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

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Sources of Error Model and Progress Metrics for Acoustic/Infrasonic Analysis: Location Estimation 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 À 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 À ; 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 À y0 have represented location capability by an estimate of ci hi À arctan the accuracy based on the azimuthal separation xi À x0 d between arrays for a given source location (e.g., e t À 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.
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