A new seismogeodetic approach applied to GPS and accelerometer observations of the 2012 Brawley seismic swarm: Implications for earthquake early warning


  • Jianghui Geng,

    Corresponding author
    1. Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California, USA
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  • Yehuda Bock,

    1. Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California, USA
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  • Diego Melgar,

    1. Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California, USA
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  • Brendan W. Crowell,

    1. Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California, USA
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  • Jennifer S. Haase

    1. Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California, USA
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[1] The 26 August 2012 Brawley seismic swarm of hundreds of events ranging from M1.4 to M5.5 in the Salton Trough, California provides a unique data set to investigate a new seismogeodetic approach that combines Global Positioning System (GPS) and accelerometer observations to estimate displacement and velocity waveforms. First in simulated real-time mode, we analyzed 1–5 Hz GPS data collected by 17 stations fully encircling the swarm zone at near-source distances up to about 40 km using precise point positioning with ambiguity resolution (PPP-AR). We used a reference network of North American GPS stations well outside the region of deformation to estimate fractional-cycle biases and satellite clock parameters, which were then combined with ultrarapid orbits from the International GNSS Service to estimate positions during the Brawley seismic swarm. Next, we estimated seismogeodetic displacements and velocities from GPS phase and pseudorange observations and 100–200 Hz accelerations collected at three pairs of GPS and seismic stations in close proximity using a new tightly coupled Kalman filter approach as an extension of the PPP-AR process. We can clearly discern body waves in the velocity waveforms, including P-wave arrivals not detectable with the GPS-only approach for earthquake magnitudes as low as Mw 4.6 and significant static offsets for magnitudes as low as Mw 5.4. Our study shows that GPS networks upgraded with strong motion accelerometers can provide new information for improved understanding of the earthquake rupture process and be of critical value in creating a robust early warning system for any earthquake of societal significance.

1. Introduction

[2] Global Positioning System (GPS) networks are able to observe crustal deformation throughout the entire earthquake cycle from slow interseismic slip to strong coseismic motions. For a large seismic event, high-rate GPS can provide rapid estimates of broadband displacements, including static offsets and dynamic motions of arbitrarily large magnitude [e.g., Nikolaidis et al., 2001; Larson et al., 2003; Bock et al., 2004; Larson, 2009]. High-rate GPS-derived displacements can quickly estimate earthquake magnitude for tsunami warnings [Blewitt et al., 2006], produce centroid moment tensor solutions [Melgar et al., 2012], model finite fault slip [Crowell et al., 2012; Ohta et al., 2012; Wright et al., 2012], and track seismic wave fields [Grapenthin and Freymueller, 2011].

[3] It is recognized that high-rate GPS can also play an important role in earthquake early warning (EEW) by providing estimates of permanent displacement within minutes of initiation [e.g., Crowell et al., 2009; Allen et al., 2011]. This is especially valuable close to the source for large (>M7) events where broadband seismometers clip and accelerometer data cannot be objectively integrated to produce reliable displacements in real time [Boore and Bommer, 2005; Emore et al., 2007; Melgar et al., 2013]. Typical EEW systems [e.g., Gasparini et al., 2007; Allen et al., 2009b] depend on conventional seismic instruments, and employ P-wave detection to predict the arrival and intensity of destructive S and surface waves [Heaton, 1985; Nakamura, 1988; Allen and Kanamori, 2003]. However, algorithms only based on seismic data tend to saturate; it is difficult to distinguish an event of magnitude 7 from a larger magnitude of 8 or 9 [Wu and Zhao, 2006; Brown et al., 2009, 2011]. Although GPS excels in providing critical estimates of static offsets, GPS-derived dynamic motions by themselves are not accurate enough to identify millimeter-level or even smaller amplitude P-waves. Furthermore, P-wave arrivals have most of their energy in the vertical direction, making it more difficult for GPS because of the significantly less precise vertical component [e.g., Bock et al., 2000]. To be able to detect P-wave arrivals and address the problem of magnitude saturation, Bock et al. [2011] applied a multirate Kalman filter [Smyth and Wu, 2006] to combine high-rate GPS (1–50 Hz) displacements and accelerometer (100–200 Hz) data in near real time to estimate 3-D seismogeodetic waveforms with millimeter-level or better precision in displacement and 1 mm/s or better in seismic velocity. They demonstrated the capability of measuring P-wave arrivals for near-source stations deployed in southern California during the 2010 Mw 7.2 El Mayor-Cucapah earthquake in northern Baja California. Thus, seismogeodesy improves on both seismic-only and GPS-only methods, by providing the full spectrum of seismic motions from the detection of P-wave arrivals to the estimation of static displacements.

[4] Because of the relatively small magnitudes of the earthquakes and the excellent distribution of nearby GPS stations, the 26 August 2012 Brawley swarm provides a unique data set to examine the lower bound on the sensitivity of seismic waveforms estimated from high-rate GPS with and without strong-motion accelerometer data. Several hundred events were recorded by the California Integrated Seismic Network (http://www.cisn.org/). The swarm started at about 15:30 UTC with six events of M < 2.0 and three M2.5 events occurring within a few minutes. The largest events and the focus of this study (Table 1) occurred at 19:20.04.5 UTC (Mw = 4.6) (“Event 1”), 19:31:22.9 (Mw = 5.4) followed immediately at 19:33:00.8 (Mw = 4.9) (“Event 2––doublet”), 20:57:58.2 (Mw = 5.5) (“Event 3”), and 23:33:25.1 (Mw = 4.6) (“Event 4”) (USGS/NEIC PDE-Q database, htp://earthquake.usgs.gov/earthquakes/eqarchives). The earthquakes occurred on a northeast striking fault zone located about 6 km north of the northwest end of the Imperial fault [http://www.scsn.org/2012Brawley.html], an area that has a history of seismic swarms including one earthquake with a maximum magnitude of M5.1 in 2005 at Obsidian Buttes [Lohman and McGuire, 2007], and another in June 2008 in the same general location as the 2012 event. Chen and Shearer [2011] summarized the history of swarm data in the Imperial Valley and characterized the migration patterns and earthquake mechanisms since 1981. Initial 3-D earthquake relocations and moment tensor inversions [Hauksson et al., 2012] using the double-difference method [Hauksson and Shearer, 2005] indicated a left-lateral strike-slip motion on near vertical fault planes for Events 1–3, with a normal faulting component for Event 2, and predominantly normal motion for Event 4 (Figure 1).

Table 1. Location and Magnitude of the Events Analyzeda
EventMwLatitudeLongitudeDepth (km)Time (UTC)
  1. a

    Source is the SCEC database (http://www.data.scec.org).

Figure 1.

Brawley seismic swarm (red dots) surrounded by real-time continuous GPS stations (blue diamonds) and available continuous strong motion stations (open yellow circles) for the period of the swarm. The focal mechanisms are those computed by the SCEC for the four events considered in this study (Table 1). Coseismic displacements and 95% confidence ellipses are from the 24 h SOPAC/JPL combination.

[5] We present a novel seismogeodetic analysis method to analyze the earthquake swarm, based on precise point positioning with ambiguity resolution (PPP-AR) [Ge et al., 2008; Geng et al., 2012], supplemented by accelerometer data at locations where GPS receivers and strong motion accelerometers are in close proximity. Precise point positioning methods are attractive because current relative network positioning approaches become more cumbersome as the number of GPS stations to be processed increases from hundreds to thousands at active plate boundaries. The seismogeodetic approach applies a tightly coupled Kalman filter to GPS and accelerometer data at the observation level as an extension of the GPS-only PPP-AR approach to estimate displacement and velocity waveforms. This one-step approach differs from the two-step approach presented by Bock et al. [2011] to apply a multirate Kalman filter to previously estimated GPS displacements and raw accelerometer data.

[6] We discuss the applicability of seismogeodetic PPP-AR to EEW systems, both in the determination of static offsets and the detection of P-wave arrivals, in light of our analysis of the 2012 Brawley seismic swarm data.

2. Theory

[7] In this section we describe the technical details of the seismogeodetic PPP-AR approach and summarize its advantages compared to current GPS-only and loosely coupled seismogeodetic methods.

2.1. Ambiguity Resolution for a Single GPS Station

[8] The two main approaches to GPS analysis can be classified as relative network positioning [e.g., Dong and Bock, 1989; Blewitt, 1989] and precise point positioning [Zumberge et al., 1997]. In either case, observations to GPS satellites from a ground receiver consist of phase and pseudorange measurements at two radio frequencies (“L1” at 1575.42 MHz and “L2” at 1227.60 MHz). The phase measurements have integer-cycle phase ambiguities, which are the total number of cycles from the satellite to the receiver. It is critical for precise real-time positioning applications to be able to resolve the phase ambiguities [e.g., Bock et al., 2000].

[9] Baseline vectors between stations in a network are estimated as part of relative network positioning. Common-mode errors due to clock and hardware biases completely cancel in doubly differenced (between satellites and between stations) phase observations, thereby revealing the integer nature of the phase ambiguities. Likewise, common-mode atmospheric errors due to tropospheric and ionospheric refraction are reduced as the distances between stations shorten. Absolute position estimates are then derived by fixing (or tightly constraining) the true-of-date coordinates of one or more reference stations within the network to precise a priori values with respect to a global terrestrial reference frame.

[10] Ambiguity resolution for a single GPS station is difficult because undifferenced phase ambiguity estimates contain noninteger biases, which originate in receiver and satellite hardware. To recover the integer properties of undifferenced ambiguities in PPP analysis, the fractional cycle parts of the noninteger biases can be estimated using a network of reference stations [e.g., Ge et al. 2008; Geng et al., 2012] outside the region of active deformation. Then the fractional-cycle bias (FCB) estimates allow clients to attempt ambiguity resolution for a single station using the PPP-AR method [e.g., Geng et al., 2011]. This approach also requires precise satellite clock and orbit information. In the following section, we describe a tightly coupled Kalman filter that extends PPP-AR analysis by adding very high-rate strong motion accelerometer data.

2.2. Tightly Coupled Seismogeodetic Filter

[11] For seismogeodesy, we have available very high-rate collocated accelerometer data in addition to high-rate GPS data. Bock et al. [2011] presented a loosely coupled multirate Kalman filter that optimally combines GPS displacement and accelerometer data in a two-step process that can be implemented in real time. In the first step, the GPS phase and pseudorange data are analyzed to estimate station displacements––this can be done using either relative network positioning or PPP-AR. In the second step, the GPS displacements are combined with the accelerometer data. There is no feedback between the two steps so we call this a loosely coupled Kalman filter. Here we present a tightly coupled Kalman filter that operates on the raw GPS and accelerometer data in a single step. This formulation is applicable to the estimation of FCBs as part of the PPP analysis of the reference GPS network outside of the zone of deformation, as well as for individual PPP-AR clients within the seismically active region.

[12] Without loss of generality, we assume that the integer-cycle “wide-lane” (the difference between L1 and L2) ambiguities have been resolved through a linear combination of phase and pseudorange measurements [e.g., Teunissen and Kleusberg, 1998]. Since the wide-lane wavelength is about 86.2 cm compared to the 19 and 24 cm wavelengths of the L1 and L2 phases, respectively, this is straightforward even for reference networks of global extent. The wide-lane ambiguities are then applied to the analysis of ionosphere-free carrier phase observations (which have noninteger ambiguities), leaving integer-cycle “narrow-lane” ambiguities with a wavelength of 10.7 cm [e.g., Dong and Bock, 1989]. Then, the narrow-lane carrier-phase measurement for reference station i (i = 1, … ,r) to satellite j (j = 1, … ,s) is given by

display math(1)

where math formula denotes the geometric distance between station i and satellite j; c is the speed of light in vacuum, ti is the receiver clock error, Ti is the zenith tropospheric delay and math formula is the mapping function, math formula is the narrow-lane wavelength where f1 and f2 are L1 and L2 frequencies, respectively, math formuladenotes the narrow-lane integer ambiguity, math formula and math formuladenote the fractional part of noninteger receiver- and satellite-specific hardware biases, respectively, and math formula denotes the random error with math formula. Multipath effects, higher-order ionospheric effects, etc. are ignored for brevity. As part of the GPS analysis we obtain a real-valued estimate for math formula; math formula is eliminated by differencing between satellites leaving the integer part math formula and the fractional part math formula to be estimated. Once the math formula estimates are collected from the r reference stations, we can derive the FCB estimate for satellite j (j = 1, … ,s) by

display math(2)

where math formula is the estimate of math formula at station i. Increasing the number of stations in the reference network will improve the reliability and accuracy of math formula [Geng et al., 2012]. Because the result is averaged over many stations, it is not necessary for the stations to be the same as the PPP client stations, only that the analysis in the PPP clients be consistent with the larger reference network.

[13] The FCB products for all satellites math formula (j = 1, … ,s) determined in the first step are then distributed to the individual PPP clients, where single-station ambiguity resolution can be attempted. Similar to equation (1), at a particular client l (to distinguish from subscript i used for reference stations) at epoch k, we linearize the narrow-lane carrier-phase observation

display math(3)


display math(4)

where math formula denotes the increment of a parameter estimate, math formula is the state vector comprising the position increment math formula, the velocity math formula and the acceleration math formula, and math formulais the design matrix in which math formula and math formula are the station and satellite positions, respectively, and math formula. The satellite bias math formula is assigned the value math formula, and the receiver math formula is assimilated into the receiver clock estimate, or equivalently can be removed by between-satellite differencing. As a result, the estimate for math formula is reduced to an estimate for math formula where the integer property has been recovered. Ambiguity resolution for a single station can then be attempted. Once successfully fixing math formula to integers for all visible satellites, we have achieved the PPP-AR solution for an individual station (client).

[14] For a tightly coupled GPS/accelerometer solution, after correcting the raw accelerometer data for gain, we model the accelerometer data at station math formula and epoch math formula as

display math(5)

where math formula is the corrected accelerometer measurement, math formulais the true acceleration, math formula is an acceleration bias which is estimated as a random walk parameter to accommodate slowly time-varying changes, especially during earthquakes when the bias can change significantly, and math formula is the random error with math formula. Other errors due to, for example, instrument tilts are reasonably presumed to be minimal during the 26 August 2012 Brawley swarm and ignored in this study. Equation (5) is combined with equation (3) for the measurement update. The transition equation for the state vector in equation (4) takes the form of

display math(6)

where math formula is the sampling interval of the accelerometer data. Equation (6) is used for the Kalman filter time update.

2.3. Advantages of the Tightly Coupled Kalman Filter

[15] The key difference between the tightly coupled Kalman filter presented here and the loosely coupled filter in Bock et al. [2011] is that in the tightly coupled case the accelerations are used as additional data to resolve ambiguities. The accelerometer data are applied as tight constraints on the position variation between epochs. This single-step process improves cycle-slip repair for GPS carrier-phase data and rapid ambiguity resolution after GPS outages [Grejner-Brzezinska et al., 1998]. This is confirmed with the Brawley swarm data as discussed in the supporting information (section 'Introduction' and Figure S1).1

[16] As with the loosely coupled filter the tightly coupled filter also minimizes step functions possibly introduced by tilt in the accelerometer observations. Furthermore, biases, bkl, in the accelerometer data are estimated along with other parameters of interest. Hence, no pre-event mean needs to be eliminated from the acceleration data before starting the Kalman filter. In addition, bkl is estimated at each epoch as a random walk parameter to mitigate possible drift in the accelerometer data due to translations (indistinguishable from rotations) [Trifunac and Todorovska, 2001] and temperature changes.

2.4. Advantages of GPS PPP-AR Over Relative Network Positioning

[17] There are several advantages to the PPP-AR approach. First, it is highly efficient because the satellite clocks and FCBs are estimated only once for positioning any number of clients. The data processing at each client is independent and does not affect any other clients. Relative network positioning is complicated by the need to assign baselines, overlapping Delaunay triangles [Crowell et al., 2009], or overlapping subnetworks [Bock et al., 2011]. This is a critical difference as one is faced with the challenge of analyzing hundreds to thousands of stations in real time. Furthermore, intermittent station dropouts complicate relative network positioning. Therefore, PPP-AR can be efficiently applied to large GPS networks deployed over a wide area such as around the Circum-Pacific Seismic Belt or at isolated stations in remote areas. Second, the PPP-AR approach compared to relative network positioning does not require a local reference station, which might be displaced during a large event. Instead, PPP-AR requires a continental- or global-scale reference network well outside the zone of expected deformation, yet still has the same satellites visible as the client stations. Finally, if undifferenced ambiguities can be successfully fixed the positioning accuracy is comparable to that of relative network positioning [e.g., Bertiger et al., 2010; Geng et al., 2010].

3. Data Analysis

3.1. An Operational Real-Time PPP-AR System at SOPAC

[18] At the time of the 2012 Brawley swarm and as part of a prototype EEW system for the Western U.S., we had already implemented at the Scripps Orbit and Permanent Array Center (SOPAC) an operational PPP-AR service center for estimating satellite clocks and FCBs. These parameters are intended for distribution to PPP clients in real time whether at a centralized processing facility, at a remote computer with internet access to data from a specific station, at a local processor at the remote station or within the GPS receiver itself. With predicted ultrarapid satellite orbits from the international GNSS service (IGS), the SOPAC service center generates satellite clocks every second for each visible GPS satellite using 46 reference stations, and FCBs every 5 s using 48 stations across North America (Figure 2—Some of the stations are overlapping). The 1 Hz reference station data are collected from IGS and UNAVCO's Plate Boundary Observatory (UNAVCO/PBO) servers. The reference network for satellite clock estimation is chosen to be of continental scale to reduce errors; another option is to use satellite clocks from existing sources based on a global distribution of stations. On the other hand, the FCB network is chosen to be as close to the area of interest as possible, while staying sufficiently outside the region of expected deformation. The reference stations for the SOPAC service are chosen to be further than 200 km from the primary zones of tectonic deformation in California, Oregon and Washington to avoid contamination of the satellite clocks and FCBs during a large seismic event in that region. For the FCB determination, we choose a reference network that is close to the western U.S. coast (rather than a single reference station that is chosen for relative network positioning). Should one of the FCB network stations be subject to dynamic motions, the impact would be minimized by the averaging in equation (2). We note that for the western U.S. the FCB determination is challenged by the sparseness of real-time off-shore reference stations in the Pacific. The reference station positions are fixed to true-of-date estimates with respect to ITRF2008 [Altamimi et al., 2011] produced through an (1–2 week) extrapolation of combined modeled time series based on SOPAC's and Jet Propulsion Laboratory's (JPL)'s routine weekly analysis of 24 h, 30 s sampled data from a global and regional set of continuous GPS stations (http://sopac.ucsd.edu/processing/coordinates/sector.shtml) and made available through the GPS Explorer data portal (http://geoapp.ucsd.edu/). Real-time SOPAC PPP-AR results for the high-rate station GLRS in southern California (Figure 1) from 11 August to 5 September 2012 show that ambiguity resolution in PPP improves the root-mean-square (RMS) difference between the position estimates and ground truth from 20, 30, and 61 mm without ambiguity resolution to 15, 12, and 40 mm for the North, East, and Up components, respectively.

Figure 2.

Distribution of high-rate GPS stations used by the SOPAC PPP-AR system. Solid green circles denote the 46 stations used for clock estimation whereas solid red triangles denote the 48 stations used for FCB determination. The solid black star shows the location of the 26 August 2012 Brawley seismic swarm.

3.2. GPS PPP-AR Analysis

[19] For the 26 August 2012 Brawley earthquake swarm, we used SOPAC's PPP-AR system to process high-rate GPS data from 16 PBO stations and 1 Southern California Integrated GPS Network (SCIGN) station in this region (Figure 1). The stations stream 1 Hz GPS data, the normal operational setting for most real-time GPS networks. For this study, we requested after the fact that UNAVCO/PBO download 5 Hz data from the receiver buffers at the 16 PBO stations. We then processed the 5 Hz data in a simulated real-time mode using SOPAC's 1 Hz satellite clocks, 5 s FCBs, and the predicted IGS ultrarapid orbits published for that period. The 1 Hz data at USGS station BOMG were also processed in this way. Further details on PPP-AR estimation are provided in section 'Theory' of the supporting information.

[20] In practice, the transmission of high-rate GPS data from the reference network (or a client station) to server has a typical latency of 0.4–1.0 s. The satellite clocks and FCB parameters are continuously estimated and made immediately available to clients. The PPP-AR processing at individual stations (clients) can then be performed at each epoch with a delay about 1 s after data arrival at the data analysis center.

3.3. Tightly Coupled Kalman Filter Analysis

[21] There are only a few collocated GPS and seismic stations in southern California (Figure 1). For this study we identified three suitable collocations. The first pair consists of GPS station P506 sampling at 5 Hz and accelerometer site WLA sampling at 200 Hz, separated by 2.6 km and approximately 8 km from the source. This site pair was the only collocation available within the Brawley Seismic Zone. Emore et al. [2007] demonstrated good agreement of 1 Hz GPS and strong-motion data with instrument separations of up to 4 km. The second pair is GPS station P494 sampling at 5 Hz and strong motion site WES sampling at 100 Hz, separated by about 80 m and 34 km from the largest event. The third and most closely spaced pair (within 10 m) is BOMG (1 Hz) and strong motion site BOM (200 Hz), about 42 km from the swarm events. The strong motion sensors are observatory grade EpiSensor accelerometers and the broadband sensors are STS2 instruments, both on 24 bit Quanterra data loggers. For each pair, we combined the 1–5 Hz PPP-AR derived displacements with 100–200 Hz acceleration measurements. We also considered pair P493/ NP.286 (Figure 1) but the strong-motion site NP.286 is located inside the second story of a building and its record is complicated by the building response.

[22] As a first step the raw accelerometer data were corrected for gain. In the tightly coupled Kalman filtering, the precision of the raw accelerometer data from site WLA was taken to be 10 mm/s2 for all three channels to account for its relatively long distance from station P506 (alternatively, we could have applied a time shift to the accelerometer data). In contrast, we applied 0.1 mm/s2 for sites WES and BOM, which are closer to their GPS counterparts. The process noise of the accelerometer bias parameters is presumed to be 0.001 mm/s2.5. As a comparison, in the loosely coupled approach of Bock et al. [2011] the pre-event means are removed from the accelerometer data. Then, the two filter parameters for the periods of shaking, the system variance q and the measurement variance r, are determined from 60 s of pre-event noise on each channel of the accelerometer and GPS, respectively. Also, a near-real-time smoother with 5 s lag is applied to the loosely coupled filter.

4. Results

4.1. PPP-AR Analysis Using Only GPS Data

[23] We evaluated the PPP-AR approach, first using only GPS data in the context of real-time analysis for EEW. The results are of interest in the case that only GPS data are available in real time near the source of a large earthquake. Furthermore, the GPS-only approach can be used for rapid and reliable estimates of earthquake magnitude, fault geometry and rupture characteristics for large events often faster than traditional seismic methods on their own [e.g., Melgar et al., 2012; Crowell et al., 2012; Ohta et al., 2012; Wright et al., 2012].

[24] The RMS of the differences between the 1 or 5 Hz GPS-derived ambiguity-fixed position estimates and the true-of-date SOPAC/JPL positions are 31, 14, and 32 mm on average while the standard deviations (1σ) are 9, 6, and 29 mm in the North, East and Up directions, respectively, based on 5 h of data for all sites before the start of Brawley swarm activity. In contrast, the RMS for the ambiguity-float positions are 29, 20, and 57 mm, and the standard deviations (1σ) are 9, 17, and 50 mm, respectively. This is consistent with earlier results that indicate that ambiguity resolution improves the positioning accuracy of real-time PPP, especially in East and Up components [e.g., Geng et al., 2011]. In addition, for the 5 h data span, we compared PPP-AR to instantaneous relative positioning [Bock et al., 2000, 2011] (Table 2). We were able to assign for the latter a reference station just outside the zone of deformation because the earthquake magnitudes were so small. We can see that PPP-AR outperforms instantaneous relative positioning by 31%, 60%, and 48% in the standard deviations for the North, East and Up components, respectively. This improvement is attributed to the forward (smoothing) Kalman filter used in PPP-AR, whereas instantaneous relative positioning processes each epoch of data independently [Bock et al., 2000], and to improved single-epoch ambiguity resolution in the PPP-AR process. Other relative positioning methods that use Kalman filter estimation should provide the same level of precision as PPP-AR [e.g., Bertiger et al., 2010; Geng et al., 2010], but are more complicated to apply in real-time scenarios. In the remainder of this paper, we take the individual standard deviation (1σ) from the real-time PPP-AR processing as the precision of the GPS position time series (Table 2).

Table 2. Standard Deviation (1σ, mm) of the Differences Between the 1–5 Hz GPS-Derived Ambiguity Fixed PPP and Instantaneous Position Estimates, and the True-of-Date SOPAC/JPL Positions Over 5 h Preceding the Brawley Swarm
 PPP-ARInstantaneous Relative Network Positioning

[25] We show the displacement waveforms for the 17 GPS stations during all four events in the supporting information (Figures S2–S5). From the horizontal components of the three stations P506, P499, and P495 that are nearest to the epicenter (<8 km) for the largest event (Event 3, Mw 5.5; Figure S4 in supporting information), earthquake-induced displacements can be clearly perceived at around 20:58:05 UTC, with a peak-to-peak amplitude of up to 100 mm, followed by about 20 s of shaking of up to 50 mm amplitude. For more distant stations, the peak-to-peak amplitudes are reduced gradually down to about 20 mm in East at station P744, which is over three times its standard deviation (see Table 2). For stations farther than 30 km from the epicenter, seismic signatures can hardly be discerned in either North or East components. For Event 2 with two subevents of Mw 5.4 and Mw 4.9 (Figure S2 in supporting information), seismic displacements can also be distinguished at stations up to 20 km away from the epicenters, although the peak-to-peak amplitudes are below 30 mm.

[26] For Event 1 and 4 with magnitudes of Mw 4.6, we cannot find any significant coseismic displacements (Figures S2 and S5 in supporting information). As expected, no significant coseismic displacements are observed in the vertical component for any events in the sequence, even at the stations closest to the epicenters. The 24 h SOPAC/JPL analysis show significant coseismic offsets at 11 of the 17 stations (Table 3). Maximum horizontal magnitudes are not greater than 25 mm for all events, except for station P499 with a magnitude of 49 mm. For P499, the estimated coseismic displacement based on all 4 events is 30 mm (Table 3), or only about 60% of the estimates for the 24 h solutions. This might be due to postseismic deformation present in the 24 h solutions, but most likely is due to the precision of the epoch-wise GPS estimates. We can conclude that real-time GPS-only results alone, although quite impressive compared to postprocessed analysis of longer spans of data, are not precise enough to reliably estimate the small coseismic offsets for the Brawley swarm data set, except for the two near-field stations (P499 and P506), and are certainly not precise enough to detect P-wave arrivals.

Table 3. Total Coseismic Offsets in mm From the SOPAC/JPL 24 h Solutions From the Day Preceding the Four Events to the Day Aftera
  1. a

    Uncertainties are one sigma values.

  2. b

    Coseismic offsets from GPS-only solutions for all four events.

  3. c

    Coseismic offsets from seismogeodetic solution of event 3.

CRRS−8.6 ± 0.34.5 ± 0.4−0.1 ± 0.4
GLRS−4.6 ± 0.3−2.6 ±0.43.0 ± 0.4
P495−27.3 ± 0.37.7 ± 0.41.7 ± 0.4
P497−1.2 ± 0.48.4 ± 0.4−0.0 ± 0.4
P4981.2 ± 0.420.7 ± 0.4−3.6 ± 0.5
P49945.6 ± 0.4−18.1 ± 0.49.5 ± 0.5
28.1 ± 3.5b−10.8 ± 2.7b23.5 ± 6.2b
P5012.6 ± 0.4−0.4 ± 0.5−1.5 ± 0.5
P50217.2 ± 0.4−3.7 ± 0.42.0 ± 0.5
P503−7.5 ± 0.40.9 ± 0.41.7 ± 0.5
P506/WLA−8.2 ± 0.4−26.4 ± 0.4−6.5 ± 0.6
−3.8 ± 2.4c−13.4 ± 1.9c11.6 ± 5.4c
P5091.7 ± 0.3−0.2 ± 0.4−0.7 ± 0.4

[27] Some systematic GPS errors, such as multipath effects and orbit/clock errors might easily result in a noise level of up to 20 mm in the real-time horizontal displacements. To ascertain whether or not multipath is a major contributor, we processed the GPS data for 25 August and shifted the resultant time series by 246 s to take into account the sidereal time shift [e.g., Genrich and Bock, 1992]; the GPS satellites have approximately 12-hour periods so that the geometric relation of the satellite pass to the location of local reflectors is repeated every 24 hours. The results are shown in Figure 3 for the largest event (Event 3, Mw 5.5) for five representative stations, the three closest ones (P506, P499, and P498) and two at distances of about 20 km (P497 and P507). The results for the other three (smaller) events are shown in Figures S6–S8 in the supporting information. We find that the time series for 25 and 26 August do not resemble each other, which makes it unlikely that multipath is contributing to the error. Satellite orbit/clock errors will affect all sites uniformly within a regional area, but we do not see any common characteristics across the time series from 15 to 30 s. Moreover, for stations P506, P499, P498, and P497 their peak displacements from 10 to 30 s are significant at the 95% confidence level since they exceed twice the GPS standard deviations. Also significant is the fact that stations P506 and P499 clearly manifest static offsets, with the P499 East component showing more than 20 mm of static offset after the earthquake. For Event 2 in Figure S7 in the supporting information, we also see no significant correlation between the time series for 25–26 August that would be indicative of repeating multipath noise. The peak displacements at stations P506, P499, and P498, which are nearer to the epicenter, are significant at the 95% confidence level. We can surmise that the noise level is primarily due to the inherent precision of real-time GPS displacements [e.g., Langbein and Bock, 2004; Genrich and Bock, 2006], rather than to any unmodeled systematic effects.

Figure 3.

GPS-derived horizontal displacements of five stations for Event 3 after 20:57:50 UTC on 26 August 2012 (black traces), compared to those (blue traces) for the same period on the previous day (25 August). All blue traces are offset by 4 cm for clarity. Dashed red lines show the ranges of twice the noise level (2σ) from the value prior to the earthquake. Vertical red lines mark the origin time of earthquake. Top-left corners of left plots show the names and epicentral distances of the five stations.

[28] Our results are consistent with previous reports of PPP-AR precision in postprocessing mode [e.g., Bertiger et al., 2010] and single-epoch, real-time, relative network positioning [e.g., Langbein and Bock, 2004; Genrich and Bock, 2006]. Thus, PPP-AR can be applied in real time at about the same level of precision as relative network positioning. Although we cannot gauge the vertical sensitivity in these examples, earlier studies indicate that single-epoch horizontal components are more sensitive by as much as a factor of 5–10 than the vertical components [e.g., Bock et al., 2000]. Also as expected from earlier studies, GPS-only displacements are sensitive enough to detect coseismic displacements for earthquakes of about Mw 5.5 and greater with near-field (∼10 km) observations. Some improvements in sensitivity could be obtained using sidereal filtering [e.g., Choi et al., 2004]. However, we have not tested this because it is more cumbersome in real-time scenarios and may not be that effective since we see no interference due to multipath in these examples, consistent with the analysis of Genrich and Bock [2006].

4.2. Seismogeodetic PPP-AR

[29] Here, we apply the tightly coupled Kalman filter (equations (3)-(6) to the 1–5 Hz GPS data and 100–200 Hz accelerations to estimate 100–200 Hz seismogeodetic accelerations, velocities and displacements of the four events for the three collocated GPS/accelerometer pairs, P506/WLA, P494/WES, and BOMG/BOM. The 108 waveforms are shown in Figure 4 over an interval of 200 s, spanning the entire period of seismic shaking. The enlarged view of the first 10 s of the seismogeodetic velocity in Figure 5 for station BOMG/BOM shows that the P-wave can be picked very accurately from the vertical component, and the S-wave from the horizontal components, since they are well aligned with Southern California Earthquake Center (SCEC) P-wave and (where-available) S-wave picks. This is true for all four events, including the Mw 4.6 event at 42 km distance. This is primarily due to the high sensitivity of the strong motion accelerometers compared to the GPS. The GPS-only velocities, differentiated from the GPS-only displacements are too noisy to detect the P-wave for this size event. Genrich and Bock [2006] examined GPS-only displacement waveforms during periods of seismic quiescence and concluded that high-frequency noise (greater than 0.5–0.3 Hz) of single-epoch GPS positions is dominated by sources with a white noise spectrum. This is consistent with our seismogeodetic results from the Brawley swarm data during shaking. In this case, the higher frequency components of the GPS/accelerometer combination are much more precise than the GPS-only displacements, which is a consequence of the greater sensitivity of the accelerometer data at the higher frequencies and to the Kalman filter which reduces systematic effects due to the accelerometers.

Figure 4.

Motions recorded at collocated stations WLA/P506, WES/P494 and BOM/BOMG. For each station, the top row is acceleration measured by the strong motion instrument. The middle row is seismogeodetic velocity. The bottom row is displacement, with the blue trace from the tightly coupled Kalman filter and the gray trace from the PPP-AR GPS-only processing. Vertically dashed lines indicate SCEC P-wave picks for all events and S-wave picks when available. Time axis is relative to event times given in Table 1.

Figure 5.

Seismic velocities at the beginning of seismic shaking for Events 1–4 for combined GPS/accelerometer station BOMG/BOM, roughly 42 km northeast of the swarm as a function of origin time. The red vertical lines are the SCEC P- and (when available) S-wave picks.

[30] As seen in Figure 6 for the Mw 5.4 event at station P506, and for the Mw 5.5 event (not shown), the seismogeodetic displacements in the first 10 s contain a clear view of the progression of the long period near-source dynamic and static ground displacements, which has not previously been available for earthquake studies. This has been shown in previous studies for much larger earthquakes with collocated GPS and seismic instruments [Bock et al., 2011; Crowell et al., 2012; Melgar et al., 2013], but this is the first time it has been recovered for these size events. Significant low-frequency displacements occur between P- and S-wave arrivals, which may be due to instrument response due to tilt when using accelerometers alone rather than to real seismic deformation. Even with a robust method of baseline correction [Boore and Bommer, 2005], integrated strong motion records can have significantly different displacements between the P- and S-wave arrivals as well as different final offsets from the GPS time series, as shown by Emore et al. [2007; Figure 6] and Melgar et al. [2013]. In real-time operations when the size of the event is not known, it is critical to have a consistent technique that recovers displacements reliably prior to S-wave shaking for both small (Figure 6) and large events. This sensitivity is important in the seismogeodetic velocities for the purposes of EEW based on, for example, the predominant period of the P-wave, Pd [Crowell, 2013].

Figure 6.

The displacements and velocities at the beginning of seismic shaking for Event 3 and the combined GPS/accelerometer pair P506/WLA. The red vertical lines are the SCEC P- and S-wave picks.

[31] The displacements for the Brawley swarm earthquakes are relatively small, and except for the near-field stations the permanent coseismic offsets are barely detectable with the GPS-only solutions. However, the seismogeodetic displacements with significantly reduced noise show considerable more detail, in particular in the vertical component compared to the GPS-only displacements seen in Figure 4. For combination P506/WLA, the seismogeodetic displacements are noisier than those for sites P494/WES and BOMG/BOM, because of the greater distance (between P506 and WLA), which is why we applied a relatively low precision to the accelerometer data at WLA.

[32] Although the seismogeodetic displacements seen in Figure 4 have reduced high-frequency noise, they exhibit some undesirable long period variations as the intensity of shaking diminishes. This is primarily due to GPS systematic errors (multipath). This illustrates the threshold of sensitivity and that the permanent displacements are small relative to the signal amplitude. The important point is that the seismogeodetic displacements are accurate over the duration of dynamic motion, here for the first 20 s or so, which include P-wave and S-wave arrivals. This information is important in developing scaling relationships to estimate earthquake magnitude from the first few seconds of shaking, in the context of EEW [Crowell, 2013]. The sawtooth pattern seen in Figure 6, might be due to a possible misorientation of the accelerometer data [e.g., Rios and White, 2002; Emore et al., 2007] and is an artifact of using only a forward filter. It could also indicate a trade-off in motion relative to the estimated accelerometer bias at very low amplitude. In Bock et al. [2011] we eliminated the sawtooth pattern by 5 s backward smoothing. Although it could also be implemented in the tightly coupled approach, this is a more complex and time consuming operation and would not change our basic conclusions.

[33] The initial directions of first-motion at P506/WLA, seen in the displacements in Figure 6, exhibit a southwest orientation for Events 1–3, but are ambiguous for Event 4, which has predominantly normal motion (Figure 1). The static offsets for the first three events are generally in the south to south-west direction, consistent with left-lateral strike-slip mechanisms on vertical faults (Figure 1, Table 3). The coseismic seismogeodetic displacements in the horizontal components of near-fault combination P506/WLA for the largest event (Event 3–Mw5.5, Figures 4 and 6), constitute a large fraction of the total coseismic displacement in the 24 h solutions; a displacement of about 4 mm in the East component and about 13–14 mm in the North component, which is in the same direction and about 50% of the total displacements estimated from the 24 h SOPAC/JPL solutions (Table 3).

[34] STS2 recordings clip at 13 mm/s, and the very impulsive S-wave for P506 (Event 3), apparent in the seismogeodetic velocity (Figure 6), has amplitudes in excess of 25 mm/s likely saturating a broadband recording at 8 km from the source. The seismogeodetic velocity at P506, however, stays on scale. These reliable peak ground velocities in the near field are potentially of value for ground motion prediction relations for peak ground velocity, once again without relying on unreliable real-time integration of the acceleration records.

[35] We compared 60 s of the seismogeodetic velocity estimates to those measured by the STS2 broadband instruments at WES (Figure 7) and BOM (Figure 8) before they clipped by deconvolving the instrument response from the seismometer traces. To stabilize the frequency domain deconvolution we first applied a 0.01–2 Hz band-pass filter to the data. We then compared the first few (unclipped) seconds of the seismometer record, which contain the small amplitude P-waves, with the velocity output by the seismogeodetic filter. For comparison the seismogeodetic velocities derived from both tightly coupled and loosely coupled filters were low pass filtered at 2 Hz. No high-pass filtering was necessary as was required to stabilize the deconvolution in the seismometer; the low-pass filtering of the Kalman filtered data was performed just to establish an objective comparison.

Figure 7.

Comparison of the vertical component of 60 s seismic velocity waveforms measured by the STS2 seismometer and loosely coupled and tightly coupled Kalman filter output from P494/WES. Note that only the first (Mw = 5.4) earthquake is shown for Event 2. Event times are given in Table 1.

Figure 8.

Comparison in the vertical component of 60 s velocity waveforms measured by STS2 seismometer and Kalman filter output of GPS displacements and accelerometer data from BOMG/BOM. Note that Event 4 is preceded by a smaller seismic event, apparently unrelated to the Brawley seismic swarm so that the first seconds are obscured by the coda of the smaller seismogram (see also Figure 4). The event times are listed in Table 1.

[36] After removing pre-event mean from all records, we can clearly see that the estimated seismic velocities are in excellent agreement with the observed broadband velocities at frequencies from 0.01 to 2 Hz with long-wavelength biases of up to 1 mm/s for some events (e.g., Event 2 at P494/WES and Event 4 at BOMG/BOM). The agreement with Event 3 (the largest event— Mw 5.5) is quite striking, and is consistent with that seen in Figure 6 of Bock et al. [2011] for the P494/WES collocation for the much larger magnitude (Mw 7.2) 2011 El Mayor-Cucapah earthquake. Table 4 shows the RMS of the differences between the Kalman filter recovered velocities and the measured velocities by the two STS2 seismometers for the entire 60 s interval. The RMS values range from 0.1 to 1.6 mm/s. Despite the presence of long period noise, we can infer that the continuous estimates of seismic velocities for earthquakes with magnitudes of Mw 4.6 or greater are, for the purpose of estimating near-source ground motions, in agreement with those measured by much more precise broadband instruments in all three coordinate components.

Table 4. RMS of the Differences Between the Kalman Filter Recovered Seismic Velocities and STS2 Velocity Measurements at Stations P494/WES and BOMG/BOM for the Four Largest Events During the 26 August 2012 Brawley Swarm.a
 P494/WES (mm/s)BOMG/BOM (mm/s)
EventsTightly CoupledLoosely CoupledTightly CoupledLoosely Coupled
  1. a

    Both tightly coupled and loosely coupled filters are presented. Pre-event biases have been removed.
2 (first event)1.371.580.140.33

[37] Figures 7 and 8 also compare the performance of tightly coupled and loosely coupled filters in recovering the seismic velocity waveforms. Overall, for all events, both filters perform well in capturing the features in the frequency band 0.01–2 Hz. However, compared to the measured velocities, the velocity estimates recovered by the loosely coupled filter have relatively larger long-wavelength biases than those by the tightly coupled filter. Specifically, in Table 4, all RMS values derived from the tightly coupled filter, except for Event 3 at BOMG/BOM, are smaller than those from the loosely coupled filter by up to 0.2 mm/s. The long-wavelength biases may be related to the time-varying biases in the accelerometer data (perhaps due to temperature-dependent drift), which are estimated in the tightly coupled filter, but ignored in the loosely coupled filter.

[38] We note that Event 4 at BOMG/BOM (Figure 4) is preceded by what appears to be local noise near the station as there is no record of an earlier event in the CISN earthquake catalog. This noise obscures the P-wave arrival at this station.

5. Applicability to EEW

[39] We have demonstrated that broadband displacement waveforms estimated from a network of collocated GPS and strong motion instruments can detect P-wave arrivals near the source for earthquakes as small as Mw 4.6 and at distances up to 42 km. Therefore, seismogeodesy not only provides the permanent deformation but also has the potential to provide a significant improvement for EEW methods that are based on the maximum amplitude of the first few seconds of the P-wave (Pd) or the predominant period ( math formula or τc). This then allows prediction of the time of arrival and intensity of S-waves based on data from a single station [Heaton, 1985; Allen and Kanamori, 2003; Kanamori, 2005; Böse et al., 2012]. The problem with systems based solely on seismic instrumentation is magnitude saturation for earthquakes greater than about M 7 [Wu and Zhao, 2006; Brown et al., 2009, 2011]. Seismogeodetic time series have been shown to be useful for large events [Bock et al., 2011; Crowell et al., 2012; Melgar et al., 2013]. This study of the 2012 Brawley seismic swarm demonstrates the lower magnitude bound for the usefulness of the seismogeodetic technique.

[40] Seismogeodetic waveforms are also important as new input for better understanding of earthquake physics by providing an unprecedented view of the progression from the dynamic ground displacements to the final static offsets. Traditional seismic methods rely primarily on broadband seismic and strong motion observations with their inherent weaknesses during large earthquakes. For example, the existence of an earthquake nucleation phase has been hypothesized [Ellsworth and Beroza, 1995] and there is ongoing controversy whether earthquakes are deterministic or not [e.g., Olsen and Allen, 2005; Rydelek and Horiuchi, 2006; Olsen and Allen, 2006]. Scaling relationships based on seismogeodetic displacements during the first few seconds of P-wave arrival for medium to great earthquakes appear to lend credence to the hypothesis that rapid estimation of earthquake magnitude can be estimated before the termination of seismic rupture [Crowell, 2013]. If so, that would have critical implications for EEW systems as well as better understanding the physics of seismic rupture.

[41] Broadband displacements from the GPS/accelerometer combination provide two advantages: (1) the ability to detect P-waves and subsequent S and surface waves on-scale in the near-source region, and (2) a precise measurement of long period and static offsets that accompany medium or greater earthquakes. Generally, only the latter advantage has been stressed in the literature [e.g., Allen and Ziv, 2011]. We can conclude that an EEW system based solely on regional GPS networks upgraded with strong motion accelerometers can effectively provide independent alerts for any conceivable earthquake large enough to require early warning, which would improve the robustness of alerts provided by a seismic network.

[42] A further benefit of our approach is related to the issue of false alarms (predicting a false event as well as neglecting to predict a significant event), which is a recognized problem for both seismic-only and geodetic-only methods, in particular when the station spacing in a network is sparse. False triggers in the geodetic-only time series can be minimized using the seismogeodetic approach described in this paper. An EEW alarm would not be issued if there is no significant change in the estimated seismic velocities (i.e., no significant seismic shaking), which are continuously estimated without clipping, as is the case for strong motion networks. However, the seismogeodetic data could independently confirm or deny the detection of a large event by a seismic network, depending on the retrieved coseismic offsets.

[43] We have shown in this paper that PPP-AR is an efficient and viable method to analyze high-rate GPS data compared to relative network positioning methods, and with the same precision but without the requirement to choose a reference site. If the client processing is implemented at the site, it enables additional advantages for EEW based on observations at single stations with on-site processing capabilities [e.g., Kanamori, 2005].

[44] There are currently hundreds of real-time GPS stations in the Western U.S., only a fraction of which are collocated with seismic instruments. One approach to achieving a seismogeodetic capability is to upgrade the existing GPS stations with low-cost MEMS accelerometers, which have been shown by extensive large outdoor shake table tests to be adequate for this purpose [e.g., Bock et al., 2011]. Other shake table tests have shown that certain low-cost MEMS accelerometers are sensitive enough to detect a M > 3 earthquake at near-field distances (10 km) and M > 5 at regional distances (100 km) (Robert Clayton, personal communication). We can infer that these types of accelerometers directly collocated at the GPS stations would have been adequate to monitor the larger events of the 2012 Brawley swarms.

6. Conclusions

[45] We have established that single-epoch GPS-only PPP-AR is a highly efficient and viable method to analyze high-rate GPS data, with the same precision as relative network positioning methods but without the requirement to choose a local reference station. Rather, positions are independently estimated with respect to an external reference frame realized through the true-of-date global coordinates of the reference network stations and estimated satellite orbits and clocks. FCBs estimated from the reference network allow for ambiguity resolution at each station within the zone of deformation. This methodology is particularly useful for continuous GPS networks of hundreds to thousands of stations deployed within zones of tectonic deformation and seismic risk because the computation time scales linearly as the number of stations increases. However, like relative network positioning, it is limited in precision to about 20 mm for detection of real-time coseismic displacements and is unable to detect P-wave arrivals.

[46] We have shown the lower bound of sensitivity for GPS-only and combined GPS/accelerometer seismogeodetic waveforms using data collected from four near-source events of the 26 August 2012 Brawley seismic swarm, ranging in magnitude from Mw 4.6 to 5.5. During periods of seismic shaking the tightly coupled seismogeodetic PPP-AR analysis provides continuous unclipped estimates of broadband displacements in all three components that clearly discern the arrival of P-waves. Seismogeodetic velocities are estimated throughout the period of seismic shaking with a precision of about 0.1–1 mm/s. Together, seismogeodetic broadband displacements and velocities from near-source stations can form the basis for EEW systems for any magnitude earthquake of consequence, which is more robust against false alarms than seismic-only or GPS-only approaches. Furthermore, seismogeodesy can be used to better understand the physics of the earthquake rupture process.


[47] We thank the two reviewers and the Associate Editor for providing useful comments. Melinda Squibb and Anne Sullivan handled the real-time GPS data. Peng Fang was responsible for the 24 h GPS analysis at SOPAC, and Angelyn Moore for the analysis at JPL. GPS 5 Hz data for the 2012 Brawley swarm were provided by the Plate Boundary Observatory (PBO) operated by UNAVCO for EarthScope (http://www.earthscope.org) and supported by NSF grant EAR-0323309. Real-time 1 Hz GPS data over North America were collected from the International GNSS Service and PBO. Accelerometer data were obtained from the California Integrated Seismic Network, and University of California Santa Barbara (courtesy of Jamie Steidl). Seismic event information is from the Southern California Earthquake Center (SCEC) data archive. This paper was funded by NASA grants AIST-11 NNX09AI67G, ROSES NNX12AK24G, 06-MEaSUREs-06-0085, and SCEC award 12083.