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An Overview of Stochastic Propagation Methods for Infrasound StudiesPhilip Blom, Stephen Arrowsmith, & Rod Whitaker

OverviewPropagation of infrasonic energy through the atmosphere is

complicated by the dynamic and poorly resolved nature of thepropagation medium. Temporal variability combined with thelimited resolution of measurements for atmospheric parametersresult in a dynamic, poorly constrained propagation medium forinfrasonic energy. A variety of methods have been studied toaccount for the resulting uncertainty including atmosphericperturbation methods and stochastic propagation models. Thedetails of the latter are presented here and demonstrated usinginfrasonic signals generated by chemical explosions in thewestern United States.

Propagation Uncertainties

I Infrasonic energy propagating through the atmosphere is influenced by variations in thetemperature, winds, and density.

I Due to the dynamic nature of the atmosphere, specific propagation effects are non-repeating and,therefore, typically investigated on a case-by-case basis.

I Specifications of the upper atmosphere are constructed from sparse measurements which producesuncertainties in the propagation medium and results in analysis with uncertainties in thepropagation effects for infrasound propagation through the upper atmosphere.

I Two approaches have been applied in the infrasound community to account for this uncertainty:perturbation methods, which update the atmospheric specifications, and stochasticpropagation methods, which aim to construct statistical models for observables.

Perturbation Methods

I Given a set of infrasonic observations and anestimate of the atmosphere specifications,perturbation methods can be employed toidentify modifications to the specificationswhich improve agreement betweenpredictions and observations.

I Typically, empirical orthogonal functions(EOFs) are calculated from a large suite ofatmosphere specifications to construct a set ofrelevant “basis functions” describing theatmospheric winds.

I Using the dominant few EOFs, corrections canbe computed by performing a parametersearch over coefficient values to minimize thedifference between the observed characteristicsand those predicted using the perturbedatmospheric specifications.

Stochastic Methods

I For a given region of the globe, annual anddiurnal variations in the atmosphere producerepeating cycles of atmospheric features whichhave predictable influences on propagation.

I From a historical archive of atmosphere states,distributions can be constructed whichdescribe likely propagation results given aregion of the globe, time of day, and time ofyear (season, month, week, etc.).

I Empirical infrasonic observations can be usedto verify and correct the distributions,improving their accuracy.

I Signal analysis methods can be informed bypropagation modeling priors to improveassociation results and both the precision andaccuracy of source localization estimates.

Constructing Stochastic Propagation Models

Stochastic Celerity Models

I Celerity, ν, is the ratio of the propagation range to thepropagation time along a given propagation path andcan be used to estimate source range and time.

I Using a suite of atmospheres, a distribution, ρν (r, ν),can be constructed by fitting the arrival characteristicsscatter with Gaussian mixture models as in Fig. 1.

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Figure 1: Computation of celerity-range propagation statistics. (a)Arrival locations computed using ray tracing methods, (b) the scatterof arrival range and celerity for a specific azimuth, and (c) the scatterof characteristics fit using a Gaussian mixture model.

Stochastic Azimuth Deviation Models

I Azimuth deviations are produced by crosswinds and horizontal variations in theatmosphere.

I Such deviations cause discrepancies betweenthe apparent and true source azimuth.

I A moving window and 1D interpolation canbe used to compute the bias, δφ (r), andvariance, σδφ (r) as in Fig. 2 following themethod in Fig. 1.

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Figure 2: Propagation statistics for azimuth deviation arecomputed using a similar method to the celerity-rangedistribution.

UTTR Rocket Motor Detonations

I The DTRA Verification Database contains anarchive of ground truth infrasound events.

I Included in the database are 94 rocket motordetonations from the Utah Test and TrainingRange (UTTR).

I The infrasonic signals generated by theseexplosions were detected on several nearbyarrays including I57US and I56US, NVIAR inNevada, PDIAR in Wyoming, and DLIAR atLos Alamos National Laboratory. The sourceand array locations are summarized in Fig. 3.

I Propagation-based priors have beengenerated for the Western US, Fig. 4, andare in general agreement with the empiricalmodels obtained by Nippress et al. [1].

Figure 3: The source location at UTTR (red star) andregional infrasound arrays (yellow triangles) used in thelocalization analysis.

Figure 4: Seasonal variability in the azimuth deviation (left) andcelerity range (right) priors computed for the western US during onemonth periods of winter, spring, summer, and fall.

Using Stochastic Propagation Models - Localization

I The source localizationhas been estimated forone of the UTTR rocketmotor detonations usingthe Bayesian InfrasoundSource Localization(BISL) framework [2,3].

I The analysis has beenperformed with andwithout the stochastic,propagation-based modelsand the results are shownin Fig. 5.

Figure 5: Localization results for a UTTR rocket motordetonation in June, 2004. Shown are the ground truth (red),maximum a posteriori (magenta), and 95% and 99%confidence regions (green). Dashed lines in the source timepanel indicate the 95% confidence bounds.

Conclusions & Implementation

I The dynamic and poorly sampled nature of the upper atmosphere introduceslarge uncertainties in the propagation of infrasound.

I A stochastic approach provides an efficient means to estimate propagationcharacteristics from constructed distributions for various observables.

I Application of the stochastic propagation methods show significantimprovement in localization estimates for large explosions in theWestern US when detected at ranged within 1,000 kilometers.

I The methods presented here have been implemented to interface with theInfraPy infrasonic data analysis pipeline being developed at Los AlamosNational Laboratory.I The stochastic propagation models are constructed using propagation modeling methods

and will be verified and augmented with empirical data.I The models are currently used to inform the location methods and inclusion in the

association algorithm are planned in the future.

References & Related Work

1. Nippress, A., Green, D. N., Marcillo, O. E., & Arrowsmith, S. J. (2014).Generating regional infrasound celerity-range models using ground-truthinformation and the implications for event location. Geophysical JournalInternational, 197(2), DOI: 10.1093/gji/ggu049.

2. Modrak, R. T., Arrowsmith, S. J., & Anderson, D. N. (2010). A Bayesianframework for infrasound location. Geophysical Journal International, 181(1)DOI: 10.1111/j.1365-246X.2010.04499.x.

3. Marcillo, O., Arrowsmith, S., Whitaker, R., Anderson, D., Nippress, A., Green,D. N., & Drob, D. (2013). Using physics-based priors in a Bayesian algorithmto enhance infrasound source location. Geophysical Journal International,196(1), DOI: 10.1093/gji/ggt353.

Contact InformationPhilip S. BlomLos Alamos National LaboratoryEarth and Environmental Sciencespblom@lanl.gov

LA-UR-15-24105

The views expressed here do not necessarily reflect the views of the United States Government,

the United States Department of Energy, or the Los Alamos National Laboratory.