**5. ElarmS: Earthquake alarms systems for California**

In Southern California, an earthquake-prone area, many cities are under earthquake risks, hence earthquake early warning systems are becoming an important role in earthquake disaster mitigation [2]. Allen [2] developed earthquake early warning systems called Earthquake Alarms Systems (ElarmS) for California. In the ElarmS methodology, three steps are designed for rapid estimations of earthquake source parameters and prediction of peak ground motions [1, 2]. First, using the time information of first-arrived signal to locate earthquakes and estimate the warning time. Second, using frequency information of first four seconds of P-wave to estimate magnitudes of earthquakes. Third, using attenuation relations and the earthquake source information, an estimated location and magnitude, to generate ground shaking maps.

Full-Wave Ground Motion Forecast for Southern California 139

moment tensor (CMT) inversions. The procedure relies on the use of receiver Green tensors (RGTs), the spatial-temporal displacements produced by the three orthogonal unit impulsive point forces acting at the receivers. Once we have source parameters of earthquakes, a nearreal time full-wave ground motion map, that considers both source and wave-propagation effects in a 3D structure model, may also available for earthquake early warning purposes.

In our CMT inversion algorithm, the RGTs are computed in our updated 3D seismic structure model for Southern California using the full-wave method that allows us to account for 3D path effects in our source inversion. The efficiency of forward synthetic calculations could be improved by storing RGTs and using reciprocity between stations and any spatial grid point in our model. In our current model, we will use three component broadband waveforms below 0.2 Hz to invert source parameters. Based on Kikuchi and Kanamori's [23]source inversion method, any moment tensor can be expressed as linear combination of 6 elementary moment tensors. In our current coordinate (*x*=east, *y*=north,

> ;2 ;3 . 010 100 0 0 1 100 0 10 0 0 0 000 0 00 10 0

0 0 0 0 0 0 100 0 0 1 0 10 010 0 1 0 0 0 1 001

There are two main advantages of using this method. First, different subsets of 6 elementary moment tensors could represent different source parameter assumptions such as M1~M6 could recover general moment tensors and M1~M5 could represent pure-deviatoric moment tensors [23]. From efficiency point of view, we only need to generate synthetic waveforms of 6 elementary moment tensors at grid points close to initial sources locations for receivers to

For centroid location <sup>1</sup> **x** and centroid time *t*1, the synthetic seismograms of 6 elementary

where *r* is receiver, *m* is index of 6 moment tensor, *i* is component index. The synthetic

1 1

1 1 (; , ) *<sup>r</sup>*

6

1 () (; , ) *r r i m mi m u t aS t t* 

From inversion point of view, the phases have less structure heterogeneous effects can reduce the nonlinear effects caused by complex 3D structure such as body wave phases that

**M MM** (8)

*mi St t* **x** , *m*:1~6 (9)

**<sup>x</sup>** (10)

4 ;5 ;6

**M1 M M**

*z*=up), the moment tensor can be expressed as below:

 

invert an optimal CMT solution.

seismogram can be expressed as:

moment tensors could be defined as:

In the ElarmS, the arrival times of P-waves are used to rapidly locate earthquake locations. The possible areas of an earthquake location could be inferred by using the information of the first two or three stations trigged by an earthquake. To locate a more accurate earthquake location, including, longitude, latitude, depth and origin time, the first arrival time form four stations are required. A grid search algorithm is used to find an optimal earthquake location that has minimum arrival time misfits. The warning time, the remaining time before the peak ground motion arrived, can be estimated by using the predicted Swave arrival times of sites. Peak ground motions are usually caused by S-wave or surface wave, so use predicted S-wave arrival times as peak ground motion times may provide additional warning time for some sites.

The magnitude, which represents the released energy of an earthquake, is an important parameter in earthquake early warning systems. The rapid magnitude estimation method of an earthquake by using the frequency information of the first four seconds of P-wave is adopted in the ElarmS [1, 2]. Basically, the magnitude estimations take two procedures. The first step is finding the maximum predominant period within the first 4 seconds of the vertical component P-wave waveforms, and then use linear relations to scale the maximum predominant period value to an estimated earthquake magnitude [1, 2]. As the number of the maximum predominant period value from different receivers increases, the average magnitude errors will decrease [2].

When the location and magnitude of an earthquake is available, attenuation relations can be used to estimate ground motions of sites and then generate a ground motion prediction map for whole California. In the ElarmS, the attenuation relations are based on the recordings of earthquakes with magnitude larger than 3.0 in California [2]. However, the empirical attenuation relations used in the ElarmS do not account effects of wave propagation in 3D structures, for example, basin amplification effects.
