14 Figure 2.2 Four simulation results of the Northridge aftershock for a 24-hour period in January calculated by the Felzer ETAS model. It consists of long-term background seismicity π πππ‘,πππ and short-term observed seismicity.
Introduction
Motivation
The success of an EEW system is often measured by the accuracy and timeliness of the warnings provided. In fact, βπ‘!β#$% can be minimized to a fraction of seconds due to the rapid advancement of electronic information flow.
Background on Earthquake Early Warning System (EEW)
- EEW concept and development
- Overview of earthquake early warning systems around the world 5
In the precision analysis in Figure 3.15, both Bayesian models outperform the waveform analysis by more than 5% in the first alarm. The predicted results of the ETAS algorithm are compared with the observed seismic activities for validation.
Earthquake Forecasting Methods
Background on Foreshock-Mainshock-Aftershock Sequences
Many seismologists have observed temporal and spatial clustering properties of earthquakes (Kagan and Jackson 1991) (M. Bouchon, et al. 2013) (Gerstenberger, et al. 2005). There are also theories that explain that pre-earthquake phenomena are the result of interplate or heterogeneity of the earth's crust (M. Bouchon, et al. 2013) (Mogi 1963).
Earthquake Forecasting and Earthquake Early Warning
As mentioned in Chapter 1, the prediction information can be applied as the prior information under the Bayesian framework, and the waveform analysis serves as the probability function. Conventional earthquake early warning waveform analysis requires a minimum of time series data before making decisions (e.g.
General Epidemic-Type Aftershock Sequence (ETAS) model
Each run of the simulation will produce different results due to the randomness of the sampling process. The Northridge aftershock simulation results for a 24-hour period in January, calculated using Felzer's ETAS model, are as follows.
Modified Epidemic-Type Aftershock Sequence (ETAS) model
The short-term seismicity rate caused by each of the historical earthquakes in the catalog is first calculated as a function of the distance from the hypocenter source, π. π‘,π , and then mapped to latitude and longitude, π. To validate the accuracy of the ETAS forecasts, Figure 2.5 through Figure 2.11 are examples of the earthquake probability forecast maps produced from the modified maps.
Summary
ETAS Prior application one: Rapid Earthquake Discrimination
Introduction
Method and Data
- Data 31
- Determination of the Model Parameters
- Model Selection
- Model Performance
A better identification of the low PGA earthquake records improves the overall performance of the earthquake detection. We took the logarithm of the model features because the ground motion amplitudes span several orders of magnitude (Bose, Heaton, and Hauksson 2012). This features the ith record at the kth half-second time window after the triggered time.
Bayesian Approach
- Bayesian approach with a Simple Prior
- Model Performance
- Bayesian approach with a Modified Prior
- Model Performance
This prediction is based on the spatial and temporal clustering properties of recent earthquakes. Assuming that the earthquake source must be near the earliest triggered stations, Eq[3.14]. The probability prediction is the result of the waveform analysis model presented in Section 4.3, and the posterior prediction is the result of the Bayesian model described in the previous section.
Comparison Results of Waveform Analysis vs. Bayesian models
In addition to the analysis of raw categorical records, the precision and accuracy metrics from Equations [3.6] and Equations [3.7] are also considered. Compromising the accuracy and precision requirements for EDN purposes, a Bayesian model with a modified prior is recommended. To summarize the signal discrimination process (seismic vs. noise classification) for real-time EDN implementation, the steps in the proposed model follow the flowchart in Figure 3.16.
Cross-validation Results
The predictive result of the new method at 0.5 s and 3.0 s is compared with the result of π!. Starting with the root of the tree, the first feature dimension (Hz frequency band) is chosen as the partition hyperplane. The process is repeated, moving recursively down the next level in the tree until the leaves of the tree are reached.
34;Designing a Network-Based Earthquake Early Warning Algorithm for California: ElarmS-2." Bulletin of the Seismological Society of America 104, no. 34;Decision Criteria for Earthquake Early Warning Applications." Proceedings of the 15th World Conference on Earthquake Engineering.
Comparison to the Οc-Pdtrigger criterion
Examples
For example, two false triggers at stations CI.CFS and CI.NEN occurred near Lancaster and San Bernardino on March 24, 2015. Figure 3.23 shows the waveforms collected at the stations closest to the hypocenter, CI.WNS and CI. MIS, show strong characteristics of an ongoing earthquake. As shown in Figure 3.24, stations CI.SMR and CI.SMW triggered a teleseismic event, but the amplitudes in the acceleration records are small enough not to disturb the local community.
Discussion and Conclusion
In all the above cases, the proposed method can optimally provide quick alerts to users near the triggered station. Furthermore, the proposed method offers the potential benefit of faster, more reliable warnings for regions near the epicenter, where the strongest shocks are experienced. The simple implementation of the model suggests that it can be incorporated into real-time analyses.
Introduction
π π,π π(π‘) is commonly called the Bayesian posterior function, π π(π‘) π,π is called the likelihood function, and π(π,π ) is called the Bayesian prior. We propose a Bayesian prior based on the principle that earthquake sequences tend to cluster in time and space. We evaluated the location estimation performance of Bayesian analysis techniques, using the GbA as a likelihood function, combined with an ETAS model for the Bayesian prior.
Method
- Bayesian Inference in EEW Location Estimation
- Prior Information β ETAS seismicity model
- Likelihood Functionβ The Gutenberg Algorithm
In single station location inference, we convert the station-to-source distance probability density function of GbA into a two-dimensional spatial distribution that will most likely produce the recorded waveform π(π‘), π!(π(π‘)|πΏππ‘ ,πΏππ), depending on the distance between the station π and the location (πΏππ‘,πΏππ).
Data
The catalog data used in the Bayesian priors were downloaded from the Southern California Earthquake Data Center (http://data.scec.org/). The waveform dataset is collected from the global waveform database compiled by Meier (2015). The subset of events used in this study includes 50750 three-component waveform records from a total of 3523 events.
Results
- M5.2 Lone Pine Earthquake
- M5.4 Chino Hill Earthquake
- Overall Performance
Due to high station density in the area, sufficient waveform data were quickly collected and GbA initial location estimation shows high accuracy with only 12 km error, as shown in Figure 4.6 a) c) and e). Although the seismicity prior indicates relatively high earthquake probabilities around 40 km east of the station, the hypothesis was immediately updated by the GbA results with the incoming waveforms, shown in Figure 4.6b) d) and f). In Figure 4.8b), the localization error is calculated using Bayesian Inference by combining waveform and catalog information; the median location error is 12 km, 8 km, and 5 km at 0.5 sec, 5 sec, and 10 sec after the first trigger.
Discussion
In such a case, estimates are quickly dominated by the likelihood function of waveform analysis, as shown in the Chino Hills earthquake. It first uses the scientific intuition of seismic knowledge to make a fast and rational approximation, and then analyzes the waveforms in real time with the help of powerful computational tools. The concept of the voronoi diagram of a grid distribution implies that an earthquake must occur within the voronoi cell of the first ignited station, since the travel time of the P wave from any point in this voronoi cell to the station is minimized (Rosenberger 2009).
Conclusion
Theoretical analysis of the KD tree search shows that the performance complexity is O(log N) versus O(N) for the linear sequential search, where N is the number of data points in the database (Friedman et al., 1977). 34; The Gutenberg Algorithm: Evolutionary Bayesian Magnitude Estimates for Earthquake Early Warning with a Filter Bank." Bulletin of the Seismological Society of America 105, No. 34; Rapid and Reliable Magnitude Determination for Seismic Early Warning." Bulletin of the Seismological Society of America 88, no.
Reducing EEW parameter search delays
Introduction
As a result, the processing delay of the real-time search will increase significantly because the time required to query databases sequentially is proportional to the size of the database. Database searching is often an application of the Nearest Neighbor (NN) search problem with the Euclidean metric. In general, we search for a point in the database that minimizes the Euclidean distance to the target point (sometimes referred to as the least square distance).
Data
The effectiveness of rapid alerts is especially valuable near the epicenter, where the strongest damage occurs very quickly after the event's onset. Our goal is to determine the search efficiency of the KD tree method for our GbA seismic database. Each of the feature dimensions represents the highest ground velocity in octave wide frequency bands for a given ground motion record with a fixed time window.
KD Tree and Method
- KD Tree
- Method
Starting from the root node of the tree, the nearest distance is initialized as the distance between the target node and the root. Then recursively move to the next level in the tree and check that the splitting hyperplane intersects the hypersphere centered on the target record with a radius of the current nearest distance. At the end of the search, the algorithm returns π points from the database that are at minimum distances from the target point. A).
Results
In Figure 5.7, the solid lines show that the average CPU search time for a database with 130,000 points is approx. 0.2 sec. for the linear sequential search method and 0.03 sec. for the KD tree search method; the significant reduction in time reduces the computational effort by 85%. The results predict that the benefits of the KD tree application will be emphasized in the future as global seismic databases grow significantly (Yu, 2016). As shown in Figure 5.8, the number of visited data points in the KD tree varies for each validation; on average, the KD tree approach only visits about 10% of the entire database to find the closest data point to the target, confirming the performance in CPU search time in Matlab.
Discussion and Conclusion
34;A Trigger Criterion for Improved Real-Time On-Site Earthquake Early Warning Performance in Southern California." Bulletin of Seismological Society of America. 34;CISN ShakeAlert - An Earthquake Early Warning Demonstration System for California." In Early Warning for Geological Disasters, 49-69. 34;Earthquake Early Warning Systems: Current Status and Perspectives." In Early Warning Systems for Natural Disaster Reduction, 409-423.
Conclusion
Final remarks
This final chapter summarizes the thesis and suggests possible directions for the extension research into earthquake early warning. In Chapter 2, I presented previous studies of earthquake sequence science and earthquake prediction modeling, specifically Epidemic-type Aftershock Sequence (ETAS) modeling, a statistical approach to predicting the probability of seismic activity in the near future. Applying the KD tree search to organize the database reduced the average search process by 85% of the time cost of the exhaustive method, making the method feasible for real-time implementation.
Future work
34;The Virtual Seismologist (VS) method: A Bayesian approach to earthquake early warning." In Earthquake Early Warning Systems, by P Gasparini, G Manfredi and J Zschau, 85-132. 34;PRESTo, the earthquake early warning system for Southern Italy : Concepts, capabilities and future perspectives." Soil dynamics and earthquake engineering. 34;ePAD: Earthquake Probability-Based Automated Decision-Making Framework for Earthquake Early Warning.β Computer Aided Civil and Infrastructure Engineering.
