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 On 19 February 2008 a bolide traveled across the sky along a southern trajectory ending in a terminal burst above Oregon. The event was well recorded by the USArray, other seismic networks, four infrasound arrays, and several video cameras. We compare the results of locating the burst using these different sensor networks. Specifically, we reverse time migrate acoustic-to-seismic coupled signals recorded by the USArray out to 800 km range to image the source in 2-D space and time. We also apply a grid search over source altitude and time, minimizing the misfit between observed and predicted arrival times using 3-D ray tracing with a high-resolution atmospheric velocity model. Our seismic and video results suggest a point source rather than a line source associated with a hypersonic trajectory. We compare the seismic source locations to those obtained by using different combinations of observed infrasound array signal back azimuths and arrival times. We find that all locations are consistent. However, the seismic location is more accurate than the infrasound locations due to the larger number of seismic sensors, a more favorable seismic source-receiver geometry, and shorter ranges to the seismometers. For the infrasound array locations, correcting for the wind improved the accuracy, but implementing arrival times while increasing the precision reduced the accuracy presumably due to limitations of the source location method and/or atmospheric velocity model. We show that despite known complexities associated with acoustic-to-seismic coupling, aboveground infrasound sources can be located with dense seismic networks with remarkably high accuracy and precision.
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 Seismic imaging techniques have evolved appreciably in the seismic exploration community during the last 40 years. One of these techniques is reverse time migration (RTM), which relies on phase coherence, between seismic reflections recorded by nearby geophones, to migrate the reflections backward in time to where they constructively interfere at the impedance contrasts from where the reflections originate. Many different reverse time migration algorithms exist [e.g., Claerbout, 1971; Stolt, 1978; McMechan, 1983; Baysal et al., 1983; Bleistein, 1987; Sun et al., 2000], but the physical concept is the same and has many applications in geophysics.
 Infrasound began receiving considerable interest since barometers around the world serendipitously recorded infrasound from the 1883 eruption of Krakatau [Evers and Haak, 2010]. Early recordings showed that, at low frequencies, there is relatively little intrinsic attenuation, facilitating the detection and characterization of large events, such as volcanic eruptions and atmospheric explosions, over great ranges [e.g., Landau and Lifshitz, 1959]. The Limited Test Ban Treaty was signed by most nations in 1963. This event had a major impact on infrasound research; most nuclear testing subsequently went underground and interest in infrasound as a nuclear test monitoring tool waned as interest in global seismology increased. The Comprehensive Nuclear Test Ban Treaty (CTBT) opened for signature in 1996, after which construction began on the International Monitoring System (IMS). The IMS comprises in part 60 globally spaced infrasound arrays, each with an aperture of several hundred meters to several kilometers. Since the signing of the CTBT and development of the IMS, there has been a renewed interest in infrasound for monitoring and scientific research.
 Of significant importance in studying geophysical phenomena is the ability to successfully predict infrasound signal arrival times. This requires accurate knowledge of the dynamic atmospheric temperature and wind fields, which determine the strongly anisotropic acoustic velocity field. The last decade has seen progress in tackling this daunting problem. A ground-to-space (G2S) atmospheric parameter specification system, updated every 3 h, has been developed by combining numerical weather prediction model data up to ∼75 km (NOAA-NCEP, NASA-GOES5, and/or ECMWF) with empirical reference models above [Hedin, 1991; Hedin et al., 1996; Drob et al., 2003, 2010b]. The raw data that go into these models originate from networks of ground-based weather stations and meteorological satellites.
 Recent studies have shown that atmospheric acoustic velocity models derived from the G2S system represent a significant improvement over traditional velocity models that are based on climatological averages; however, some observed arrivals are still not predicted by these high-resolution G2S models [McKenna et al., 2008; Arrowsmith et al., 2009; Gibson, 2009]. In some instances, the inability to predict certain phases may result from limitations of the wave propagation model chosen rather than from errors in the background atmospheric specifications. For example the assumption of range independence in the atmospheric velocity model can effectively negate any value added of improved atmospheric models. Other considerations involved in explaining unmodeled arrivals include the influence of topography [e.g., Arrowsmith et al., 2007], finite frequency effects in shadow zones [de Groot-Hedlin et al., 2010], gravity wave perturbations [e.g., Kulichkov et al., 2010], and nonlinear propagation [de Groot-Hedlin et al., 2010]. To evaluate these hypotheses and address our current inability to predict all observed arrivals, simple explosive events with known source locations and times, that give rise to infrasound arrivals recorded at many spatial locations, are quite useful [e.g., Drob et al., 2010a].
 In this paper, we apply reverse time migration to the infrasound source location problem. We show that this method is useful in infrasound research when the 1 to 5 Hz phase incoherent infrasound, as detected by hundreds of broadband vertical component seismometers, is made phase coherent (by calculation of its envelope function), decimated, and filtered with an automatic gain control. In the example of the northeast Oregon bolide of 19 February 2008 [Hedlin et al., 2010], we show that the method resolves the source location of the terminal burst with favorable accuracy and precision compared with the wind-corrected infrasound array source location. Furthermore, we show that the near-field seismic stations within 87 km of the source are sensitive to source altitude as expected; arrival times at these stations determine with good precision a source altitude of 27 km. The precise source location and time of the burst, which was registered by hundreds of USArray seismometers out to 800 km range, provides an excellent data set with which to validate atmospheric velocity models and test propagation physics hypotheses. Finally, our results suggest that reverse time migration could be automated and applied in near real time to seismic network data to locate aboveground, explosive sources of infrasound.
2. Video Camera Analysis
 The skies over the U.S. Pacific Northwest lit up during the early Tuesday morning of 19 February 2008. Many people during their early morning commute observed the 5:30 A.M. event. Fewer people heard the event; analysis of the unsolicited human reports to the American Meteor Society suggests the acoustic disturbances were felt or heard out to ∼150 km range (data courtesy of R. Lunsford).
 Three security video cameras and two all-sky video cameras witnessed the event either directly or indirectly (Table S1). Camera operators provided the exact locations of these cameras. For the three security cameras, we estimated the azimuths to the event in an ad hoc way by cross-referencing foreground objects with objects observed in Google Earth. Figure 1 shows the analysis for the camera at the Portland Providence Medical Center (PPMC). A circle was drawn to encompass the region of maximum brightness. The center of the circle was used to estimate the optimum direction and the half width of the circle the directional standard deviation.
 An azimuth was also measured from an all-sky camera located in West Kelowna, British Columbia by the site operator (J. Brower, personal communication, 2008). A second all-sky camera located in Calgary, Alberta was too far north to see any part of the bolide trajectory, but did precisely record the time that the sky lit up during the event. The security cameras and Kelowna all-sky camera place the terminal burst above the Blue Mountains in NE Oregon (Figure 2).
 The security cameras indicate that the event had a southerly trajectory. The southern trajectory is not consistent with any known meteor shower. The nearest active meteor shower radiant was that for the Delta Leonids, which were just below the horizon to the northeast at the time. Even though the entire meteor trail was not directly visible at Kelowna, the all-sky camera there clearly saw the southern sky light up during a terminal flash just after the bolide descended below the horizon. The visible light amplitude at Kelowna was estimated by summing pixel amplitude for all pixels above a threshold amplitude for each all-sky video frame (Figure 3, courtesy of J. Brower). The total duration of the signal is ∼2 s. The event has a well-defined terminal flash, which we interpret to be a terminal burst. Optically, this terminal flash is at least 40 dB above the background noise and 8 dB above the brightest part of the trajectory through the atmosphere.
 The maximum altitude of the bolide can be constrained by the Kelowna all-sky camera because a mountain was located between the camera and the terminal flash. Using the elevation of the highest point on the mountain visible from the site of the camera in the direction of the terminal flash Zm at a range dx and the elevation of the camera Zc, the elevation angle of the mountain top is
One can project a line with this elevation angle from the camera, grazing the mountain top, to above the bolide flash. For small angles such as this, the altitude of this point is
where x is the arc distance between the camera and the flash and is the average Earth radius along the arc. Substituting measurements for Zm, Zc, dx, x, and , we calculate an elevation angle of 3.8° and an altitude of the projected line from the camera to above the bolide flash 470 km away of 32 km, which is a maximum constraint on the altitude of the bolide flash.
3. Seismic Data Analyses
3.1. Seismic Observations
 The Oregon bolide occurred above the USArray, the Pacific Northwest Seismic Network (PNSN), and two temporary IRIS PASSCAL seismic networks (Figure 2). Picks of impulsive signals recorded by the PNSN were used with a slight modification to standard earthquake location software to locate the terminal burst. A homogeneous half-space model was assumed with an acoustic velocity of 315 m/s. The source was located in northeastern Oregon at an altitude of 28 km (S. Malone, personal communication, 2010). Our analyses below use additional seismic stations, range- and altitude-dependent velocity models, and different methods to determine the source location of this bolide. Hedlin et al.  also analyzed the waveforms from these seismic stations to identify and illuminate in unprecedented detail travel time branches associated with atmospheric multipathing through the troposphere, stratosphere, and thermosphere. Finally, de Groot-Hedlin et al.  compared the seismically observed stratospheric and thermospheric infrasound arrivals to those predicted by finite difference time domain modeling.
 The USArray is part of the Incorporated Research Institutions for Seismology (IRIS) EarthScope program and comprises some 400 broadband, three-component seismic stations on an average interstation spacing of ∼70 km, spanning an area of ∼2,000,000 km2. The network is continuously being redeployed station-by-station to “roll” across the continental United States in ∼9 years. The average stationary time for each seismic station is 24 months.
 Two regional IRIS PASSCAL seismic networks were in operation at the time of the bolide. The Wallowa Flexible Array comprised about ten three-component broadband seismometers. The High Lava Plains Seismic Experiment comprised about 90 similar broadband seismometers. These networks were designed to study the crustal and upper mantle structure beneath southeast Oregon [Warren et al., 2008; Long et al., 2009; Scarberry et al., 2009].
 Infrasound generated by the bolide was recorded by many of the seismometers within 800 km of the event. In general, the observed signals moved out across the seismic networks linearly at near-acoustic wave speeds indicating that the infrasonic wavefronts propagated along the Earth's surface at grazing angles. Figure 4 shows a record section from the source location toward the northwest. Two infrasonic phases are shown that have approximately linear move out velocities of ∼325 m/s.
 The signal recorded by the seismometers is the result of acoustic-to-seismic coupling or a mechanical response of the sensor itself to the grazing pressure wave. Regardless of the mechanism, the seismic methods we use in this paper are not affected. We defer a more detailed analysis of the waveforms to Hedlin et al. .
3.2. Seismic Source Location
 The seismic data are analyzed in two different approaches. The first approach is with reverse time migration (RTM). This method is used on all the vertical component seismic waveforms to determine the source location and uncertainties in latitude, longitude, and time. The second approach uses travel time picks of the first arrival for the stations within 87 km of the source to determine source time (with higher accuracy and precision) and altitude with uncertainties.
3.2.1. Reverse Time Migration
 The reverse time migration (RTM) approach works by “back projecting” or “stacking” recorded energy that travels at a predicted apparent velocity (or velocities) to all possible source locations on a prescribed spatiotemporal grid. Possible event locations in the grid are marked by constructively interfering back projected energy. A similar approach was used by Shearer  to estimate the source locations of earthquakes by reverse time migrating P wave, S wave and surface wave energy generated by earthquakes and recorded by the IDA seismic network. He found 32 new events over the course of 11 years (most of which were from the South Pacific basin) that were not detected in the earthquake catalogs because the relatively high-amplitude surface waves from these events were implemented in this multiarrival technique, whereas the relatively low-amplitude P waves from these events were below the detection threshold used by traditional P wave detection and location algorithms. More recently, a similar technique was used to detect and locate earthquakes caused by glacier movements [Ekström et al., 2003, 2006] and to image the rupture details of very large earthquakes [Ishii et al., 2005, 2007; Walker et al., 2005; Walker and Shearer, 2009; Xu et al., 2009], the rupture details of the 2004 Parkfield and 2001 Nisqually earthquakes [Allmann and Shearer, 2007; Kao et al., 2008], and earthquake tremor [Kao and Shan, 2004, 2007].
 The basic concept as applied to acoustic event location is shown in Figure 5. Due to the velocity structure of the atmosphere, the acoustic energy from an event on the Earth's surface travels via multiple paths and at different move out velocities to the receivers. Using the location of the event as a reference point in space, when this energy is shown in a time-distance waveform plot, the arrivals have different apparent move out speeds and are spatially and temporally coherent; the arrivals follow predicted travel time curves for an event at that reference point. Consequently, summing the amplitudes of the waveforms along one of the travel time curves yields Q(t), which is a pseudo source time function for that grid point if the assumed move out velocity is correct. If the energy at each station has unity amplitude, Q(t) has a signal-to-noise gain of 10*log(N), where N is the number of stations. Using any other location in space for the reference point, or if the assumed apparent velocity is incorrect, the back projected energy is not coherent, and Q(t) generally consists of noise.
 The Oregon bolide is located in latitude, longitude, and time using RTM on the USArray 1 to 5 Hz vertical component seismograms. In order for RTM to work, the energy that is back projected must be phase coherent between multiple sensors. The spectrum of interest for most regional infrasound propagation studies is 0.5 to 5 Hz. Because the correlation distance of infrasound in this frequency band is only several kilometers, one cannot assume phase coherence between seismic stations separated by the average USArray interstation spacing of 70 km. Furthermore, there are great variations in the amount of signal dispersion observed at each station with typical signal durations between 10 and 50 s. Therefore, we calculate the envelope function of the frequency filtered seismic data, apply an anti-alias filter, and decimate the envelope to a 10 mHz sampling rate (Figure 6). This simple process regularizes the observed duration of the infrasound signals and creates an impulsive phase coherent signal that is back projected efficiently and effectively for appropriate spatiotemporal grids.
 Given the 10 mHz sampling rate, at a typical acoustic velocity of 300 m/s, each sample in the envelope functions sweeps across the potential source locations at maximum increments of 30 km. The potential x/y source grid is consequently discretized with a 15 km sampling interval. An automatic gain control (AGC) is used to regularize the time varying amplitude of the decimated envelopes. Specifically, in this technique the decimated envelopes are demeaned, the maximum of the absolute value of the demeaned envelopes is calculated at every time sample over a centered window of 1000 s duration, and the demeaned envelopes are finally divided by the maximum values.
 The acoustic velocity of the atmosphere is continuously changing at different spatiotemporal scales. We therefore do RTM of the processed envelopes at eight different apparent velocities ranging from 0.28 to 0.35 km/s, defining Q, the “stack” or summation of waveform amplitude at the predicted arrival times. Q is a function of longitude x, latitude y, time t, and apparent velocity c, representing a pseudo source time function for the trial grid point
where a, is the amplitude-normalized, decimated envelope function, and i, j, k, l, m are the indices associated with x, y, t, c, and seismic station, respectively. The station weighting operator w is defined in the section 3.2.2. The maxima of Q are assumed to identify possible sources at the associated latitudes, longitudes, and times, the signals from which propagated on average at the associated apparent velocity c. The problem of detecting events of interest is simply the problem of finding the local maxima of Q that are not artifacts or a result of noise. For this purpose, we calculate a detector function
D is then high-pass filtered with a cutoff period of 6 h to eliminate long-period noise. We then estimate the noise level N by calculating the median of the envelope function of D every day. The signal-to-noise ratio SNR in dB is then
Typically values greater than 15 dB are considered statistically significant in standard detection theory [Helstrom, 1994].
3.2.2. Potential Problems Affecting RTM Approach
 This event detection and location technique suffers from a few potential issues. A dense cluster of stations in an otherwise regularized station distribution will cause the maxima associated with an event to be smeared in time and in the spatial direction orthogonal to the source-receiver plane. To reduce this effect while improving accuracy and precision, we weigh seismograms from stations that are close together less than seismograms from stations that are separated by greater distances. Specifically, we apply a weighting operator to each station wm = 1/n(r), where n(r) is the number of stations within a threshold radius r (50 km).
 Another potential problem is if the event duration is too long. Because this technique uses envelope functions, an anomaly in the envelope function will only be defined for transient signals (signal durations of a few tenths of a second to a few hundred seconds) that stand above more continuous background noise. This background noise can be any combination of electronic sensor noise, transient incoherent acoustic or seismic energy, or even a continuous “hum” such as that often observed with microseisms and microbaroms. If we were sampling the envelopes at the raw sampling rate of the seismic data (∼40 Hz), the estimated source times would be biased late because causality is not assumed in the method; the maximum in Q corresponds to the alignment on the envelope peaks, not the envelope risetimes. However, we decimate the envelopes to 10 mHz (coarse resolution) and 100 mHz (finer resolution) sampling rates. The typical signal duration ranges from 10 to 50 s. Therefore, at 10 mHz sampling, the absence of assumed causality does not affect the accuracy. However, at 100 mHz sampling, the bias may exist and be 5 to 50 s depending on the predominant dispersion.
 Another potential issue is the resolution of source altitudes up to 100 km. In the far field where source-receiver distances are greater than ∼100 km, the raypath for an elevated source is very similar to that for a source on the surface. In other words, although source time is well resolvable, this technique has no source altitude resolution power in the far field. However, in the near field, source altitude is resolvable, and it would give rise to a hyperbolic move out of observed arrivals corresponding to the transition between the downgoing tropospheric arrival and the more distant ducted arrivals that have nearly linear move out velocities.
 Finally, a potential issue that is more difficult to resolve is the problem of (1) poor station-receiver geometry and (2) preferential horizontal ducting of energy away from the source. If energy from a source is only observed by stations located in a specific azimuth range from the source, either due to preferential ducting or poor station-receiver geometry, then a similar smearing effect will result when this energy is back projected to the source location. Visual inspection of Q and the waveforms from stations contributing to Q indicates that this is not an issue for the Oregon bolide.
3.2.3. Source Latitude and Longitude Using RTM
 The seismic data are back projected in two different phases. The processing parameters are shown in Table 1. The first (coarse) phase is generally used for detection. A peak of 28 dB exists in the coarse detector function at 1330:00 UTC in northeast Oregon (Figure 7). During phase 2, a refinement of the source location is estimated by recomputing the source location on a finer grid using only stations within 250 km of the previously detected location. The refined source location is within 1 coarse-resolution grid point of the coarse-resolution source location (Table S2).
Table 1. Analysis Parameters for RTM, Bootstrap Resampling, and Arrival Time Picks Grid Searchesa
Parameters without a range were fixed.
Picks: altitude and time
Picks: altitude only
 The detection is not only well resolved at a scale of hours, but also at a scale of days (Figure 8) for both the coarse- and fine-resolution cases, even though the number of stations contributing to each peak is different (409 and 38 stations, respectively). This shows that the detection phase, which because of its 10 mHz sampling rate is computationally efficient, resolves this event with an accuracy of ±100 s. For an acoustic velocity of 0.3 km/s, ±100 s is equivalent to ±30 km distance, which is about twice as long as the horizontal RTM grid interval of ∼15 km.
 We apply a bootstrap technique to estimate the 95% confidence regions in the RTM source location parameters as the final step in the phase 2 analysis. The bootstrap technique is widely used in the sciences to obtain empirical measures of the probability distribution function, even if the shape of that function is unknown a priori. Therefore, this is attractive in the estimation of confidence regions regardless of the noise model or parameter estimation method. We refer the reader to Efron and Tibshirani  for more details. Keeping the station weights the same as those used in the optimum solution, we resample with replacement, 300 times, the sample set of 38 stations within 250 km of the bolide burst to result in 300 new sample sets of 38 stations. This resampling of the original sample set is performed randomly with replacement. In other words, to form a new sample set, a station is randomly picked 38 times from the original sample set. Each station pick does not remove that station from the original sample set. Thus it is possible that in forming a new sample set, one station may be selected more than once. Also possible is the extremely unlikely scenario that only a single station will be randomly selected 38 times to form a new sample set. Each of the 300 new sample sets of 38 stations is then used in the RTM analysis, and a new source location is computed. The 300 new source locations are then used to estimate the probability distribution function of the apparent velocity and source latitude, longitude, and time (Figure 9). The cumulative distribution function is calculated, normalized by the maximum, and the locations corresponding to the 0.025 and 0.975 values are obtained, yielding the 95% confidence region (Table S2). The source time and apparent velocity have a generally Gaussian distribution. The source time uncertainty extends from 1330:40 to 1331:40 UTC, but does not include the source time constraint from the video camera of 1330:29 UTC. This is likely because of the upward bias in the time estimate discussed earlier.
The seismic preferred location (denoted with the asterisk) is the location identified by a star in all maps in this paper, and this location is not the center of the bootstrap error ellipse (denoted by two asterisks). The seismic preferred location was selected as “ground truth” and was used to calculate the misfit of the four infrasound locations. The video location has been included but we have not attempted an error analysis.
Seismic networks (RTM+ picks)
27 ± 3
28 ± 1
 Conversely, the longitude and latitude have asymmetric distributions. To visualize better these distributions, we plotted all the 300 source locations in map view. They clustered tightly together near the center of the RTM grid used in phase 2. We then defined a new region with an even higher spatial resolution (but still 100 mHz sampling rate) around the cluster of 300 locations (Figure 10a), and we performed another RTM and subsequent bootstrap resampling using that grid. The seismic preferred location did not change appreciably, but the bootstrap results were much smoother (Figure 10b). To characterize this asymmetric distribution of source locations, we performed a grid search over the five model parameters of an ellipse to minimize an objective function that sums (1) the absolute value of the misfit between the number of bootstrap source locations inside the ellipse and the number of bootstrap source locations that corresponds to 95% of the 300 events and (2) the area of the trial ellipse. Each of these terms in the objective function has an appropriate weight assigned based on some numerical experiments. The smallest ellipse that encompasses the 95% confidence region is shown in Figure 10 and detailed in Table 2. The distance from the optimum seismic location to the center of the ellipse is just 300 m. This indicates that there is no bias in the RTM estimate of source latitude and longitude and that the bootstrap is providing a reliable measure of the 95% confidence region.
3.3. Source Altitude and Time Using First Arrival Picks
 RTM did not have adequate resolution power for source altitude and time. The video camera results constrained the source time and altitude to be 1330:29 UTC and less than 32 km. Because the source time was from only a single camera reported to have an accurate time that was synchronized to UTC, and because the altitude estimate had no lower bound, we used first arrivals picked by hand for distances out to 87 km from the source latitude and longitude in two grid searches for the optimum altitude and time (Table 2). The “celerity” is the great circle distance between source and receiver divided by the travel time. Arrival times for all arrivals were picked by using the video source time and location, then searching an arrival time window at each seismic station corresponding to a minimum and maximum celerity of 200 and 400 m/s, which should span all tropospheric, stratospheric, and thermospheric arrivals for a point source. However, this method would also find arrivals related to a hypersonic Mach cone in the vicinity of the event epicenter because the differential travel time between a point source and a line source would be small enough to be observed in those celerity time windows. Concentric contours of the picked arrival times for the first arrivals at all stations as well as just stations within 87 km of the epicenter (Figure 11) suggest that the observed signals were due to a terminal burst. We defer additional details of the picking procedure to Hedlin et al. .
 The picks for all stations within 87 km of the epicenter were used in two grid searches to minimize the L2 norm of the misfit between the observed and predicted times (Figure 12a). The predicted times for these 13 stations were generated using 3D ray tracing in a range-dependent environment [Drob et al., 2003] with a G2S-ECMWF model, a product of 0.5° × 0.5° resolution (with 91 levels) European Centre for Medium-Range Weather Forecasts (ECMWF) analysis products [Persson and Grazzini, 2007] up to 75 km and the HWM07/MSISE-00 empirical climatologies above [Picone et al., 2002; Drob et al., 2003, 2008]. Of the meteorological analysis fields available at the time to construct G2S profiles for the event, the ECMWF system has the highest resolution and has undergone the most operational validation in the middle atmosphere. A complete comparison of the available middle atmospheric specification systems (such as ECMWF, NASA GEOS5 [Rienecker et al., 2008], and NOGAPS-alpha [Eckermann et al., 2009]) can provide additional insight into the influence of atmospheric uncertainties of infrasound propagation calculations, but is beyond the scope of this study.
 We also applied a least squares technique (Figure 12b) [Jenkins and Watts, 1968] and the bootstrap technique (Figure 12c) to determine the 95% confidence regions. The least squares technique assumes the noise follows a χ2 distribution and will be overly optimistic when the χ2 distribution assumption is incorrect; the bootstrap solution gives a more robust characterization of the uncertainty.
 The first grid search over trial source time and altitude resolve the same source time as that provided by the video camera (1330:29 UTC). Furthermore, the probability distribution function (PDF) is Gaussian in shape with an uncertainty of ±15 s. However, the optimum altitude of 27 km is not as well resolved, and the PDF is complicated.
 The second grid search was over altitude, fixing time to be that constrained by the video constraint. The optimum altitude was also found to be 27 km, the associated PDF to be Gaussian in shape, and the uncertainty to be much smaller at ±3 km. This is the preferred altitude and uncertainty.
4. Infrasound Array Analyses
4.1. Observations and Modeling
 The bolide generated infrasound that was recorded by several North American infrasound arrays at various ranges: IS56 (Newport, Washington, U.S.; 300 km), NVIAR (Mina, Nevada, U.S.; 810 km), IS57 (Palm Desert, California, U.S.; 1360 km), and IS10 (Lac du Bonnet, Manitoba, Canada; 1710 km). Three of these arrays are part of the International Monitoring System discussed earlier, which has an average interstation spacing of 2200 km. Bolide signals were identified on the IMS arrays by using the seismically determined source location (x, y, and z) and time, and then searching a time window at each array corresponding to a min and max celerity of 250 and 360 m/s. Using the Progressive Multichannel Correlation Method (PMCC) [Cansi, 1995], in these time windows, we calculated the back azimuth and apparent speed of the infrasound arrivals. This information is then used in the infrasound source location technique.
 At IS56 four signals are observed over a 6 min period, with three having fairly impulsive characteristics (Figure 13). The great circle azimuth from the array to the seismic location is 196°. PMCC indicates that all signals have back azimuths between 192° and 196°. The apparent speed of the first two impulsive arrivals is ∼338 m/s. The third arrival comes at the tail end of the second arrival and has a much lower signal-to-noise ratio, but has a higher apparent speed of 354 m/s. The fourth impulsive arrival crosses the array at 380 m/s. This latest signal has a notably higher apparent speed, which suggests a higher elevation angle and a turning point in the thermosphere. The celerities of the arrivals are 330, 300, 275, and 245 m/s. These celerities suggest that the first arrival is tropospheric and the second two arrivals are stratospheric. The fourth arrival has a celerity of 245 m/s, which is fairly low and also suggests an arrival that refracted in the thermosphere. It is also worth noting that this fourth arrival has a relatively higher frequency content than the previous arrivals, which is unexpected for thermospheric arrivals because of high levels of attenuation expected for propagation through the thermosphere [Sutherland and Bass, 2004].
 Based on the asymptotic approximation of high-frequency infrasound waves, we use ray tracing with a G2S-ECMWF range-independent atmospheric velocity model to approximately identify the raypaths of the observed arrivals. For practical purposes we assume that the contributions of range dependence in the velocity models will be insignificant for the task of identifying the raypaths of observed arrivals. We consider that pressure perturbations are relatively small so that the motion of the atmospheric medium is governed by the linearized hydrodynamic equations for a compressible fluid. This implies that the signal wavelengths are smaller than those of the atmospheric property variations. The propagation modeling is performed using the Tau-P method assuming a uniform distribution of horizontal wind and temperature along the raypaths [Garcés et al., 1998]. Applying a shooting procedure, 80 rays are launched from the preliminary source location toward each infrasound array. Only rays with bounces contained within 50 km of the arrays are selected. Diffracted energy from rays propagating in elevated ducts as high as 10 km from the ground level are also considered (Figure 14). Finally, the azimuthal deviation, celerity values and attenuation are calculated for each ray trajectory.
 Considering the observed complexity of infrasonic raypaths, and a need to easily reference phases that propagate along all possible raypaths that eventually reach the ground, Hedlin et al.  proposed a new nomenclature for infrasonic propagation. We now briefly describe this nomenclature and refer the reader to Hedlin et al.  for more details. The nomenclature allows one to represent any arbitrary path through the atmosphere from an infrasound source to a receiver on the ground with a simple code. A code that is assigned to such a path is constructed by the following rules. First, any complex path is broken down into a sequence of simple segments between the source and receiver and the term that represents the entire path is simply a concatenation of basic terms that represent each simple segment of the overall path. The three basic terms are the letters W, S, and T to represent infrasound ducted in the troposphere, stratosphere, and thermosphere, respectively, where the lower bound of the duct is Earth's surface. When the lower bound of the duct is not the Earth's surface, and energy is trapped in an elevated duct, we use the terms We, Se, and, Te to represent elevated tropospheric, stratospheric and thermospheric ducts, respectively. Second, the order in which the overall code is constructed from left to right reflects the order of propagation segments beginning with the source and ending at the receiver. Third, a prefix to each code describes the direction of sound propagation as it leaves the source, with the letter u representing initial upward propagation and d initial downward propagation. For example, the term dW represents propagation down from the source followed by one leg of the overall path ducted in the troposphere. The term dWW represents a path like dW except there is one additional reflection at the Earth's surface and one extra turn in the troposphere. The last rule is to condense the code where possible by using subscripts to represent the number of turns within a duct. Therefore, dWW is rewritten as dW2. With this in mind, to describe an arbitrarily large, and perhaps unknown, number of turns in the duct, we use the term dWn.
 For IS56, three different arrivals are generally predicted (Figure 14). The predicted arrivals correspond to uSe1, dSe1, and uT1 paths. The first two arrivals are uSe1 and dSe1, originating from ducting in the stratosphere. We assume the waveguides are “leaky” in order to produce the two observed stratospheric arrivals. The third predicted arrival uT1 is consistent with the observed thermospheric arrival. The observed tropospheric arrival was not predicted by the ray tracing and could be attributed to an insufficient velocity model within the first ten kilometers above the ground.
4.1.2. Other Arrays (NVIAR, IS57, and IS10)
 At NVIAR an immersive signal is observed over 4 min in length. Although the signal-to-noise ratio is low, PMCC detects a coherent arrival in the 1 to 3 Hz frequency band with an apparent speed of ∼338 m/s and a back azimuth of 359° close to the great circle azimuth from the array to the seismic location of 1°. The celerity of this phase is 300 m/s, suggesting the arrival was stratospherically ducted. Ray tracing also predicts two dominant arrivals to be from lower stratospheric ducting (uSe4 and dSe3).
 IS57 is located along the same relative source-receiver azimuth as NVIAR. At IS57 a 4 min long immersive signal is observed. Although the signal-to-noise ratio is very low, PMCC detects a coherent arrival in the 0.5 to 1.5 Hz frequency band with a back azimuth of 355°, close to the 354° azimuth to the source. The apparent speed is 350 m/s. The celerity of this arrival is 300 m/s, which is the same celerity as that found for the arrival at NVIAR, suggesting a stratospherically ducted raypath. Ray tracing for IS57 also predicts three dominant arrivals originating from ducting in lower (dSen and uSen) and upper stratosphere (uSen). Based on ray densities, the two lower stratospherically ducted arrivals are likely to have the greatest amplitudes, which is consistent with the IS57 and NVIAR array observations.
 IS10 observes a 4 min long signal below the noise. Although the signal-to-noise ratio is very low, PMCC detects a coherent arrival in the 0.5 to 1.5 Hz frequency band with a 258° back azimuth (262° to source) and apparent speed of about 325 m/s. The celerity of this arrival is 290 m/s, which suggests a stratospheric arrival. Ray tracing predicts only two arrivals uSen and dSen (from stratospheric ducting).
4.2. Infrasound Source Location
 The location of the bolide terminal burst is computed by solving a nonlinear system of equations describing the infrasonic propagation through the atmosphere. This inverse location algorithm is based on Geiger's approach [Geiger, 1910], but modified to also take station azimuth into account [e.g., Bratt and Bache, 1988; Lienert and Haskov, 1995; Schweitzer, 2001] to iteratively obtain the best source location results via a linearized least squares inversion. The assumption of a homogeneous half-space is fulfilled by starting with a typical celerity value for each individual phase at each contributing station and correcting iteratively this value based on the results obtained by ray tracing. Specifically, two location results are first obtained: with back azimuths only (A) and with arrival times and back azimuths (AT). These first location results assume a homogeneous half-space with a typical celerity value of 300 m/s for each individual phase (A-NWC and AT-NWC). Because the accuracy of the source location strongly depends on the atmospheric wind and temperature profiles at the place and time of the event, improved wind-corrected location results are then iteratively obtained using station azimuth corrections and celerity values for the fastest identified arrivals derived from the ray tracing (A-WC and AT-WC). Tables 3–5 summarize all phases used for the four locations. Table 2 and Figure 15 list the different source locations and their uncertainty estimates.
Table 3. Infrasound Observations Used in the Infrasound Array Source Locations
Back azimuth (deg)
Arrival time (UTC)
Table 4. Interpreted Phase and Assumed Back Azimuth Perturbation and Celerity for the Two Infrasound Array Source Locations Without Wind Corrections
Table 5. Interpreted Phase and Estimated (From Modeling) Back Azimuth Perturbation and Celerity for the Two Infrasound Array Source Locations With Wind Corrections
 Location errors are determined by assuming that uncertainties in measured signal back azimuth and apparent wave speed are 1° and 5 m/s, respectively. Hundreds of simulations were performed by randomly perturbing the measurements going into the source location by amounts within these uncertainty bounds and reestimated the source location. Then a confidence ellipse was calculated that minimizes the ellipse area while enclosing 95% of the simulated source locations.
5.1. Point Source and Residuals
 Infrasound generated from meteors and aircraft have been previously studied with seismic networks [e.g., Anglin and Haddon, 1987; Kanamori et al., 1991, 1992; Qamar, 1995; de Groot-Hedlin et al., 2008]. Ishihara et al.  used travel time picks from 21 out of 28 seismic stations in Japan to model the hypersonic trajectory of the nighttime 1998 Miyako bolide. They performed the same type of grid search to minimize the difference between observed and predicted travel times, but for a six-parameter source model using a constant atmospheric sound velocity of 320 m/s. Their best model had an RMS residual of 1.1 s. Langston  also performed a grid search analysis to model first arrival travel times from the nighttime 2003 Arkansas bolide recorded by 22 stations of the CERI network. Using a constant velocity of 330 m/s, he found that he could minimize his residual to ∼1.5 s with a hypersonic trajectory. These authors did not report attempts to fit the seismic data travel times with simpler point source; there was no evidence (such as a terminal flash) to suggest a point source was preferred to a typical line source associated with a Mach cone.
Lin and Langston  analyzed a daytime seismic wave train recorded by the CERI network with a group velocity of about 330 m/s. They performed a similar grid search to find the parameters for a point source model. The source-receiver geometry was inadequate to solve for a hyperbolic trajectory model. Assuming a point source model, they were able to locate the source latitude, longitude and time at a range of 120–280 km with an average residual of 2.4 s. Arrowsmith et al.  analyzed 99 seismic stations that registered the nighttime 2004 Washington State bolide terminal burst. The source-receiver geometry was adequate to distinguish between a hypersonic line source and point source model. They used the “SUPRACENTER” atmospheric explosion location program [Edwards and Hildebrand, 2004], which comprises a nonlinear, genetic optimization algorithm to sample and determine the assumed point source position. This method involves ray tracing to predict the travel times of direct arrivals. A global minimum in the misfit between observed and predicted travel times is obtained by eliminating observations that do not correlate with direct arrivals. Their final solution uses 43 of the 99 initial times and has a mean absolute residual of 1.1 ± 2.1 s. These 43 stations are generally within 70 km of the source location.
 We find no evidence that suggests the dominant infrasound signals observed in this study are from a Mach cone due to the hypersonic trajectory. One of the video cameras was synchronized with UTC and recorded a terminal flash of light for the Oregon bolide at 1330:29 UTC (Figures 1 and 3). As is well known, the reverse time migration (RTM) method has the potential to image the source function in space and time. Therefore, this method would indicate whether the source function is a point source or a line source. The video cameras suggest a southward trajectory. However, Figures 7 and 10 show a minor smearing of the migrated energy in the ESE-WSW plane (an imaging artifact), indicating that the dominant signals are inconsistent with a southward advancing line source and more consistent with a point source. The concentric contours of the first arrival times within 87 km of the source also suggest a point source (Figure 11). Our grid search for source altitude and time using stations within 87 km of the flash location fit a point-source model, recovering the same video time of 1330:29 UT and an altitude of 27 ± 3 km, with a misfit RMS of 7 s (Figure 12).
 Although the source time provided by the seismic picks inversion is known to be accurate to the second, we perceive the 7 s picks inversion residual for the altitude grid search as fairly large given the residuals reported in other studies for both point and line sources. Although we assume a constant elevation of 876 m for all stations, the average absolute deviation of site elevation is 280 m, predicting a maximum absolute travel time misfit of only 1 s. We expect that the G2S-ECMWF model should capture the velocity variations better than the constant velocity models used by most others to obtain ∼1 s residuals. We interpret the large 7 s residual to be the result of the hypersonic velocity of the object as it exploded. The light curve in Figure 3 suggests that the burst had a duration of ∼0.1 ± 0.03 s. Meteors typically have hypersonic velocities ranging from 4 to 70 km/s, with an average of about 25 km/s [Taylor and Elford, 1998], and begin ablating from atmospheric friction at an altitude of at least 100 km [Millman, 1959; Allen, 1976]. If we assume that the onset of the 2 s light curve began at a source altitude of 100 km, and if we use the shortest distance (vertical) to the terminal altitude of 30 km, one gets a rough estimate of the minimum bolide speed of 40 km/s (assuming vertical incidence). The bolide had an observed southerly trajectory, so it did not come in vertically; the speed must have been greater than 40 km/s. Nonetheless, if we use 40 km/s as the speed, the burst likely occurred over a distance of 4 km. Assuming our grid search found the center of this 4 km north-south ellipsoid, the ±2 km tails translate into ±7 s is arrival time variation. This may also explain why the video and seismic location are in the north-south plane (Figure 15) and separated by 2 km.
5.2. Accuracy and Uncertainty Comparisons
 Dense seismic networks are now quite common in many areas of the world. Compared to the relatively sparse IMS global infrasound array network of about 60 arrays, denser seismic networks are theoretically in a much better position to accurately locate sources of infrasound when the infrasound is energetic enough to create seismic signals via acoustic-to-seismic coupling to ranges of a few hundred kilometers. Testing this hypothesis, Cochran and Shearer  analyzed vertical broadband seismic data of the Southern California Seismic Network (SCSN). They detected and located 76 sources of infrasound off the coast of Southern California in 2003. They used a cross-correlation approach on envelope functions in order to determine the travel time differences between acoustic-to-seismic coupled signals, then inverted the arrival times for source position and time. Their study showed that a small regional seismic network is very effective at infrasound source location for tropospherically ducted propagation.
 The Cochran and Shearer  study detected and located events that were outside the area spanned by the SCSN. This poor source-receiver geometry yields large uncertainties in space and time. Conversely, the 2008 Oregon bolide exploded directly over several seismic networks, including the USArray. The excellent source-receiver geometry affords us an opportunity to assess the true performance of seismic techniques with respect to infrasound array techniques for infrasound source location.
 The infrasound arrivals from the 2008 Oregon bolide registered on the USArray out to 800 km range. Our RTM results detected and located the bolide in latitude and longitude with good accuracy and precision. This seismic location had a 95% uncertainty ellipse area of 90 km2 and was 2 km from the location provided by the video cameras. Furthermore, near real time earthquake location techniques using a homogeneous atmospheric half-space model of 315 m/s located the burst only 5 km south of the video location (S. Malone, personal communication, 2010). The video location is within the 95% uncertainty ellipse. The PNSN location is very close to the ellipse as well. The seismically derived source location is our preferred epicenter for the bolide burst.
 The most accurate infrasound array source location was that which used just the wind-corrected azimuths (A-WC; 20 km to the east of epicenter). The second closest location was about 66 km away for the location that used wind-corrected azimuths and time (AT-WC). The other two locations that did not employ the wind correction are the least accurate as expected, about 100 and 120 km from the video location. The seismic location is more accurate because there are simply more stations, the source-receiver geometry is better, and the stations are closer to the source, which provides absolute arrival times that are less perturbed by winds.
 The infrasound array source location 95% uncertainty ellipses were estimated via a Monte Carlo approach where the source was relocated hundreds of times by perturbing the observed azimuths and ray-tracing-predicted celerities by up to 1° and 5 m/s, respectively. The uncertainty bounds used for the observations were arbitrary. A different set of bounds would give rise to ellipses of different sizes. Consequently, comparison of these ellipses to the seismic ellipse is not appropriate. However, comparison of the ellipse sizes between infrasound array locations is useful. Although the simpler A-WC location was more accurate than the AT-WC location, the AT-WC location was more precise. The AT-WC ellipse of 3800 km2 compares favorably to the ellipses of the AT-NWC (7400 km2), A-WC (26,300 km2), and A-NWC locations (30,100 km2). In all cases, these ellipses span the preferred epicenter location. The accuracy of the source location, that is, the convergence of the algorithm used, strongly depends on the source-station geometry as well as the considered atmospheric profiles, with respect to both station azimuth correction and celerity value for each individual phase. Although there is a clear improvement in precision when including arrival times in infrasound array source location methods, additional work and/or more accurate velocity models may be required to make azimuth-time methods more accurate than simpler azimuth methods. It should be noted that all four inverted infrasound array source times are late, suggesting that the forward-modeled celerities were too fast, or in other words, the arrivals that predominated the solutions arrived later than expected. The A-WC source time is the most accurate of the four at +57 s, corresponding to a distance of ∼20 km. The RTM source time was also late, but this is because of a known bias due to the method. The source time determined by the seismic picks inversion is accurate to the second (Figure 12).
 On 19 February 2008 a bolide entered the atmosphere above the U.S. Pacific northwest. Video cameras and eyewitness accounts suggest that the bolide moved across the sky along a southern trajectory for a duration of about 2 s, ending in a terminal flash just over northeast Oregon at 1330:29 UTC. The southern trajectory is not consistent with any known meteor shower occurring at that time.
 The 2008 Oregon bolide occurred during a time when the USArray was completely deployed along the western U.S., consequently making it one of the best seismically recorded bolides to date. The bolide generated signals that were recorded by two temporary IRIS PASSCAL seismic arrays and on the USArray out to a range of 800 km with an average move out velocity of ∼280 m/s. Infrasound from the burst was also recorded on four North American infrasound arrays out to a range of 1700 km. Reverse time migration (RTM) of envelope functions of USArray seismic data unambiguously locates the latitude and longitude of the source of acoustic energy to 45.719°N and 118.122°W, which is within 2 km of the location of the flash provided by video camera constraints, suggesting that the signals were due to a terminal burst. There is no lineation of the relocated energy in the north-south orientation, as one would expect for a southward hypersonic trajectory. Using 3-D ray tracing to predict travel times with a G2S-ECMWF velocity model, inversion via grid search of first arrival travel time picks for source time and altitude using stations within 87 km of the flash resolve the same source time provided by a video camera (1330:29 UTC) and an altitude of 27 ± 3 km. The 7 s RMS residual between predicted and observed arrival times may be explained by the spatial distribution of the terminal burst, which may have occurred at ∼40 km/s over a time duration of 0.1 s.
 The 95% confidence ellipse in source location provided by bootstrap resampling of the stations used in the USArray RTM is remarkably small and encloses the video source location with a principle axis of 13 km length and an area of 90 km2. Data from the four infrasound arrays were also used to locate the source, but the accuracy was not as good as that provided by the seismometers due to the fewer number of arrays compared to seismometers, greater distances to the arrays, and a less favorable source-receiver geometry for the arrays. While correcting for the wind provided in the G2S model clearly improved the accuracy of the infrasound array source locations, and while the uncertainty ellipses of all four infrasound array source locations span the epicenter, the most accurate of the wind-corrected locations is 20 km to the east of the epicenter. Implementing observed arrival times in the source locations provided by the infrasound array improved the precision, but reduced the accuracy presumably due to limitations of the method or atmospheric velocity models.
 This study has would not have been possible without generous contributions from a large group of people. Boulder Real Time Technologies provided waveform plotting and data manipulation software. Frank Vernon provided access to the USArray seismic waveform database and assisted with questions regarding Antelope software. Matt Fouch (University of Arizona) and David James (Carnegie Institution of Washington) permitted access to waveforms from their High Lava Plains Seismic Experiment. Gene Humphries (University of Oregon) provided waveforms from the Wallowa Flexible Array Experiment. The public affairs office at Gowen Field in Boise, Idaho provided information on the location of the security camera that clearly recorded the bolide entry and terminal burst. Paula Negele and Renee King of the Providence Portland Medical Center and Rob van Anrooy of the Valley Hospital Medical Center in Spokane, WA provided images and GPS coordinates from their security cameras. Jeffrey Brower supplied the light amplitude curve from his all-sky camera in West Kelowna, B.C. and a measurement of the azimuth to the terminal burst. Alan Hildebrand, of the University of Calgary, and Don Hladiuk made available the Calgary all-sky video and terminal burst time. The ECMWF model was supplied by the Provisional Technical Secretariat of the CTBTO solely for the purpose of CTBT and related scientific and technical activities. Robert Lunsford of the American Meteor Society provided a quantitative summary of human reports of the meteor. We would like to acknowledge the support of IRIS, the Incorporated Research Institutions for Seismology, for collecting and giving access to seismic data from the USArray and regional PASSCAL experiments. Last, two anonymous reviewers made thoughtful suggestions that improved this paper.