- © 2015 by the Seismological Society of America
Rapid detection of local and regional earthquakes and issuance of fast alerts for impending shaking is considered beneficial to save lives, reduce losses, and shorten recovery times after destructive events (Allen et al., 2009). Over the last two decades, several countries have built operational earthquake early warning (EEW) systems, including Japan (Hoshiba et al., 2008), Mexico (Espinosa-Aranda et al., 1995), Romania (Mărmureanu et al., 2011), Turkey (Erdik et al., 2003), Taiwan (Hsiao et al., 2011), and China (Peng et al., 2011). Other countries, such as the United States (Böse, Allen, et al., 2013), Italy (Satriano et al., 2011), and Switzerland (Behr et al., 2015), are currently developing systems or evaluating algorithms in their seismic real-time networks.
Over the past eight years, scientists at the California Institute of Technology (Caltech), the University of California–Berkeley, the University of Southern California, the University of Washington, the U.S. Geological Survey (USGS), and the Swiss Federal Institute of Technology (ETH Zurich, Switzerland) developed the U.S. west-coast-wide ShakeAlert EEW demonstration system for California, Oregon, and Washington (Böse, Allen, et al., 2013). Real-time alerts are currently being shared with around 300 individuals, companies, and emergency response organizations to gather feedback about system performance, to educate potential end users about EEW, and to identify needs and applications of a future operational warning system.
To quickly determine earthquake magnitudes and (point-source) hypocenter locations, the Californian ShakeAlert system processes and interprets real-time waveform data streams from several hundred seismic broadband velocity and strong-motion acceleration sensors as part of the California Integrated Seismic Network (CISN). Designed as a hybrid system, ShakeAlert combines the estimates from one single-sensor and two network-based EEW algorithms that run in parallel, including τc-Pd Onsite (Wu et al., 2007; Böse, Hauksson, Solanki, Kanamori, Wu, et al., 2009; Böse, Hauksson, Solanki, Kanamori, and Heaton, 2009), ElarmS (Allen, 2007; Kuyuk et al., 2014), and the Virtual Seismologist (Cua et al., 2009; Behr et al., 2015). Once an earthquake has been detected, each algorithm starts independently sending reports to the ShakeAlert Decision Module, which—based on these reports—determines the most probable event parameters (location, magnitude, and origin time) and uncertainties, which are then continuously updated with progressing time as new data arrive. Using these estimated source parameters, the ShakeAlert UserDisplay software, which is installed at the end user’s site and subscribes to the ShakeAlert system, predicts and displays the arrival and intensity of expected peak shaking (Böse, Allen, et al., 2013).
Encouraged by its promising real-time performance during the recent moderate-size 2014 M 5.1 La Habra and M 6.0 South Napa earthquakes in southern and northern California, the ShakeAlert Science team decided in 2014 to include the Finite-fault rupture Detector algorithm, FinDer (Böse et al., 2012), as a fourth seismic algorithm in the ShakeAlert system to enable the use of rupture-to-site distances in ground-motion predictions and hence improve EEW performance during large-magnitude (M≥6.0) earthquakes. Based on a rapid near- or far-source classification and comparison with precalculated templates, FinDer provides rapid estimates of the centroid position (latcentroid, loncentroid), length L, and strike Θ of an ongoing fault rupture, assuming a line source (Fig. 1). The integration of FinDer into ShakeAlert was finalized in April 2015. Currently, FinDer is operated as a MathWorks MATLAB (www.mathworks.com/products/matlab, last accessed September 2015) stand-alone code with a C++ waveform-processing module installed at three CISN datacenters at Caltech/USGS-Pasadena, UC Berkeley, and USGS-Menlo Park. Translation of the FinDer algorithm to C++ by USGS-Menlo Park, ETH Zurich, and Caltech is currently under way.
We will start this article with a brief review of the FinDer algorithm developed by Böse et al. (2012), followed by a summary and demonstration of recent improvements to the algorithm, including error estimates, usage of generic and fault-specific templates, and extension to subduction-zone earthquakes. We will demonstrate and evaluate the real-time and off-line performance of FinDer during the recent 2014 M 5.1 La Habra and M 6.0 South Napa (California) earthquakes, as well as the 2010 M 7.2 El Mayor–Cucapah (Mexico) and 2011 M 9.0 Tohoku-Oki (Japan) earthquakes.
REVIEW AND EXTENSION OF THE FinDer ALGORITHM
The FinDer algorithm uses image-recognition techniques to detect and model finite-fault ruptures using spatial images of observed ground motions and theoretical templates modeled from empirical ground-motion prediction equations (GMPEs). As described by Böse et al. (2012) and illustrated in Figure 1, FinDer processing involves three main steps: (1) near- or far-source classification of spatially interpolated high-frequency observations, which gives a binary image I(x,y); (2) application of matching by correlation (e.g., Gonzales et al., 2004) to determine the correlation R(x,y|L,Θ) of template T(x,y|L,Θ) and I(x,y) at any spatial location (x,y); the geographic coordinates latcentroid and loncentroid of the rupture centroid come from the template spatial location that corresponds to the maximum spatial integral of the given template cross correlation with the data; (3) minimization of the misfit between image I(x,y) and templates T(x,y|L,Θ) gives L, Θ, and latcentroid and loncentroid of the assumed line source. The output parameters are updated whenever a new set of ground-motion amplitudes becomes available (for instance, every second). This way, FinDer keeps track of a rupture evolving from a small point source to a large finite-rupture event.
Images I(x,y) (Fig. 1, left) are obtained from map-projected and phase-independent (Böse et al., 2012) interpolated logarithmic peak ground acceleration (PGA) amplitudes. We define PGA as the largest absolute value recorded on any of the three ground-motion components over a constant time window (e.g., 120 s), corresponding to the rupture duration of the largest expected earthquake in a given region. Because the large high-frequency motions are typically observed at only small rupture-to-site distances (e.g., Yamada et al., 2007), a ground-motion threshold, gm_threshold, is applied for near- or far-source classification, where image pixels with PGAobs≥gm_threshold are set to 1 and otherwise are set to 0. For the examples shown in this article, we set gm_threshold=70 cm/s2. We are using the term “near source” not in a strictly physical sense, but rather to characterize the spatial zone around the fault rupture with PGA values exceeding some arbitrary threshold.
Templates T(x,y|L,Θ) (Fig. 1, right) are precalculated binary images generated for various rupture lengths L and strikes Θ from empirical GMPEs, in which pixels close to the rupture (PGAGMPE≥gm_threshold) are set to 1 and all other pixels (PGAGMPE<gm_threshold) to 0. The templates thus consist of equidistant buffer zones around the line source, bordered by two parallel lines and two semicircles, which result in quasi-elliptical shapes (Fig. 1, right). The relationship between the cutoff distance and the rupture length L (and thus magnitude M) is nonlinear due to the nonlinear nature of the underlying GMPEs for PGA, which saturate at large magnitudes and close distances.
Because of the assumed symmetry of the generic templates, the results of Θ and Θ+180° are equivalent. It is assumed that near-source PGAs are not affected by rupture directivity, as discussed by Spudich and Chiou (2008). For the application of FinDer to earthquakes in California and northern Mexico as described in this article, we use GMPEs by Cua and Heaton (2009) and empirical rupture length–magnitude relations by Wells and Coppersmith (1994); for application to the Tohoku-Oki subduction-zone earthquake (Japan), we apply relations after Si and Midorawaka (2000) and Blaser et al. (2010).
Modeled templates T(x,y|L,Θ) are used as spatial filters to determine the correlation R(x,y|L,Θ) with an observed image I(x,y) at each spatial location of T in I (the spatial extent of I is much larger than of T). This method is known as matching by correlation (e.g., Gonzales et al., 2004; Fig. 1, middle). To increase computational speed, we implemented the algorithm in the Fourier domain by taking advantage of the correlation theorem: (1)which relates the spatial correlation to the product of the Fourier transforms and in the wavenumber domain (kx,ky), in which the star denotes correlation and the asterisk denotes the complex conjugate. This approach is computationally highly efficient and could be easily parallelized for additional speed, though this has not been done yet in the current FinDer implementation (Böse et al., 2012).
Although FinDer was originally developed for generic symmetric templates assuming simple line sources with symmetric quasi-elliptical ground-shaking distributions around the finite-fault rupture (Böse et al., 2012), we recently added a new set of fault-specific templates to provide more accurate rupture estimates along curved fault segments, such as along the Big Bend section of the San Andreas fault (SAF) in southern California. In addition, we created a third set of generic asymmetric templates, particularly designed to meet the requirements of subduction-zone environments, where seismic observations are typically limited to the hanging wall side of the fault rupture (Fig. 1, right; shaded area corresponds to downward-dipping fault plane). Table 1 gives a summary of the three currently used sets of templates.
The finite-fault parameters (L, Θ, and centroid position) are determined in a two-step procedure. In the first step, matching by correlation is used to determine the optimum spatial position (x′,y′) of a given template T in image I. The position (x′,y′) refers to the lower left corner of the template, assuming that the origin (0,0) of both T and I are in the lower left corner. The rupture centroid position (latcentroid, loncentroid) is determined from the template midpoint at the position (x′,y′). In the second step, we minimize the normalized sum of squared errors to find the optimum template and thus L and Θ. We modify the original error function defined in Böse et al. (2012) and define the new misfit E for a given image and a generic or fault-specific template for length L and strike Θ as (2a)in which the summation is done over x′=0…w−1, y′=0…h−1 for template dimensions w×h. The weighting term in equation (2a) accounts for the model uncertainties of the GMPEs (σGMPE) used for template generation, which we define as (2b)in which Rgm_threshold is the rupture-to-cell distance at which PGAmean=gm_threshold (e.g., gm_threshold=70 cm/s2), Rmin is the rupture-to-cell distance at which PGAmean−σGMPE=gm_threshold, and Rmax is the rupture-to-cell distance at which PGAmean+σGMPE=gm_threshold. Equation (2b) describes a simple bilinear function that increases linearly from 1 to 2 for distances between Rmin and Rmean and then decreases linearly back to 1 for distances between Rmean and Rmax. For distances smaller than Rmin or larger than Rmax is 1.
The template (and thus L and Θ) that shows the best agreement with image I(x,y) is found through minimization of the misfit function in equation (2a), that is E(L,Θ)→min. For the generic templates, we apply the simplex search algorithm by Lagarias et al. (1998) with upper and lower bounds for L and Θ, which is a direct search algorithm that does not require numerical or analytic gradients. The convergence rate toward the minimum is excellent and usually requires 30–50 iterations only. For fault-specific templates, we consider all possible templates (and thus all L) for a given region (northern, middle, and southern SAF; Table 1); and, for each of these templates, we determine E and the optimum solution. If its minimum misfit is smaller than for the generic templates (for a simple 1D line source), the fault-specific template is preferred, and otherwise we use the generic one. At the moment, we test both generic symmetric and fault-specific templates in California and asymmetric templates only in subduction-zone environments (Japan). In our current MATLAB implementation, the total optimization procedure takes ∼1–2 s on an i686 @2826.177 MHz machine.
As a new feature of FinDer, we recently started to estimate uncertainties for the best solutions of rupture length and strike by approximation of the multivariate likelihood function . For generic templates, we keep the centroid position and rupture length of the best solution () fixed and vary the strike Θ from 0° to 179° to determine the estimated univariate likelihood function for strike as (3)
Equation (3) is a probability density function that describes how well the predictions from a given set of model parameters (Θ,L)—and thus from a given template T—fit the observed data image I. The standard deviation σd describes the combined effects of assumed errors in the observations (including effects of interpolation) and the assumed prediction errors in the forward model, that is the GMPEs used for template generation. We experimented with various σd and found that σd=0.1 gives reasonable results that are in good agreement with geodetic inversions (Minson, Murray, et al., 2014).
In the next step, we keep the centroid position and strike of the best solution () fixed and walk through all L (5–300 km) to determine , similar to equation (3). For fault-specific templates, we determine the misfit for each template and thus for each L, and can easily apply equation (3) to calculate the likelihood function.
Although a simultaneous inversion of the likelihood functions for L, Θ, and the centroid position would be preferred, such computations are unrealistic under the strict time constraints in EEW. Also, assuming that L and Θ are largely uncorrelated appears valid for at least moderate-to-large earthquake ruptures.
We will now demonstrate the performance of FinDer with the new features described above for four recent earthquakes. Three of them are crustal strike-slip, normal, and oblique faulting events that occurred recently in California (2014 M 5.1 La Habra and M 6.0 South Napa earthquakes) and in northern Mexico (2010 M 7.2 El Mayor–Cucapah); the fourth event is the 2011 M 9.0 Tohoku-Oki (Japan) subduction-zone earthquake. The latter is particularly challenging because station coverage is along one side of the fault rupture only. USGS ShakeMaps (Wald et al., 1999) and finite-source solutions (Mai and Thingbaijam, 2014) for the four earthquakes are shown in Figure 2.
The M 5.1 La Habra (California) earthquake on 28 March 2014 was felt widely throughout Orange, Los Angeles (LA), Ventura, Riverside, and San Bernardino Counties with a maximum observed instrumental intensity of VII close to the epicenter, located 1 km east of La Habra (Table 2). The Global Centroid Moment Tensor (Global CMT) moment tensor (see Data and Resources) shows oblique faulting, with a northward-dipping plane that approximately aligns with the Puente Hills thrust fault. The strike of the rupture is determined as Θobs=232°, which, due to symmetry in our 2D approach, is equivalent to Θobs=52° (Table 2). The ShakeAlert EEW demonstration system detected the La Habra earthquake within 4.3 s of the event origin and provided 4 s of warning to Caltech in Pasadena, around 30 km from the epicenter (see Data and Resources).
During the La Habra earthquake, FinDer was running in real-time test mode at Caltech and getting waveform streams from 420 CISN strong-motion stations. However, FinDer was not connected to the ShakeAlert system. Although processing speed was not yet optimized, FinDer detected the earthquake within 11.5 s of the event origin and sent out a sequence of three internal reports with updated event information. The finite-fault solutions in these reports show an excellent agreement with the CMT solution (Table 2), as well as with the aftershock distribution of the La Habra earthquake (Lobs≈10 km; Fig. 3).
The 2014 M 6.0 South Napa earthquake on 24 August at 10:20:44 UTC occurred close to the West Napa fault. The Global CMT solution shows a strike-slip event with Θobs=157°; from the aftershock distribution and empirical relations by Wells and Coppersmith (1994), we estimate Lobs≈15–20 km. ShakeAlert detected this event within 5.1 s (Grapenthin et al., 2014). The initial event location and moment magnitude were off by 3 km and 0.9 magnitude units (estimated magnitude was 5.1) compared with the Advanced National Seismic Network catalog. FinDer, again operating in real-time test mode but not connected to the ShakeAlert system, detected the event within 16 s. The fairly sparse distribution of strong-motion stations around the Napa earthquake led to larger uncertainties in the FinDer-estimated rupture strike, compared, for example, with the La Habra earthquake. Although the final strike estimate is off by around ∼30°–40°, the CMT solution of Θobs=157° is within the FinDer real-time-estimated uncertainty range (Fig. 3).
Following the La Habra and South Napa earthquakes, we started to improve the FinDer algorithm and code in terms of robustness and processing speed. To test our new implementation, we replayed archived waveforms from historic and simulated earthquakes using the EarthWorm Tankplayer software. In this article, we present the off-line-results from the La Habra and Napa earthquakes, as well as from the 2010 M 7.2 El Mayor–Cucapah and 2011 M 9.0 Tohoku earthquakes.
Figure 4 shows the FinDer-estimated rupture length L, strike Θ, and magnitude M for the four events. Magnitudes were estimated from empirical L–M relations by Wells and Coppersmith (1994) and Blaser et al. (2010). The shaded areas show the estimated uncertainties of the rupture parameters; they refer to the standard deviation estimated from the likelihood functions , assuming Gaussian distributions; if is non-Gaussian (e.g., likelihood function for strike at an early stage of the La Habra earthquake, Fig. 5), only the value with maximum likelihood is shown. Figure 5 displays three randomly picked screenshots for each event to illustrate the temporal rupture evolution.
The off-line-predicted rupture parameters for the La Habra and South Napa earthquakes (Figs. 4 and 5) are quite similar to the real-time results (Fig. 2). Again, because of the sparseness of seismic instrumentation around the South Napa earthquake, uncertainties in the FinDer output are quite large.
The M 7.2 El Mayor–Cucapah earthquake on 4 April 2010 occurred in northern Baja California in an area with a high level of historical seismicity, around 60 km south of the Mexico–United States border (Hauksson et al., 2011). The event exhibited complex faulting, possibly starting as a smaller M∼6 normal-faulting earthquake, followed ∼15 s later by the normal or strike-slip faulting mainshock with Θobs=132° (Wei et al., 2011). The aftershock zone extends from the southern end of the Elsinore fault zone in southern California almost to the northern tip of the Gulf of California, over a length of Lobs=120 km (Hauksson et al., 2011).
At the time of the El Mayor–Cucapah earthquake, ShakeAlert did not yet exist. However, all three point-source algorithms that are contributing to the current system were running in real-time test mode: τc-Pd Onsite detected the event within 16 s, Virtual Seismologist within 28 s of origin. Both algorithms estimated the event as M∼6, that is, they were obviously confused by the smaller foreshock and underestimated the size of the mainshock. ElarmS did not process this event, because it was outside of the CISN network. At the time of the El Mayor–Cucapah earthquake, none of the Centro de Investigación Científica y de Educació n Superior de Ensenada (CICESE) Baja California, Mexico Seismic Network (Red Sismica del Noroeste de Mexico [RESNOM]) stations deployed in northern Mexico was streaming real-time waveform data to CISN, so only Californian stations were available in real time. Only recently, eight CICESE stations were added to the CISN live streams and are now being processed routinely by ShakeAlert.
For our FinDer off-line-test, we complemented the CISN waveform dataset with the data from eight CICESE stations (Fig. 5; see Data and Resources). Although the near-source station coverage is still quite poor, both the length and strike of the northwestern part of the bilateral rupture can be well recovered (Figs. 2, 4, and 5). The rupture centroid appears to be slightly shifted toward the east but is within the uncertainty range of our current map resolution (5 km). The final rupture length is estimated as 70 km, which corresponds to M∼7.1 (Wells and Coppersmith, 1994) and is thus in good agreement with the observed moment magnitude. The output of FinDer seems to be largely unaffected by the smaller M∼6 foreshock and inherent complexities of this event.
The last earthquake that we will analyze here is the 2011 M 9.0 Tohoku-Oki (Japan) megathrust earthquake, which caused tremendous numbers of casualties and damage in Iwate, Miyagi, and Fukushima, particularly from a Pacific-wide tsunami. Simons et al. (2011) estimate that peak displacements of around 60 m occurred along the central section of the fault plane (Fig. 2). Kinematic inversions by Minson, Simons, et al. (2014) suggest that the rupture propagated with a low average velocity of about 1.2 km/s and that most of the rupture occurred within ∼120–125 s.
The EEW system operated by the Japanese Meteorological Agency (JMA; Hoshiba et al., 2008) detected the event within ∼25 s from event origin and successfully released a warning to the Japanese public. However, because the event magnitude was underestimated and source finiteness not considered, ground motions were largely underestimated, in particular in the Kanto district (Hoshiba et al., 2011).
For our FinDer off-line test, we use strong-motion records of the Tohoku-Oki earthquake from 273 K-NET stations operated by the Japanese National Research Institute for Earth Science and Disaster Prevention (NIED; see Data and Resources). Because the seismic observations in our test are limited to onshore stations and are thus restricted to one side of the fault rupture (Fig. 5, bottom), we use our generic asymmetric template set (Fig. 1, right; Table 1). Constrained by the geometry of the Japan trench, we assume a lower and upper strike limit of 90° and 270°, respectively, that is a westward-orientated dip.
In general, FinDer results (Fig. 4) become available a bit later than in the JMA EEW system, mainly because we are considering K-NET stations only. Although the strike stays quite stable after 40 s, we observe a steady increase in rupture length (and thus magnitude) up to 270 km and M 8.5 within 160 s after rupture nucleation, which seems to be consistent with the source time function of the Tohoku-Oki earthquake (Minson, Simons, et al., 2014). The rupture centroid, in general, is not well constrained for a low-dipping fault plane and is also affected by boundary conditions of the ground-motion interpolation caused by the one-sided station coverage. In the test shown in this article (Figs 4 and 5), we set image pixels at ≥10 km distance from the closest recording station to 0 to avoid artifacts from interpolation.
Using KiK-net stations in addition to K-NET stations has no significant impact on the FinDer performance. The apparent underestimation of rupture length (Lest≈270 km) is thus likely not due to station density, but mainly a result of using the GMPE by Si and Midorikawa (2000), which predicts quite large shaking far from the fault rupture. The FinDer solution is consistent with the observed ground-motion distribution and applied GMPE and, as such, is useful to predict future shaking at larger distances (using the same GMPE) as needed for EEW. For illustration, in Figure 6 we compare the temporal evolution of observed and predicted JMA intensities in Tokyo. The predicted values are computed from Midorikawa et al. (1999) and Si and Midorikawa (2000) using the distance to the FinDer-estimated finite-fault rupture. Lead times between predicted and observed intensity levels range up to 50 s.
Minson, Simons, et al. (2014) report that high-frequency motions in the Tohoku-Oki earthquake were predominantly radiated down-dip of the regions of largest fault slip, particularly south of Sendai. Because FinDer uses high-frequency motions to determine rupture dimensions, the lack of correlation between high- and low-frequency motions could potentially lead to an underestimation of rupture dimensions, too.
Aside from the estimated finite-fault rupture parameters, there are two further aspects that make FinDer distinct from other current EEW algorithms: (1) FinDer searches for suspicious ground-motion patterns by looking at observed ground-motion images as a whole. This means that the FinDer output is a true network solution that combines spatially distributed observations instead of averaging over them, and (2) FinDer can be operated in two modes: either as a complete stand-alone algorithm or by being triggered by another algorithm or module. In the first mode, FinDer scans real-time ground-motion amplitudes continuously for suspicious patterns, and whenever the correlation between the observed ground motions (in space and time) and the theoretical templates exceeds some predefined threshold (e.g., R>0.9), it starts sending out reports with the computed source parameters, completely autonomous from any other (point-source) algorithm. In the second mode, FinDer requires a trigger from another algorithm to get started and can then be used to verify a potential detection and compute source parameters.
Traditional picker and (pick-to-event) associators are designed to provide high-fidelity locations. If there is a complex sequence, such as a seismic swarm or increased aftershock activity, traditional associators can become confused, because it becomes unclear which picks go with which event. This was, for instance, the case during the intense aftershock activity following the M 9.0 Tohoku-Oki (Japan) earthquake, causing numerous false and missed alerts in the JMA EEW system (Hoshiba et al., 2011). In EEW, we do not really care about these details, we just want to know the general time and place where the shaking originates. FinDer is therefore a simpler and more robust approach to association. These characteristics make FinDer likely also well suited for applications in highly noisy environments, as is typically observed in dense low-cost seismic and geodetic sensor networks, such as QuakeCatcher (Cochran et al., 2009), the Community Seismic Network (Clayton et al., 2011), or future crowd-sourced networks based on consumer smart devices (e.g., Minson et al., 2015).
It is important to point out that the FinDer-estimated line sources depend on the GMPE used for template generation. Usually, FinDer results agree well with the observed fault ruptures; however, there is a chance that source dimensions are under- or overestimated (as could be seen in the case of the Tohoku-Oki earthquake; Figs. 4 and 5). Still, at any given time after rupture nucleation, the solution is consistent with the current spatial seismic ground-motion observations and the applied GMPE, and this is exactly what is needed for EEW (Fig. 6). To minimize the effects of shortcomings in the GMPEs on the FinDer result, we build our templates from ground-motion thresholds rather than complete GMPEs. The resulting binary images and templates are also less affected by uncertainties caused by the spatial interpolation of ground-motion amplitudes, particularly in sparsely instrumented regions.
To account for increasing uncertainties in spatially interpolated ground-motion values with increasing distances from the recording stations, we recently explored the usefulness of down-weighting image pixels that are far from observational sites, similar to what is done in the USGS ShakeMaps (Worden et al., 2010). However, we found that for large gm_thresholds and application to dense station networks as in California, the effect of down-weighting is quite negligible. However, for subduction-zone events with one-sided station coverage, the benefit of down-weighting becomes more important. Böse et al. (2012) found that consideration of site effects of seismic ground motions has no significant impact on the FinDer solution.
It is also important to keep in mind that FinDer does not predict the future evolution of the fault rupture. Still, FinDer-estimated rupture dimensions allow prediction of future shaking at larger distances from the fault (as needed for EEW), which are more accurate for large earthquakes compared with what a point-source algorithm can achieve, because rupture-to-site distances can be taken into account. An instructive example is given by the M 7.8 ShakeOut scenario earthquake (Graves et al., 2008) with a 300-km-long fault rupture along the SAF, starting at Bombay Beach and heading toward LA. Using a point-source approximation of the earthquake, shaking intensities in LA are predicted as light to moderate (modified Mercalli intensity [MMI] IV–V), whereas shaking in LA predicted with the FinDer finite-fault solution is severe (MMI VIII; Böse et al., 2014). This value is much more consistent with seismic ground-motion simulations by Graves et al. (2008), which predict severe to violent shaking (MMI VIII–IX). In a big (finite-source) earthquake, much larger areas are affected by damaging ground-shaking compared with a small-to-moderate event; thus, many more people could benefit from EEW with warning times of several tens of seconds (Heaton, 1985).
Although FinDer itself does not provide predictions of future rupture, its output can be used for recognition of the fault along which rupture is occurring. This information, along with observed slip amplitudes and known fault characteristics, has potential to provide estimates of future rupture evolution (Böse and Heaton, 2010). Also, as demonstrated by Böse et al. (2014) using the Southern California Earthquake Center CyberShake dataset, the FinDer output can help to determine the direction in which a fault rupture is propagating and thus can help to enhance ground-motion predictions with consideration of directivity effects.
Last but not least, FinDer source dimensions and uncertainty estimates can constrain Global Positioning System (GPS)-based inversions of fault slip and magnitudes without saturation in large earthquakes. With the development of the FinDer-GPSlip and FinDer-BEFORES algorithms, Böse, Heaton, and Hudnut (2013) and Minson, Böse, et al. (2014) provide the first seismic-geodetic approaches to EEW that are consistent with both seismic and geodetic observations at any time after rupture nucleation. Traditionally, finite-fault-slip models are inverted for a known fixed-fault geometry. In an EEW setting, however, rupture geometry is unknown a priori, and thus, it becomes necessary to simultaneously solve for the fault geometry and slip, which is a nonlinear and computationally expensive inverse problem (Minson, Murray, et al., 2014). Using both seismic and geodetic real-time observations helps constrain both source geometry and slip and can replace simplified assumptions such as of San Andreas parallel rupture strike, which is typical in GPS inversions (e.g., Grapenthin et al., 2014).
CONCLUSIONS AND OUTLOOK
Finite-fault rupture extent and azimuth are crucial for accurately predicting seismic ground motions in large earthquakes with moment magnitudes M≥6.0 where source finiteness, rupture-to-site distances, and rupture directivity control ground shaking. Thus, detecting and modeling finite-fault ruptures in real time are essential to EEW and rapid emergency response. Following a period of extensive real-time and off-line testing, the finite-fault rupture detector algorithm, FinDer (Böse et al., 2012), was recently successfully integrated in the California-wide ShakeAlert EEW demonstration system. Since April 2015, FinDer has been actively contributing to real-time ShakeAlert reports automatically sent to several hundreds of test users in California, thus complementing the three previous point-source algorithms (τc-Pd Onsite, ElarmS, and Virtual Seismologist) and improving ShakeAlert performance during large earthquakes.
Currently, FinDer is operated as a MATLAB stand-alone code with a C++ waveform-processing module installed at three CISN datacenters (Caltech/USGS-Pasadena, University of California–Berkeley, and USGS-Menlo Park) and is continuously scanning real-time waveform data streams from around 420 strong-motion stations in California for PGA patterns indicative of earthquakes. In a joint effort of USGS-Menlo Park, ETH Zurich, and Caltech, we have recently started to translate the current FinDer code to C++. The goal is to obtain a faster and more flexible implementation that allows easier maintenance and better integration into various seismic processing systems, including EarthWorm/AQMS (as currently used in ShakeAlert) and SeisComp3 (as currently dominantly used in Europe; Olivieri and Clinton, 2012). The new C++ code will benefit from existing and widely tested free software libraries for computer vision (Open Source Computer Vision; http://opencv.org, last accessed September 2015) and geographic mapping (Generic Mapping Tools; Wessel et al., 2013).
During the next two years, we plan to increase the robustness of the current code and develop the second-generation FinDer 2 algorithm with important new features: the current FinDer code supports utilization of a single ground-motion threshold only, which in the current ShakeAlert installation is set to 70 cm/s2. This value is usually exceeded only in moderate-to-large-magnitude earthquakes, for instance within 20 km from the fault rupture for M∼6.0 or within 40 km for M∼7.0 (Cua and Heaton, 2009). A high threshold provides stable detection of large events at the cost of reduced detection speed and missed detections of smaller earthquakes.
FinDer 2 will combine multiple ground-motion thresholds: starting with small values that are typically observed in small earthquakes or shortly after rupture nucleation, FinDer 2 will progressively increase these thresholds to allow detecting earthquakes with M>3.5 with a gradual refinement of finite-fault parameter estimates in large events. This refinement will also benefit from the new error estimates in FinDer as described in this article.
DATA AND RESOURCES
Seismic waveforms used in this study were downloaded from California Integrated Seismic Network (CISN) (http://www.cisn.org, last accessed July 2015), NIED (http://www.kik.bosai.go.jp, last accessed July 2015), and Red Sismica del Noroeste de Mexico (RESNOM)/Centro de Investigación Científica y de Educació n Superior de Ensenada (CICESE) (http://resnom.cicese.mx/sitio/, last accessed July 2015). A description of the ShakeAlert performance during the 2014 La Habra earthquake was obtained from http://earthquake.usgs.gov/earthquakes/eventpage/ci15481673#general_summary (last accessed August 2015). The Global Centroid Moment Tensor (CMT) project database was searched using www.globalcmt.org/CMTsearch.html (last accessed August 2015). USGS ShakeMaps in Figure 2 were downloaded from http://earthquake.usgs.gov/earthquakes/shakemap/ (last accessed August 2015). Maps in Figures 3 and 5 were made using Generic Mapping Tools (GMT; Wessel et al., 2013).
The authors would like to thank Sarah Minson, Deborah Smith, Egill Hauksson, Men-Andrien Meier, Yannik Behr, Carlo Cauzzi, John Clinton, and two anonymous reviewers and editors for discussions on FinDer and/or proofreading and reviewing of the manuscript. This work was funded by the U.S. Geological Survey and the Gordon and Betty Moore Foundation.