2]. Here we propose a rapid full-wave Centroid Moment Tensor (CMT) inversion method for earthquakes in Southern California [6]. The algorithm has potential for (near) real time CMT inversion and then use optimal CMT solutions to generate peak ground motion maps for earthquake early warning purposes. In addition, the full-wave ground motion forecasts, which include basin amplification effects, source effects and wave propagation effects in the 3D structure model,

In the United States, the USGS incorporates different geophysics and geological information to continually update the National Seismic Hazard Maps for log-term ground motion forecasts[4, 3]. In USGS hazard maps, source models, including seismicity models and faults source models, and attenuation relations are two main components[3]. The Southern California is included in the western U.S. hazard maps, so here we take western U.S. as an

To estimate potential seismicity, we need to consider earthquake recurrence in or near the locations of past earthquakes occurred and the possibility of earthquake occurrences in areas never have earthquakes. First, the gridded-seismicity models are based on earthquake catalogs and historical earthquakes. The seismicity rates in each grid (0.1° longitude by 0.1° latitude) are based on the number of earthquake in it [3]. To smooth the seismicity rates, a 2D Gaussian function is applied to the model[3]. In most of areas the correlation distance is 50 kilometers, but in high seismicity regions the correlation distances parallel to the seismicity trends is 75 kilometers and normal to the seismicity trend is 10 kilometers to avoid effecting the seismicity estimations near the fault zones[3]. The uniform background seismicity models are used to estimate the possibilities of random earthquakes in aseismic regions [3]. The western U.S. region is separated into few sub-regions and the uniform background seismicity rate in each sub-region is based on the annual seismicity rates of earthquakes with Mw ≥ 4 since 1963 [3]. Now, there are two seismicity rate estimations in each grid cell. If the uniform background seismicity rate is larger than the griddedseismicity rate in a grid, the final seismicity rate is the sum of 67% gridded-seismicity rate and 33% of uniform background seismicity rate in that grid; otherwise, the final seismicity

Existing fault zones have relative high possibilities of occurring destructive earthquakes. The fault source models are based on geological fault studies, geodesy and seismological date to estimate geometries, maximum magnitudes and recurrence periods for fault zones [3, 7]. To obtain fault geometries, the geological surveys and earthquake location distributions are used for estimating fault areas. The maximum magnitudes in fault zones could be inferred from relationships between fault areas and magnitudes or historical magnitudes [3, 7]. The Gutenberg-Richter magnitude-frequency distribution and the characteristic rate on a fault, ratio of the slip rate to the slip of the characteristic earthquake In California region, the gridded-seismicity model is derived form earthquake catalog and estimates probabilities of earthquakes between Mw 5 to 7.0 [3]. In addition, the fault models also estimate the possibilities of earthquakes with Mw larger than 6.5 to consider the possibilities of destructive earthquakes in fault zones [3]. When the two types of source models are put into seismic hazard maps the probabilities of earthquakes between Mw 6.5 to 7.0 may over estimated. For more accurate estimations, the seismicity rates of Mw ≥ 6.5 in gridded-seismicity model reduced by one-thirds in fault zones [3].

**Figure 1.** The California seismic hazard map of 1 Hz spectral acceleration (SA) for 2% exceedance probability in 50 years. Adopted from [3].

The Next Generation Attenuation (NGA) database developed by Pacific Earthquake Engineering Research Center (PEER) is used in USGS hazard maps as attenuation relations for ground motion predictions[8, 9, 3]. The NGA database is not only an empirical ground motion model derived from selected recordings but also includes 1D ground motion simulations, 1D site response, and 3D basin response results from other studies [8]. So, the database includes many essential effects, including, for example, basin response, site response, earthquake rupture properties and style of faulting.

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 are controlled by the major faults in California.

Full-Wave Ground Motion Forecast for Southern California 135

( , ; ') ' ( , ; '), *<sup>k</sup> ij j ki ut M G t* **rr rr** (1)

<sup>1</sup> ( , ; ') ' ( , ; ') ' ( , ; ') . <sup>2</sup> *<sup>k</sup> j ki i kj ij ut G t G t M* **rr rr rr** (2)

<sup>1</sup> ( , ; ') ' ( ', ; ) ' ( ', ; ) . <sup>2</sup> *<sup>k</sup> j ik i jk ij ut G t G t M* **rr r r r r** (4)

*H t Gt Gt jik j ik i jk* **rr rr rr** (5)

R S S R ( ,; ) ( ,; ) *<sup>k</sup> ij jik u t MH t* **rr rr** or RS SR **ur r M Hr r** ( , ; ) : ( , ; ), *t t* (6)

R S S R ( , ; ) : ( , ; ). *m m* **g r r M Hr r** *t t* (7)

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

( , ; ') ( ', ; ), *Gt G t ki ik* **rr r r** (3)

For a given receiver location **r** = **r**R, the receiver Green tensor (RGT or SGT) is a 3rd-order

Using this definition, the displacement recorded at receiver location **r**R due to a source at **r**<sup>S</sup>

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

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

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

R RR <sup>1</sup> ( ', ; ) ' ( ', ; ) ' ( ', ; ) . <sup>2</sup>

moment tensor, we also have

equation (2) can be written as

expressed as

equation (6).

Applying reciprocity of the Green's tensor

tensor defined as the spatial-temporal strain field

with moment tensor **M** can be expressed as
