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].

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].

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.