Although Mnˆ is a monotonically increasing function of time, the noisy environment of the seismic network may create artificial events. A merging or canceling event criterion that allows steppingMnˆ backward is necessary to improve robustness of the system. Here are two suggestions:
1. Deleting based on picking time alignment: After the trigger of the first few stations of an event, the hypocenter and origin time estimates will start to converge. From this moment, if the observed picking times of the stations deviate from the theoretical P-wave arrival times based on the current parameter estimates, this event is likely to be falsely identified and can be deleted from the algorithm.
2. Merging based on hypocenter and origin time estimate: To avoid false alarm due to a dupli- cated event caused by noise data, it is beneficial to maintain a unique set of event records in the algorithm. Two events are merged if their converged hypocenter and origin time estimates are reasonably close. In some cases, even if the two events are actually not identical events, it is beneficial to merge them within the EEW system in order to avoid confusing warning.
3.4.2 Selective data subset
Theoretically, in the absence of noise, four independent pieces of information are enough to pinpoint the location and origin time of an earthquake. In most earthquakes, their parameters can be accurately identified based on data from around five to ten stations closest to the hypocenter.
Furthermore, due to the attenuation effect of the seismic waves, information from stations that are far from the hypocenter has negligible contribution to the posterior PDF. Instead of using all stations for every event,Ftis reduced to include only information from stations within theeffective rangeof the first triggered station (the theoretically closest location to the hypocenter) of an event.
This is equivalent to assumingp(Fj(t)|θl) = 1 for all stationj outside the effective range for event Ml.
Distance is not the only factor for selecting a subset of the stations to be used for an earthquake.
For offshore earthquakes, stations are often available on only the land side of the event. A wide az- imuth coverage can significantly improve the estimation of hypocenter and origin time. Combining both factors, a fixed number of stations based on a newly triggered station can be selected in two steps:
1. Select a subset of stations that have the closest distance to the triggered station.
2. Select the remaining stations one-by-one that lead to the most increase of azimuth coverage from the existing set of stations.
Using Japan as an example, Figure 3.4 shows the station selection for both inland and coastline stations. The proposed two-step selection scheme will automatically result in a purely distance- based selection for the inland case, and a combine-factors selection in the coastline case.
Figure 3.4: Example of station selection in Japan for coastline (left) and inland (right) station. Seismic stations are denoted in triangles. The green area represents the Voronoi cell of the newly triggered station. The red stations are selected stations for the newly triggered station (green triangle).
3.4.3 Sample prior and update
From empirical experience, even if noise is included, it is highly probable to obtain a likelihood function p(Ft|θ˜l) that is peaked around the true earthquake parameter values soon after the first triggered (P-wave picked) station occurs, especially for inland earthquakes. The speed of con- vergence increases as the network density increases. For example, it only takes a few seconds to converge to an inland earthquake under the combined network of JMA and Hi-net stations in Japan.
As a result, instead of using a prior (the initial proposal PDF in RBIS) that covers all possible space and time within the region of interest, one may sample from a uniform distribution around the first triggered station of a new event, and a reduced time range depending on the spatial area of the location prior. The spatial extent of the uniform distribution can be determined based on the Voronoi cell methodology.
Because of the lack of station coverage on the sea, the Voronoi cell of a station on the coastline can be very large. Instead of using the large Voronoi cell as a prior, one may use a smaller cell around the station and add a sample updating scheme. When it is an offshore event, the updating scheme will guide the samples to converge toward the hypocenter after each time step. A possible updating scheme conditioning on the hypocenter estimate from the previous time step is:
1. Shift samples toward the direction of the new expected hypocenter location if the change of estimate from the previous time step is large
2. Resample based on the sample weights from the previous time step for better convergence of the hypocenter estimate if the change of the estimate from the previous time step is small 3.4.4 Algorithm summary
Actual implementation of the method can be summarized as a two-step algorithm at each given time step t (Figure 3.5). Starting from an initial step t= 1, first, earthquake parameters of each existing event are updated based on the newly received seismic data from the network. Second, the number of concurrent events is updated by the suboptimal model class selection scheme with the predetermined creating, merging and deleting criteria. The process is repeated until the termination of the system.
Figure 3.5: Flowchart of a two-step RBIS EEW algorithm at each time stept.
The update of the earthquake parameters of each existing event n can be broken down into three parts and the algorithm may stop after all ˆnevents are updated (Figure 3.6):
1. Extract information from the waveform data to update the features used in eventn.
2. Update samples based on new information and earthquake parameter estimates from the previous time step (suggested method in Section 3.4.3).
3. Update all earthquake parameter estimates using the RBIS method explained in Section 3.3.2.
Figure 3.6: Flowchart of a three-step earthquake parameter updating scheme for each event n based on RBIS.
Terminate when all ˆnevents processed.
The update of the number of concurrent events can also be broken down into three parts (Figure 3.7):
1. Merge existing events (reduce number of concurrent events) that have similar converged estimates of earthquake parameters.
2. Delete existing events (reduce number of concurrent events) that have inconsistent theoretical P-wave arrival times comparing to the observed P-wave picking times from the current data.
3. Create a new event (increase number of concurrent events) with a newly triggered station as the theoretical first triggered station for the event if all three criteria are met: (a) Equation 3.6, 3.8 or 3.9; (b) waveform amplitude of the first triggered station exceeds the predetermined threshold; (c) More than one consecutive trigger of stations close by the first triggered station.
Figure 3.7: Flowchart of a three-step updating scheme for the number of concurrent event.