Pure Appl. Geophys. 171 (2014), 587–597 Ó 2012 Springer Basel AG DOI 10.1007/s00024-012-0576-3 Pure and Applied Geophysics

Sources of Error Model and Progress Metrics for Acoustic/Infrasonic Analysis: Location Estimation

1 2 1 1 STEPHEN ARROWSMITH, DAVID NORRIS, ROD WHITAKER, and DALE ANDERSON

Abstract—How well can we locate events using infrasound? infrasound has the potential to play a key role in This question has obvious implications for the use of infrasound identifying mining blasts and other manmade events within the context of nuclear explosion monitoring, and can be used to inform decision makers on the capability and limitations of that become prevalent at these low seismic magni- infrasound as a sensing modality. This paper attempts to answer tudes. In addition, infrasound can provide constraints this question in the context of regional networks by quantifying on source depth, which can be critical for reliably current capability and estimating future capability using an example regional network in Utah. This example is contrasted with estimating the yield from seismic data and for source a sparse network over a large geographical region (representative identification purposes. of the IMS network). As a metric, we utilize the location precision, Within the context of treaty monitoring, it is a measure of the total geographic area in which an event may occur important to communicate to decision makers the at a 95 % confidence level. Our results highlight the relative importance of backazimuth and arrival time constraints under dif- capability of different technologies. Recent papers ferent scenarios (dense vs. sparse networks), and quantify the (LE PICHON et al. 2009;GREEN and BOWERS, 2010) have precision capability of the Utah network under different scenarios. quantified the detection capability of the IMS infra- The final section of this paper outlines the research and develop- ment required to achieve the estimated future location precision sound network in terms of yield thresholds. However, capability. there has not yet been any attempt to quantify what is achievable with regional networks of infrasound Key words: Infrasound, event location, nuclear explosion monitoring. arrays, or to formally quantify localization uncer- tainty. With the recent deployment of a prototype infrasound network in Utah, it is possible to provide a preliminary assessment of the capability. While the 1. Introduction capability will depend on the network configuration (e.g., number and density of stations), which will differ Infrasound has been used for decades as a sensor from network to network, there is value in providing an modality to monitor atmospheric nuclear tests. assessment of the Utah network for decision makers as Within the last ten years, the deployment of the an example scenario. The results will both quantify the international monitoring system (IMS) infrasound current state-of-art capabilities in localization, as well network under the comprehensive nuclear-test-ban as project what might be achievable in the future by treaty (CTBT), in addition to successes from proto- leveraging research advances. type regional networks, is highlighting the additional The purpose of this paper is to outline a formal value of infrasound as a supplemental tool for mon- approach for assessing network location precision for itoring underground tests. With the drive towards decision makers. Previous studies at IMS scales have monitoring low yield tests at regional distances, assessed location accuracy using some measure of the azimuthal gap. However, in treaty monitoring appli- cations the question of more relevance is how large a geographic area a given test is constrained within. For onsite inspection activities, areas of up to 1,000 km2 1 Los Alamos National Laboratory, Los Alamos, USA. E-mail: [email protected] are permitted. We discuss a methodology for esti- 2 Applied Physical Sciences, Arlington, VA 22203, USA. mating location precision for a regional infrasound 588 S. Arrowsmith et al. Pure Appl. Geophys. network, then illustrate both existing capability and rhðÞtotal¼ rhðÞmeasured þ rhðÞmodel an estimate of future capability using the Utah r/ðÞtotal¼ r/ðÞmeasured þ r/ðÞmodel infrasound network as an example. Finally, we out- line the research needed to move from the first to the where, h represents back azimuth and / represents second scenario. arrival time. This paper uses the Bayesian infrasound source As a crude estimate of the total uncertainty in back location (BISL) (MODRAK et al., 2010) to formally azimuth, r(h)total, we can make no correction for back assess location precision. The advantage of BISL as azimuth deviation due to wind bias, and simply resort compared with other techniques for this purpose is to empirical observations of back azimuth deviations that both measurement error and model error are to define the uncertainty. As a first order enhancement formally accounted for, and prior constraints can be we can expect that propagation modeling would allow readily folded into the solution. As a forward method, us to correct the azimuths for wind bias and reduce the BISL contrasts with the standard inverse approach corresponding model uncertainty. For arrival times, that is used for infrasound location (BROWN et al., we may assume that phase is unknown and different at 2002a;CERANNA et al., 2009). Such inverse tech- each array; therefore r(/)model should be sufficiently niques are based on Geiger’s method (GEIGER, 1912). large to capture the range of possible arrival times at For using azimuthal information in addition to arrival the arrays. Similarly, as a first-order enhancement, we time constraints, BRATT and BACHE (1988) outline a can utilize a distance-dependent probability density formulism that has been used by researchers in the function on group velocity, with additional levels of infrasound community (CERANNA et al., 2009). BROWN sophistication that may include azimuthal and tem- et al. (2002b) and EVERS et al. (2007) implemented poral dependence. Such an approach is currently methods where bearing intersections were weighted being explored by MARCILLO et al. (2012). These by the sine of the angle of intersection. An innovative choices and level of sophistication affects the approach for event location that uses a space–time subsequent model error. approach has also been developed (SZUBERLA and These uncertainties are implemented in the ARNOULT, 2011;SZUBERLA et al., 2009) but is not calculation of the likelihood, assuming Gaussian considered in this study because it is applicable for distributed errors, over all possible locations (latitude, near-source recordings and not to events recorded at longitude), origin times (t0), and group velocities (v). regional and global distances. Following MODRAK et al. (2010), the likelihood is calculated from: Yn 2. Methodology PdmðÞ¼j HiðÞhijm UiðÞtijm i¼1 2.1. The Bayesian Infrasonic Source Locator: where, A Recap "# 2 MODRAK et al. (2010) introduced the Bayesian 1 1 ci HiðÞ¼hijm qffiffiffiffiffiffiffiffiffiffi exp infrasonic source location (BISL) method for local- 2 2 rh 2prh izing infrasound events using a regional network of "# 2 infrasound arrays. BISL uses both arrival time and 1 1 ei UiðÞ¼tijm qffiffiffiffiffiffiffiffiffiffiffi exp ; back azimuth constraints to provide credibility 2 2 r/ 2pr/ bounds (analogous to confidence bounds in frequency statistics) on event location. This probabilistic represent the individual likelihood components for approach accounts for uncertainties in both measure- the backazimuths and arrival times, respectively. ment and model error relevant to the infrasound With di = di(x0, y0, xi, yi) as the distance from each location problem. We can represent the uncertainties hypothetical source to the i’th array, and for Cartesian associated with each parameter by: coordinates, the residual terms are: Vol. 171, (2014) Sources of Error Model and Progress Metrics for Acoustic/Infrasonic Analysis 589  yi y0 have represented location capability by an estimate of ci hi arctan the accuracy based on the azimuthal separation xi x0 d between arrays for a given source location (e.g., e t t þ i : i i 0 v LE PICHON et al., 2009;GREEN and BOWERS, 2010). Location accuracy (expressed in km) can be differ- Location solutions are computed from the multi- entiated from precision (expressed in km2). Within variate posterior probability distribution of location the context of the CTBT, where onsite inspection parameters. A uniform prior on the group velocity is activities can occur inside an area of 1,000 km2, used in our initial development of BISL (that is, the precision is a more useful measure (assuming, of group velocity can vary over some range, typically course, that the model uncertainties are appropriately chosen to represent the possible range of infrasonic defined). group velocities at a particular distance scale). The Using BISL as our location technique, precision limitation of the initial development, as outlined can be calculated in a straightforward manner by in MODRAK et al. (2010), is the assumption that the calculating the area enclosed by a location polygon at group velocity is the same for each array in the a specified credibility. These polygons are derived model. In practice, different phases will typically be from the posterior distribution of location parameters, observed in different directions due to wind, which where the posterior integrating constant is derived introduces anisotropy not accounted for in our with numerical integration, with the initial model preliminary model. At present, we account for the formulation. In this study, we use a credibility of 0.95 model anisotropy through the standard deviation in for calculating the polygons, because this corre- arrival time, which is implemented in the likelihood sponds to a typical level at which confidence regions equations. As long as this standard deviation is set are calculated. Three different scenarios are consid- sufficiently large to capture the possible range of ered: (1) a best case scenario where each event is arrival times for different phases, the model error is detected at every array, (2) a ‘typical’ northern adequately accounted for. Future development of hemisphere winter scenario where the stratospheric BISL will include construction of source-path spe- wind jet blows towards the east, and (3) a ‘typical’ cific priors for group velocity including priors based northern hemisphere summer scenario where the on atmospheric predictions of group velocity with stratospheric wind jet blows towards the west. For associated errors. These improvements should better scenarios 2 and 3 we assume that no arrivals are account for model error through explicitly accounting observed at distances greater than 200 km in the for anisotropy and by incorporating different priors to counter-wind direction (i.e., no stratospheric arrivals different stations (this is discussed in the last section are observed in the counter-wind direction). How- of this paper). ever, within 220 km, tropospheric arrivals are observed 50 % of the time, regardless of direction. Although these assumptions are simplistic, the resul- 2.2. A Location Metric tant maps provide a more realistic assessment of the Event location capability should ideally be esti- location capability than the simulation shown in mated by the precision of a location estimate (this is Fig. 1, and also provide a sense of the effect of the area of uncertainty of the location ellipse or seasonal variations. polygon). If both measurement and model errors are adequately estimated, the location ellipse or polygon should enclose the actual event location on most 3. The Utah Infrasound Network occasions (the credibility or confidence level at which the ellipse or polygon is estimated should define the The Utah infrasound network was deployed in percentage of times the solution will not enclose the two phases. In 2006, three infrasound arrays were location). Previous studies of infrasound location installed around Great Salt Lake to record infra- capability, which have focused on the IMS network, sound signals from rocket motor detonations at the 590 S. Arrowsmith et al. Pure Appl. Geophys.

Figure 1 Simulation results showing location uncertainty (in km2) as a function of location for the Utah infrasound network. Based on the arguments outlined in the paper, these values are representative of current localization capability

Utah Test and Training Range (UTTR) (STUMP et al., 4. Results 2007). In 2008–2009, the network was extended to include six new arrays in order to study infrasound 4.1. The Utah Infrasound Network from small earthquakes in the intermountain seismic The location precision estimates have been com- belt. The full 9-array network is an excellent test bed puted for two scenarios. The first scenario represents for research into the capability of high-density an estimate of current capability. The second scenario regional infrasound networks. The locations of the attempts to assess what might be possible in the arrays in the network are provided in Table 1 and future given further research (we discuss the research shown as black triangles in the figures. that is required to fulfill these goals as outlined in the following section). Each scenario is tested and applied on the Utah infrasound network (representa- tive of a spatially-dense network). Table 1 Under the first scenario (current operational Locations of arrays in the Utah infrasound network capability) the following assumptions are made. First, Array name Latitude Longitude for back azimuth we assume that the existing sum of

measurement and model error, r(h)total, at any given BGU 40.9204 -113.0309 BRP 39.4727 -110.7409 array can be represented by a standard deviation of EPU 41.3901 -112.4099 3°. This value is consistent with recent empirical FSU 39.7196 -113.3900 observations of tropospheric and stratospheric signals HWU 41.6071 -111.5642 from ground-truth explosions at the Hawthorne Army LCM 37.0109 -113.2444 NOQ 40.6526 -112.1186 Ammunition Depot in Nevada (Negraru, Pers. PSU 38.5332 -113.8555 Comm.) in addition to azimuth deviations observed WMU 40.0795 -111.8310 from measurements of earthquakes in the western Vol. 171, (2014) Sources of Error Model and Progress Metrics for Acoustic/Infrasonic Analysis 591

USA (MUTSCHLECNER and WHITAKER, 2005). Second, The simulations of typical summer and winter we assume that the identification of phase is non- scenarios, using estimates of present capability, are unique, and therefore that group velocity could vary shown in Fig. 3. These plots represent averages of ten from 0.28–0.34 km/s (neglecting thermospheric realizations for each season (as discussed above, each returns). For the size of the Utah network this could realization has a random distribution of observations, result in a spread as large as *180 s (this value is with 50 % of arrays detecting signals inside 220 km). calculated from the maximum distance between all These results provide a more realistic estimate of pairs of arrays and the subsequent difference in travel location precision, and how it differs at different time for the mean group velocity of 0.31 km/s and the times of the year. Location precisions of \400 km2 slowest group velocity of 0.28 km/s). Setting r(h)total are possible close to individual arrays, with a more equal to 100 s, it is clear that, for this network typical location precision of *800 km2 surrounding configuration, back azimuth dominates the location most of the network. During the summertime, since capability (Fig. 1). On this basis, the most significant the stratospheric winds blow towards the west in the improvements to current capability can be made by northern hemisphere mid-latitudes, the network does reducing the back azimuth model error. The mea- not detect events at distances greater than 220 km to surement error for back azimuth, typically quoted as the west. This scenario is reversed during winter *0.5° but dependent on the array configuration and when the stratospheric winds at these latitudes blow processing parameters, is small in comparison to towards the east. model error (SZUBERLA and OLSON, 2004). Of course, this conclusion is based on the Utah network, which 4.2. The IMS Network: A Test for the European is a relatively dense infrasound network. For sparse Region networks, the importance of arrival time on the solution should be greater. For comparison to small regional scales, consider As shown in Fig. 1, location precisions of 50 km2 a large region with spatially limited stations. For this are possible in the densest portion of the network. The case, arrival times are much more important, as is whole network region is enclosed by the 400 km2 illustrated for the two example events in Fig. 4. The contour, indicating that any event within this region top panel in Fig. 4 represents current operational will have a location precision better than this value. capability (r(/)total = 1,000 s to account for any ° As one moves away from the region spanned by the phase at any array, and r(h)total = 3 ) while the network, the location precision degrades as expected. bottom panel represents future capability (r(/)total = Most notably, the location precision does not improve 100 s to account for any phase at any array, and by adding arrival time constraints with the large r(h)total = 1.5 ). We note that by operational capa- model error used. For comparison, under the second bility we refer to automatic or real-time methods. The scenario (future capability), we assume that a realistic improvements suggested by the future scenario maps attainable improvement in the total back azimuth require enhancements to the BISL algorithm, in uncertainty is r(h)total = 1.5° and that a realistic addition to enhancements in propagation models, as attainable improvement in arrival time estimation is outlined below. 20 s (HEDLIN et al., 2011). We expect that these improvements will be primarily driven by the reduc- tion of model error. The resultant simulations, shown 5. Research and Development Needed for Location in Fig. 2, can be compared with the simulations Improvements shown in Fig. 1. The improvement in localization precision is dramatic, with the network now enclosed This paper argues that, for dense deployments like by a precision of 50 km2. Additionally, it is clear that the Utah network, key enhancements to location although the dominant effect is back azimuth, the capability will come through propagation modeling inclusion of arrival times does improve the location that can reliably predict the azimuthal deviation capability at these smaller model errors. caused by the propagation of infrasound from source 592 S. Arrowsmith et al. Pure Appl. Geophys.

Figure 2 Simulation results showing potential localization uncertainty (in km2). Based on the arguments outlined in the paper, these values are representative of potential future localization capability

Figure 3 2 Summer (left) and winter (right) maps using r(h)total = 3° and r(/)total = 100 s. Colors represent the location precision in km . Areas shaded white denote regions where B1 station would detect an event, and therefore localization using BISL is not possible to receiver. The prior on azimuth is constructed by algorithm are needed that can incorporate physics- embedding physical azimuthal predictions into the based priors and account for propagation anisotropy. appropriate error model. For sparse network config- The steps required to meet these enhancements can urations, however, enhancements to the localization be broken down into three categories, which are Vol. 171, (2014) Sources of Error Model and Progress Metrics for Acoustic/Infrasonic Analysis 593

Figure 4 Location simulations for two hypothetical events in Europe with four IMS arrays discussed separately below. A final major enhance- Although the Bayesian prior accounts for the ment can be made through combining seismic and unknown group velocity, it does not adequately infrasonic data for the combined geolocation of account for different phase arrivals at different arrays; seismo-acoustic events; this is discussed as a fourth this scenario is currently accounted for by increasing category. the standard deviation in arrival times to include a model error component. Model anisotropy may be a second-order effect at global distances where strato- 5.1. Improvements to the Mathematics spheric returns are the predominant arrival, and such of the Location Framework arrivals are typically observed along similar azimuths The current implementation of BISL assumes the in the direction of stratospheric wind. However, at same group velocity to each array in the network. regional distances, where tropospheric returns are 594 S. Arrowsmith et al. Pure Appl. Geophys. common, model anisotropy is more pronounced. orthogonal to that for azimuth. Therefore, when the Further research and development of BISL is required two measurements are combined, the localization is to enable the inclusion of more sophisticated model more tightly constrained, with an uncertainty ellipse predictions, incorporating state-of-the-art propagation that is more circular in nature. [As an example, see models and atmospheric specifications, in the form of NORRIS and GIBSON (2002)]. Bayesian priors (MARCILLO et al., 2012). The Utah network simulations suggest that back azimuths are 5.2. Improvements to Propagation Models, the dominant effect on the location precision; how- Atmospheric Specifications ever, for global scale monitoring using the IMS network, where perhaps only two arrays will detect an For predicting arrival times and back azimuth event, the inclusion of arrival times will be essential. deviations at regional distances (\2,000 km), 3D ray In this scenario, refinements to the existing BISL tracing is state-of-the-art. To first order, existing framework are expected to lead to dramatic improve- implementations do a reasonable job at predicting ments in location precision. The key refinement arrivals beyond the zone of silence with state-of-the- needed is the inclusion of an array-specific group art 4D atmospheric specifications (e.g., the Ground- velocity; in other words ei in the likelihood equation to-Space model, DROB et al.,(2003)). There are would equal: however, improvements to the propagation models  that would increase the fidelity of the predictions by di ei ¼ ti t þ : accounting for additional physics. 0 v i As ray tracing is a geometrical approximation, it Included in this framework advance is the devel- does not account for frequency dependent effects. opment of BISL-specific algorithms to derive the The model is applicable as long as the acoustic multivariate posterior distribution of location para- wavelength is small in comparison with the physical meters, specifically a Gibb’s sampling algorithm scales of the medium (KINSLER et al., 1982;JENSEN (CASELLA and GEORGE, 1992). This development will et al., 1994). As this assumption breaks down, the enable the use of BISL in a near-real-time operational resulting effect for infrasound propagation is that setting. we begin to observe geometric dispersion. Each Another case where travel time information has a frequency component takes a slightly different prop- large impact on performance is sparse or poorly agation path and there is a spreading of the wave distributed networks, regardless of their spatial packet as observed at the array. Time-domain para- extent. Poor azimuth-only localizations occur when bolic equation models (TDPE) (NORRIS et al., 2007) the arrays are grouped along similar azimuthal can be applied along a given azimuth to predict this directions with respect to the source. The resulting effect. Higher fidelity travel time predictions could localization uncertainty ellipse is very narrow along then be made by comparing the observed and its major axis, elongated along the direction to the predicted waveforms, where the same phase arrival arrays. The quantification of this effect is achieved (peak picking) algorithm would be applied. using geometric dilution of precision (GDOP) Although the TDPE approach can be used for (YARLAGADDA et al., 2000;LEVANON, 2000). GDOP travel times, it does not account for deviations along metrics are derived by quantifying the sensitivity of a given azimuth, which the 3-D ray model quantifies source localization to array measurements, and good with the azimuthal deviation metric. Research could GDOP is supported when the arrays span a variety of be pursued to account for these effects using full- azimuthal directions. wave models. The approach could either be based on In the case of poor GDOP, travel time information exploring 3-D implementations, or in developing can supplement the azimuthal data and result in hybrid N by 2D solutions. significantly improved localization precision. This Another area of research is in the prediction of the improvement occurs because the uncertainly ellipses propagation paths (phases). The well-established for travel-time only localizations are elongated paths of interest are capped at the top of the Vol. 171, (2014) Sources of Error Model and Progress Metrics for Acoustic/Infrasonic Analysis 595 troposphere and stratosphere. Quantifying their sta- appropriate error model provides the priors for the bility, strength, and evolution can be captured with advanced framework. the high-resolution atmospheric specification pro- posed below, coupled with Monte Carlo simulations. 5.3. Validation of Propagation Models, Atmospheric An additional propagation path may also be relevant: Specifications infrasonic energy gets trapped in the stratopause and ‘‘rides’’ this height for an extended distance before Perhaps the most neglected area of research to ultimately escaping and refracting back down to the date has been the adequate validation of propagation ground. The trapping occurs as the energy bounces models using large ground-truth datasets (comprising between layers of inhomogeneities driven by gravity 1,000’s of arrivals). In part, this has been a result of waves. This path is significant because the group the limited infrasound data openly available to velocities are much larger than those for a strato- researchers. Recent work with USArray data has spheric path. More research is needed in further illustrated how spatially-aliased most infrasound quantifying the condition needed and frequency to networks are, and how USArray is enabling such which this additional propagation path occurs. validation for the first time (HEDLIN et al., 2010). For the atmospheric specification, at distances Unfortunately, USArray comprises single acoustic inside 200 km, the addition of fine-scale structure is elements and therefore cannot be used to validate typically required in order to predict observed model predictions of back azimuth deviations. To arrivals. The key research required, associated with address this limitation, research deployments like the improvements to propagation models and atmo- Utah network are essential for gathering sufficient spheric specifications for location purposes,is ground-truth data with which to properly test models. related to the incorporation of this fine-scale structure Such deployments are in their infancy, and little and its effect on the prediction of travel times and research has been done to date on this aspect. back azimuth deviations. Research is needed on the However, based on the findings presented in this implementation of such methods for the prediction of paper, such work is critical to validate the model Bayesian prior PDF’s on azimuthal deviations and implementations, which will ultimately improve the arrival times. localization capability that can be obtained using Recent work has illustrated the value in incor- regional infrasound networks. porating spectral models for gravity waves in propagation simulations (KULICHKOV, 2004;GIBSON 5.4. Seismo-acoustic Location et al., 2009). With the use of such stochastic models, Monte Carlo methods are needed to adequately The complementary nature of infrasound and sample the solution space. Due to the dynamic nature seismic data argues for combining both datasets for of the atmosphere, the solution space is spanned both simultaneous localization of seismo-acoustic events. spatial and temporally. Predictions that capture the Seismic data provide better traveltime constraints relevant scales are on the order of 0.1–1 degree in whereas infrasound back azimuths are superior owing space and hourly in time. Obviously this modeling to the relatively low lateral heterogeneity in the fidelity must be balanced with the resulting payoff atmosphere. CHE et al. (2009) demonstrate the and computation loads they introduce. The modeling advantage of combining both technologies by dem- turn-around time for analysis and operational groups onstrating how a combined seismo-acoustic location must also be considered. With these issues in mind, is more accurate, compared to both seismic and research in optimization of the front-to-end modeling infrasound locations, for a ground-truth mining chain would also be beneficial. explosion in Korea. PINSKY et al. (2012) report on In all cases, these more sophisticated group highly accurate seismo-acoustic locations for a series velocity and back azimuth models are predictions of of explosions in Israel. These papers show promise stochastic atmospheric processes and therefore but there has been little research on how to best have error. Embedding these predictions into the combine seismic and infrasound data for localization. 596 S. Arrowsmith et al. Pure Appl. Geophys.

Towards this goal, we plan to explore an extension of atmospheric explosions, Geophys. Res. Lett., 29. doi:10.1029/ the BISL framework discussed in this paper through 2001GL013778. CASELLA, G. and GEORGE, E., 1992. Explaining the Gibbs sampler, the inclusion of seismic traveltime constraints. The American Statistician, 46, 167–174. CERANNA, L., LE PICHON, A., GREEN, D.N. and MIALLE, P., 2009. The Buncefield explosion: a benchmark for infrasound analysis across Central Europe, Geophys. J. Int., 177, 491–508. 6. Conclusions and Future Research CHE, I.-Y., SHIN, J.S. and KANG, I.B., 2009. Seismo-acoustic loca- tion method for small-magnitude surface explosions, Earth We have discussed metrics for regional infra- Planets Space, 61, e1-e4. DROB, D.P., PICONE, J.M. and GARCES, M., 2003. Global morphol- sound monitoring, and how these might be improved ogy of infrasound propagation, J. Geophys. Res., 108. doi: with improvements to existing atmospheric specifi- 10.1029/2002JD003307. cations and propagation models. Similar metrics are EVERS, L.G., CERANNA, L., HAAK, H.W., LE PICHON, A. and WHI- needed to guide the development of atmospheric TAKER, R.W., 2007. A Seismoacoustic Analysis of the Gas- Pipeline Explosion near Ghislenghien in Belgium, Bull. Seism. specifications and infrasound propagation models Soc. Am., 97, 417–425. doi:10.1785/0120060061. (e.g., how well one can predict the arrival times and GEIGER, L., 1912. Probability method for the determination of amplitudes of signals), but these are not the focus of earthquake epicenters from the arrival time only, Bull. St. Louis. Univ., 8, 60–71. this paper. Ultimately, for the CTBT monitoring GIBSON, R., DROB, D.P. and BROUTMAN, D., 2009. Advancement of problem, the key parameters are detection, location, Techniques for Modeling the Effects of Fine-scale Atmospheric and yield estimation. The authors are currently Inhomogeneities on Infrasound Propagation. in 2009 Monitoring Research Review, Tucson. developing acoustic/infrasonic yield estimation GREEN, D.N. and BOWERS, D., 2010. Estimating the detection methods that require good source location for path capability of the International Monitoring System infrasound corrections. By providing metrics to quantify the network, J. Geophys. Res., 115. doi:10.1029/2010JD014017. capability of infrasound technology in estimating HEDLIN, M.A.H., DE GROOT-HEDLIN, C.D. and DROB, D.P., 2011. A Study of Infrasound Propagation Using Dense Seismic Networks these parameters, the community can better provide American Geophysical Union Fall Meeting, Abstract A31A- decision makers with the tools they need to under- 0037, Bull. Seism. Soc. Am., Submitted. stand both existing and potential capability. HEDLIN, M.A.H., DROB, D.P., WALKER, K.T. and DE GROOT-HEDLIN, C.D., 2010. A study of acoustic propagation from a large bolide using a dense seismic network, J. Geophys. Res., 115. doi: 10.1029/2010JB007669. Acknowledgments JENSEN, F., KUPERMAN, W., PORTER, M., SCHMIDT, H., 1994. Computational Ocean Acoustics, AIP Press, Woodbury, NY, Sec. 3.3.1. We thank David Green for his comments and sugges- KINSLER,L,FREY, A., COPPENS, A. and SANDERS, J. 1982. Funda- tions on a draft of this manuscript and two anonymous mentals of Acoustics, 3rd. Ed., Wiley, NY, Sec. 5.13. reviewers for their constructive feedback. We also KULICHKOV, S.N., 2004. Long-range propagation and scattering of low-frequency sound pulses in the middle atmosphere, Meteor. thank Leslie Casey for proposing this manuscript and and Atmos. Phys., 85, 47–60. doi:10.1007/s00703-003-0033-z. for funding this work. This work was completed under LE PICHON, A., VERGOZ, J., BLANC, E., GUILBERT, J., CERANNA, L., the auspices of the U.S. Department of Energy by Los EVERS, L.G. and BRACHET, N., 2009. Assessing the performance of the International Monitoring System’s infrasound network: Alamos National Laboratory. Geographical coverage and temporal variabilities, J. Geophys. Res., 114. doi:10.1029/2008JD010907. LEVANON, N., 2000. Lowest GPS in 2-D scenarios, IEE Proc.-Radar, REFERENCES Sonar Navig., 147 (3), 149–155. MARCILLO, O., ARROWSMITH, S.J., WHITAKER, R.W. and ANDERSON, BRATT, S.R. and BACHE, T.C., 1988. Locating Events with a Sparse D.N., 2012. Enhancements to the Bayesian Infrasound Source Network of Regional Arrays, Bull. Seism. Soc. Am., 78, Location Method. in 2012 Monitoring Research Review, Albu- 780–798. querque, NM. BROWN, D.J., KATZ, C., LE BRAS, R., FLANAGAN, M.P., WANG, J. and MODRAK, R.T., ARROWSMITH, S.J. and ANDERSON, D.N., 2010. GAULT, A.K., 2002a. Infrasonic Signal Detection and Source ABAYESIAN framework for infrasound location, Geophys. J. Int., Location at the Prototype International Data Center, Pure appl. 181, 399–405. doi:10.1111/j.1365-246X.2010.04499.x. geophys., 159, 1081–1125. MUTSCHLECNER, J.P. and WHITAKER, R.W., 2005. Infrasound from BROWN, P., WHITAKER, R.W., REVELLE, D. and TAGLIAFERRI, E., earthquakes, J. Geophys. Res., 110. doi:10.1029/2004JD005067. 2002b. Multi-station infrasonic observations of two large NORRIS, D., BHATTACHARYYA, J. and WHITAKER, R.W., 2007. bolides: signal interpretation and implications for monitoring of Development of Advanced Propagation Models and Application Vol. 171, (2014) Sources of Error Model and Progress Metrics for Acoustic/Infrasonic Analysis 597

to the study of Impulsive Infrasonic Events. in 29th Monitoring Energy Generation and Propagation at Local and Regional Research Review, edn 2007. Denver, CO. Distances: Phase I—Divine Strake Experiment. Air Force NORRIS, D. and GIBSON, R., 2002. InfraMAP Enhancements: Research Laboratory. Environmental/Propagation Variability and Localization Accu- SZUBERLA, C.A.L. & ARNOULT, K., 2011. Locating explosions, racy of Infrasonic Networks. in 24th Seismic Research Review, volcanoes, and more with infrasound, Physics Today, 64, 74–75. pp. 809–813, Ponte Vedra Beach, Florida. doi:10.1063/1.3580503. PINSKY, V., GITTERMAN, Y., BEN HORIN, Y. and ARROWSMITH, S.J., SZUBERLA, C.A.L. and OLSON, J.V., 2004. Uncertainties associated 2012. Seismo-acoustic analysis for series of ammunition demo- with parameter estimation in atmospheric infrasound arrays,J. lition explosions at Sayarim, Israel. in European Geophysical Acoust. Soc. Am., 115, 253–258. Union General Assembly, Vienna, Austria. SZUBERLA, C.A.L., OLSON, J.V. and ARNOULT, K., 2009. Explosion STUMP, B., BURLACU, R., HAYWARD, C., PANKOW, K.L., NAVA, S., localization via infrasound, JASA Express Letters, 126. doi: BONNER, J., HOCH, S., WHITEMAN, D., FISHER, A., KIM, T.S., 10.1121/1.3216742. KUBACKI, R., LEIDIG, M., BRITTON, J., DROBECK, D., O’NEILL, P., YARLAGADDA, R., ALI, I., AL-DHAHIR, N. and HERSHEY, J., 2000. JENSEN, K., WHIPP, K., JOHANSON, G., ROBERSON, P., READ, R., GPS GDOP metric, IEE Proc.-Radar, Sonar Navig., 147 (5), BROGAN, R. and MASTERS, S., 2007. Seismic and Infrasound 259–264.

(Received November 29, 2011, accepted August 12, 2012, Published online September 20, 2012)