I would like to thank my advisor, Tom Heaton, for broadening my knowledge of engineering seismology and increasing my confidence. I would like to thank the person who introduced me to the importance of earthquake early warning and to the idea of a PhD at Caltech: Lucy Jones.
1 Introduction
- General Concept of Earthquake Early Warning (EEW)
- EEW in the World
- Statement of Problem
- Objectives of Thesis
The current EEW system for the West Coast of the United States is called ShakeAlert. Therefore, Method I of the algorithm is a standard grid search that matches Cua-Heaton ground motion envelopes to the incoming ground motion envelopes, using probabilistic measures.
2 Data collecting and processing
- Raw Data Collection
- Processing Methodology
- Phase Determination for Offline Analyses
- Initiation of Algorithm by Prior for Real-Time Analyses
- Converting Full Waveforms to Envelopes
- Summary
A lit station indicates the start of calculations, and the trigger is based on the arrival of the P wave. Therefore, another way of doing things using the data is to distinguish the arrival of different phases.
3 Method I: Grid search
- Introduction to the Grid Search Method
- Creating the Grid Space
- Defining the “Goodness-of-Fit”
- Interpreting the Best Fits with Error Bands
- Assessing Convergence: a Test Sweep on 5<M<7 Events
- Assessing Robustness: a Test Sweep on 4.5<M<7 Events
However, it is important to know the disadvantages of grid search before applying it to data. In general, the success of a grid search depends on the coverage of the station around the observed epicenter.
2 criteria are suggested for 4.5<M<7
Application to Past Real Earthquakes
The network search is able to estimate the magnitude as M>5 within the first 5 seconds after the initial P-wave arrival, which FinDer fails to do. However, the network search estimates the size to be 0.3 units closer to the true size and 5 seconds faster than FinDer's solutions.
Comparing Magnitude Estimates for the 2020 Northern Coast Offshore Event
Given the best-fitting cataloged envelopes, what is the error band that provides specified confidence
Comparison of best-fit cataloged (in red) and incoming observed envelopes (in black) for the 2020 north shore offshore event. Consistent comparison with current system solutions is valid up to 10 seconds past origin time.
Comparing Magnitude Estimates for the 2020 Lone-Pine mainshock
Given the best-fitting cataloged envelopes, what is the error band that provides specified
Comparison of the best-fit Cua-Heaton (in red) and upcoming observed envelopes (in black) for the 2020 Lone Pine main shock. A grid search finds the final magnitude to be M6.9, which is 0.6 units more accurate than the current system.
Comparing Magnitude Estimates for the 2019 Ridgecrest mainshock
Given the best-fitting cataloged envelopes, what is the error band that provides the specified
As mentioned earlier, a strong earthquake like the M7.1 Ridgecrest is the upper limit of the grid search. By visual inspection, as the crack progresses through time, the mesh search finds a significantly more accurate envelope fit for the M6.4 foreshock than for the M7.1 mainshock. In order to obtain a better fit for the observed M7.1 main shock envelopes, additional suggestions are considered (see Chapter 6).
Comparing error bands M7.1 mainshock and M6.4 foreshock for envelope fits
Further Magnitude Constraints Using Amplitude Ratios
Maximizing waveform-based likelihood (using P-wave data from 1 station)
Summary
A test sweep of 4.5
4 Method II: Extended Catalog Search
The Usefulness of Catalog-Based Search Algorithms
This previous observation strongly implies that an event already exists in the catalog that closely matches the incoming earthquake. The unique matches of the extended catalog search especially help with reliability in estimates for single station approach. To change the focusing mechanisms, another model is needed to further expand the catalog (Heaton 1979).
Defining the “Goodness-of-Fit”
The total posterior probability of the cataloged earthquake is taking the product of the individual probabilities (Eq. 4.1.2) for channels 𝑁, stations 𝑀 and time points 𝑃. As mentioned before, the extended catalog search uses the minimization of the sum of the squared residuals to find the best parameter estimates. Therefore, the use of logarithmic amplitudes makes the goodness-of-fit assessment more robust.
Interpreting the Best Fits with Error Bands
𝑋!"# is the logarithmic (base 10) amplitude of the cataloged earthquake, and 𝜂 is the error band that is adjusted accordingly to meet the confidence band. Because a normal distribution is assumed for the logarithmic difference of the envelope fits ( log-normal distribution for absolute difference), the mean for best fit would approach a mean of 0. Therefore, one standard deviation would be the error band around the best fit envelope, which would contain at least 68% of the incoming ground motion amplitudes.
Defining the Original Catalog
However, integrating the raw acceleration sometimes leads to a linear trend due to tilt, the transducer's response to vigorous shaking, or analog-to-digital conversion problems (Yamada et al. 2007). As mentioned earlier, the feature of the enhanced catalog search that sets it apart from other search algorithms is its uniqueness to the seismic station in question. However, since most of the earthquakes in the catalog are medium magnitude (M<7) where point source characterization is valid, a drawback is the inability to account for the effects of fault propagation trajectory.
Extending the Catalog
The spectra of the aforementioned Ridgecrest series earthquakes provide an excellent comparison of the real observation with the synthetic one. Similarly, to create the synthesis of a M6.4 earthquake, the transfer function is applied to scale the true spectra of the real M5.36 earthquake. A synthetic M6.4 produced by upscaling spectra lacking long-period components fails to capture the behavior of the real M6.4.
Application to Past Real Earthquakes
4.8 the extended catalog search finds matches to the incoming observed acceleration, velocity and displacement envelopes. The solutions found by the extended catalog search 20 seconds after the origin have higher confidence than those found by the grid search. The performance of the extended catalog search is successful in terms of both speed and accuracy in obtaining parameter estimates.
Comparing Magnitude Estimates for the 2020 Lone Pine mainshock
Summary
The simplest form of extended catalog search is the uniform prior assumption and considering only waveform-based probabilities. To ensure that the extended catalog search finds envelopes from the past that resemble those observed in the input, a simplified spectral scaling model is applied. Looking at the results, in general, the error bands of the parameter estimates are smaller for the extended catalog search compared to those for the grid search.
5 Optimizing Method II with KD trees
- Introduction
- Re-structuring the Format of the Dataset
- Constructing the KD Tree
- Searching the KD Tree
- Advantages Compared to Brute-Force Search
- Conditions
- Application to Current SCSN Catalog
- Summary
The advantage of looking for the nearest neighbor of the KD tree is the pruning process of certain nodes. The closest neighbor search of the KD tree (left) is faster as it searches 60% of the total data set, while the brute force search (right) searches 100%. As shown in Table 5.3, the impact of searching for the nearest neighbor of the KD tree remains similar as the number of waveform envelopes increases.
6 Complex Earthquakes
Point Source vs. Finite Fault Characterization
The effectiveness of using the early frequency content of the waveforms to estimate the final magnitude estimate is questioned for larger earthquakes. Larger earthquakes are more complex, with multiple sources rupturing close together in time and space.
Additional Templates
Application to Real Complex Earthquakes
The main feature of the extended search of the catalog is the accuracy of the initial estimates of its size. With the initial mainshock rupture arriving at the first station 2 s after the origin time, the subevent delayed by rupture propagation would arrive at the first station. However, using two subevents to represent the M7.0 mainshock works for the rest of the stations.
Comparing Magnitude Estimates for the Mw7.0 Kumamoto Mainshock
M6.4 followed by M6.9 best describe the
Time delay of second subevent is ~5 seconds
Given the best-fitting synthetic envelopes, what is the error band that provides 68% confidence
Locations of the stations relative to the epicenter of the mainshock, the epicenter of the past event, and the rupture for the 2016 Kumamoto mainshock. At this point, the fault band decreases significantly, further satisfying the implication of a second rupture arriving at the stations. 6.4 is the arrival of the second subevent when the fault bands begin to diverge, indicated by the vertical red line.
Comparing Magnitude Estimates for the Mw7.2 El Mayor-Cucapah Mainshock
Locations of stations relative to the epicenter of the main shock, the epicenter of past events, and the ruptured fault for the 2010 El Mayor-Cucapah main shock. However, most of the stations considered in the extended catalog search have epicentral distances greater than the rupture slit. For stations further away from the error, the point source approximation produces relatively small and satisfactory error bands.
Error bands produced by complex sequence compared to error bands produced by point
Summary
Therefore, if seismicity is not high in the region, it may not be sufficient to look back only 1 month in earthquake history. Here, the extended catalog search can look back more than 10 years in the earthquake history and still not find envelopes that fit the incoming ground motions well. Here, the extended catalog search must look back 10 years in earthquake history for envelope fits that produce acceptable error bands.
7 Parallel execution of Methods I and II
Application to past real earthquakes
Comparing Magnitude Estimates for the 2020 Northern Coast Offshore Event (missed
7.3, the extended catalog search immediately recognizes the incoming earthquake as M5.6 using the first 2 seconds of data. B and D, the gaps between the fault bands are larger in this earthquake than those in the previous 2020 offshore north coast event, highlighting the reduced confidence in the grid search estimates for the Lone Pine mainshock 2020. Instead, the envelopes cataloged from the preshock provide more accurate fits than the Cua-Heaton envelopes from the grid search not only for the initial time points but for the entire rupture.
Comparing Magnitude Estimates for the 2020 Lone Pine mainshock
7.5, the extended catalog search estimates the incoming earthquake as M5.4 based on the first 4 seconds of data. This estimate grows to M6.5 10 seconds after the origin time and to M6.9 27 seconds after the origin time. On the other hand, the grid search estimates resemble those of the expanded catalog search 13 seconds after the origin time.
Comparing Magnitude Estimates for the 2019 Ridgecrest mainshock
Summary
While the grid search is generally a robust method for different types of earthquakes, the extended catalog search provides more accurate fits to the envelope, most likely due to location-specific consideration and path effects at the specified stations. In other words, if the earthquake history at the specified stations contains ground motion envelopes that resemble those of the observed incoming earthquake, the extended catalog search is robust. When both methods agree on error bands and magnitude estimates, as in the 2020 North Coast offshore event, the user can have high confidence in the solutions.
8 Prior Information
Introduction
Seismicity Prior for Faster Event Detection
From each recorded earthquake, the amplitude associated with the arrival of the P-wave and the amplitude of the noise preceding the signal are extracted. The histogram is generated using the noise amplitudes before the signal and a lognormal distribution is fitted. With each amplitude of the ground motion envelopes there is a corresponding probability, 𝑃𝑟 > 𝑝𝑔𝑎, which is the probability that the input ground motion is an earthquake.
Location prior using ETAS model
The chosen values for the constants 𝐾, 𝑐, 𝑝, 𝑛 and 𝛼 are based on the ETAS model for Southern California (Felzer 2009). Probability of occurrence according to ETAS model of estimated location for the 2020 North Coast offshore event, based on prior information (no waveforms involved). Probability of occurrence according to ETAS model of estimated location for the 2019 Ridgecrest main shock, based on previous information (no waveforms involved).
Magnitude Estimate Using Amplitude Ratios
The uncertainty, 𝜎, depends on the phase, which can be found using a standard STA/LTA analysis or the polarization analysis (Ross et al. YEAR).
Bayes’ Theorem: Applying Prior to Likelihood
For the main Brawley shock, waveform-based probabilities are sufficient, but prior information provides. 8.10, the prior information has virtually no influence on the location and size estimates for the extended catalog search. The application of advance information had little impact on location estimation in the expanded catalog search for the 2020 North Coast offshore event.
Comparing Magnitude Estimates for the 2019 Ridgecrest mainshock
Summary
Applying additional prior information and constraints to a probabilistic Bayesian approach can reduce the trade-offs between magnitude and location at initial earthquake rupture time points, trade-offs that occur due to insufficient waveform data. However, as additional data is acquired over time, the influence of the prior information diminishes and the waveforms have a dominant influence on the final solutions. As seen with the offshore event, advance information is most valuable for regions with sparse station coverage and regions subject to an earthquake sequence.
9 Concluding Remarks and Future Work
Concluding Remarks
Wait for three triggered stations for increased accuracy in parameter estimates to warn regions further away.
Future work
Bibliography
Estimation of strong ground motions from hypothetical earthquakes in the Cascadia subduction zone, Pacific Northwest.
