INFRASOUND DETECTION FROM BALLOON-BORNE PLATFORMSELIOT YOUNG, ZACH DISCHNER, JED DILLER, STEVE SMITH (SWRI); ALFRED BEDARD (NOAA, CIRES) COLLABORATORS: PETER BROWN (UNIV. WESTERN ONTARIO); DOUGLAS DROB (NRL); MARK BOSLOUGH (SANDIA NATIONAL LABORATORIES)

Project OverviewGOAL:Detect the infrasound signatures of bolides (meteors that explode in the Earth’s atmosphere).APPROACH:• Model the infrasound SNR at various altitudes.• Design a balloon-borne sensor package to improve SNR

over existing ground-based detectors.• Build a sensor package; perform ground-based tests.• Integrate sensor package onto a balloon payload; perform

tests at altitude.

WHY IT’S IMPORTANT:This experiment may detect many more small Earth impactors; it will characterize properties of the NEO population (intrinsic strength, size distribution, families of impactors, etc.)

Detection of Bolides, 1994-2013

Chelyabinsk 500 kt impact (15 FEB 2013)

NOTE: 4.185 gigajoules = 1 ton

556 bolide detections recorded between 1994-2013. Only about 30% of 0.1 kt events (or smaller) are presently identified by the CTBT-IMS network.

February 15, 2013

An interesting day in Chelyabinsk, Russia

The Chelyabinsk Meteor: A 500 kt explosion heard ‘round the world

Infrasound: acoustic waves at frequencies below 20 Hz, the nominal threshold of human hearing.

Infrasound waves can propagate vast distances with little attenuation, so they are useful signatures of explosive events.

The IMS (International Monitoring System) of the CTBTO (Comprehensive Nuclear Test Ban Treaty Organization) has a network of 45 infrasound stations around the world. Infrasound waves from the Chelyabinsk bolide were detected by stations over 5000 miles away.

JID:EPSL AID:12433 /SCO [m5Gv1.5; v 1.126; Prn:7/02/2014; 15:03] P.2 (1-9)

2 C.D. de Groot-Hedlin, M.A.H. Hedlin / Earth and Planetary Science Letters ••• (••••) •••–•••

in the TA at ranges of 6000–10 000 km from the source. The latterdataset is the subject of this study.

The high efficiency of infrasound transmission, which makespropagation to great distances possible, results, in part, from thestratification of horizontal wind and air temperature (sound speedis proportional to the square root of the temperature) withinthe Earth’s atmosphere. This creates transmission ducts, wheresound is trapped between reflections at the Earth’s surface andrefractions within either the stratosphere or lower thermosphere(Drob et al., 2003). Also, atmospheric attenuation of acoustic en-ergy is significantly lower at infrasonic frequencies within thestratospheric duct than at audible frequencies – e.g. approxi-mately 10−3 dB/km at 2 Hz vs. 1 db/km at 250 Hz (Sutherlandand Bass, 2004). However, acoustic absorption increases as atmo-spheric density decreases, particularly at high frequencies, so thatinfrasound returns from the thermosphere have much lower fre-quency content than stratospheric returns (de Groot-Hedlin, 2008;de Groot-Hedlin et al., 2011).

Some of the main goals of infrasound studies related to nu-clear monitoring efforts are to estimate the source energy fromsignals recorded at several hundreds of kilometers distance (e.g.Mutschlecner and Whitaker, 2010) and to estimate the seasonalprobability of detection for a given source size (Le Pichon et al.,2009). These studies generally rely on simplified models of in-frasound propagation, chiefly that the signals are stratosphericallyducted. A primary objective of our study is to examine how long-range infrasound propagation depends on atmospheric propertiesalong a broad swath of travel paths using recordings of infra-sound signals from the Chelyabinsk meteor at USArray sites, alongwith time-varying estimates of global winds and temperatures. Wecompare transmission losses for a large number of infrasound de-tections across a broad region with the objective of understandinginfrasound attenuation within the atmosphere. There have beenfew opportunities to use a large suite of infrasound recordingsof a single event to evaluate infrasound transmission losses overa broad range of propagation paths, due to the scarcity of largeevents that generate detectable infrasound signals at long dis-tances. Signals analyzed in this study were recorded over a widearea, with some sites located within a stratospheric duct, otherswithin a thermospheric duct, and others located near a boundarywhere propagation appears to shift from primarily stratospheric tothermospheric ducting.

In the next section, we discuss infrasound signals recorded atover 200 pressure sensors deployed at USArray sites in Alaska andthe continental United States, and describe the key observationsregion by region. In Section 3, we discuss the atmospheric specifi-cations used to characterize wind and static sound speed profiles,and apply ray-tracing through time-varying atmospheric modelsto synthesize several key features of the data. In Section 4, wecompare infrasound signal energies using estimates of transmis-sion losses that are based on approximate formulae derived fromparabolic equation simulations applied to simplified range inde-pendent models (Le Pichon et al., 2013), modified to account forthe effects of source altitude. These expressions account for bothacoustic absorption and geometrical spreading and are applicableto both thermospherically and stratospherically ducted infrasoundpropagation. Finally, we compare the results of our propagationmodeling with the key observations, and make inferences aboutglobal infrasound propagation losses.

2. Infrasound data

The USArray, a continental scale seismo-acoustic observatorythat includes the USArray Reference Network (USRN) and theUSArray Transportable Array (TA), provided atmospheric pressuredata for this study. The USRN consists of permanent stations, each

Fig. 1. A global map showing the site of the Chelyabinsk meteor burst (dark greystar) [54.836◦ N, 61.455◦ E] and the USArray barometers. Stations where a signalwas detected are shown by black circles; grey triangles indicate stations that did notrecord a detectable signal. Grey lines marked A through C show infrasound propaga-tion paths with initial directions of 13◦ , 3◦ , and −29◦ from the source, as measuredin degrees east of north. Data for stations along these transects are shown in Fig. 2.

equipped with seismometers and barometric pressure sensors, de-ployed across the United States at an average spacing of 300 km.The TA portion of the USArray comprises approximately 400 sim-ilarly equipped seismo-acoustic stations. Each station within theTA forms the node of a nearly Cartesian grid having an averageinter-station spacing of 70 km, with the entire grid spanning afootprint of approximately 2 million km2 (Busby et al., 2006). TheTA is a rolling network; each station is in operation for 2 yr beforebeing moved from the western trailing edge of the array to theleading, eastern edge of the array. On the date of the Chelyabinskmeteor, the USArray comprised a network of several stations inAlaska, another 27 stations along the northwest coast of the con-tiguous US, with the remainder of the array located in the Midwestand near the eastern United States. Fig. 1 shows the configura-tion of the USArray on February 15, 2013 in relation to the siteof the Chelyabinsk meteor burst, with black circles indicating sta-tions at which signals were detected; grey triangles mark wheresignals were not detected. High noise levels over large regions ofthe US masked infrasound signals from the Chelyabinsk meteor.In all, 415 USArray stations were in operation at the time of theevent, and infrasound signals from the meteor were detected atover 200 stations. The Chelyabinsk event is one – albeit particu-larly large – entry in a growing database of atmospheric eventsdetected by the USArray. This database is TAIRED (TransportableArray Infrasound Reference Event Database) and can be found athttp://www.iris.edu/spud/infrasoundevent.

We use data from the National Center for Physical Acoustics(NCPA) infrasound sensors deployed at each site to investigate in-frasound signals from the meteor. The pass band of these piezo-ceramic microphones extend from 200 s to 100 Hz. The data aredigitized at 1 and 40 sps.

Fig. 2 shows infrasound waveform data corresponding to infra-sound propagation along paths marked A, B, and C in Fig. 1, corre-sponding to propagation paths to Alaska, to the US west coast, andto a transect traversing the eastern end of the TA. Traces are band-passed from 0.008 to 0.12 Hz, a frequency band with a relatively

The CTBT-IMS Network

Perforated pipes…

0.01 0.1Frequency (Hz)

Pow

er D

ensi

ty (P

a2 /Hz)

1 10

102

100

10-2

10-4

10-6

To help remove high-frequency noise, microphones typically have inlets to which perforated pipes or hoses are attached. This can reduce noise by ~100x.

Advantages of balloons?For ground-based infrasound stations: most of the high frequency noise is due to wind. Balloons float with the wind – noise may be much lower.

Because the vertical profile of the speed of sound has a minimum in the stratosphere, there is a stratospheric waveguide that channels most of the infrasound energy in the atmosphere.

Question 1: Can we deploy a useful infrasound microphone or microphone array from a balloon?

Question 2: Can we predict the signal-to-noise ratio (SNR) from an explosion by a balloon-borne array vs a ground-based array?

Short-term goals of this project and follow-on long-term goals

Model the expected SNR on balloon-based and ground-based sensors due to various explosions.

Determine an optimal configuration of sensors on a balloon payload.

Perform an actual experiment: measure the infrasound signature of an explosion from a balloon and from ground stations.

Short-term goals: Long-term goals:Build a network of long-duration balloon payloads to detect small bolides entering the Earth’s atmosphere.

Determine properties of the Near Earth Object population from new detections of smaller bolides: size distribution, strength of NEOs, identification of NEO families…

Work Plan(Phase 1)Run existing codes to model refraction & propagation of infrasound waves.

Estimate the SNRs from bolide events as a function of altitude. Quantify the advantage to being in the stratosphere.

Design a balloon-borne payload given a host gondola: configuration of sensors, plus simple avionics, power & C&DH.

Deliverable 1: Paper or conference proceedings on the expected advantages of balloon-borne infrasound detection.

Deliverable 2: CDR report outlining the modeling effort and the preferred design for stratospheric infrasound sensors.

SNR simulation for ground-based sensors: minimum detectable explosive energy in tons of TNT by at least two IMS stations.

Work Plan(Phase 2)Work with flight provider (either SwRI, Near Space Corp. or NASA/HASP) to understand interfaces: communications protocol, allowable form factors, mass limits & power.

Design and build avionics: flight computer, housekeeping and data logger and power distribution.

Model and test performance of electronics in stratospheric conditions (e.g., no convective cooling).

Schedule goal: payload ready for flight by March 31, 2015. Turnaround winds expected in late April, possible date for flight.

Model 20/24 infrasound sensor from Chaparral Physics

The DAYSTAR star tracker: a CU/Aero Senior Project from 2011/2012.

BACKUP SLIDES

HASP (High Altitude Student Payload) Interface Documents

http://laspace.lsu.edu/hasp/documents/public/HASP_Interface_Manual_v21709.pdfVersion 02.17.09 4

Figure 2: Large student payload mechanical interface plate

Version 02.17.09 6

III. HASP – Student Payload Mounting Plate Connectors Your payload mounting plate includes two connectors. A DB9 for serial up and down link and a EDAC 516-020 for power, discrete commands and analog output. Both connectors already include a 24” wire pigtail from the topside of the mounting plate. These pigtails can be fitted with your own connectors or wired directly to internal components of your payload. HASP will interface to both of these connectors on the bottom of the plate using a corresponding plug.

A. Serial Connector Student payloads will send data to and receive commands from the HASP flight system via a single RS-232 serial connection using 8 data bits, no parity, 1 stop bit and no flow control. The serial port speeds will be 1200 baud for the small payloads and 4800 baud for the large payloads. The serial connection will be a DB9 DTE (Data Terminal Equipment) device connector. Only the transmitted data, received data, and signal ground wires will be used. Figure 4 shows the pin layout of the DB9 connector with the pins used for the HASP serial interface labeled. As the student payload will be a DTE device, you will need to wire the DB9 pigtail as a NULL modem to your payload (i.e. pin 3 to your receive, pin 2 to your transmit). This HASP serial connection is mounted on the student payload base plate that is provided to you.

B. The EDAC 516 Connector A twenty pin EDAC 516 (manufacture number 516-020-000-301) will be used to interface with HASP system power, analog downlink channels and discrete commands. A diagram of the EDAC receptacle is shown in Figure 5. Pins are labeled A through X and functional assignments are listed in Table 2 as well as described in the following sections. The wires from the connector are color coded according to function as listed in Table 2. Note that the signal return (pins L,R) is used for both the analog and discrete channels and should not be confused with the power ground (pins W,T,U,X).

Figure 4: DB9 pins used for the HASP

serial interface

Figure 5: The EDAC

516-020 receptacle pin layout.

Table 2: Pin Layout of EDAC 516-020 Function EDAC Pins Wire Color +30 VDC A,B,C,D White with red stripe

Power Ground W,T,U,X White with black stripe Analog 1 K Blue Analog 2 M Red

Signal Return L, R Black Discrete 1 F Brown Discrete 2 N Green Discrete 3 H Red with white stripe Discrete 4 P Black with white stripe

Importance of Detecting Small Bolides

There are many more small Near Earth Objects than big ones. The classic Dohnanyi power law:(i.e., you expect about 11x more objects in the 50% mass bin).

We see the big objects - how many small ones are there, really? How strong are NEOs?

Can we detect discrete catastrophic collisions that produced families of NEOs?

procedures and measurements are given in the SupplementaryInformation.

To establish the nature and source height of the airblast that causeddamage in Chelyabinsk, we used the known trajectory10 and a suite ofvideos (see Supplementary Table 5) that recorded both the airburstand the main airblast arrival. We computed acoustic travel times fromeach point on the airburst trajectory to each video location using apropagation model including winds that was developed for earlierairburst infrasound analyses11. The results show that the first airblastwave (which also produced the damage) arrived from different alti-tudes at different sites, consistent with a cylindrical shock from theextended airburst, as opposed to a more point-like explosion. Thetiming residuals between the observed and expected arrivals followthe bolide trail size, as shown in Fig. 2b, consistent with the shockbeing strong early in its propagation. The airblast reaching the city ofChelyabinsk was generated at altitudes of 24–30 km, roughly from thepeak to the end of the main airburst.

In Fig. 2a we show overpressure predictions from standard airblastrelations based on nuclear explosions7, as used by most impact-effectmodels4,6,12. For comparison, the predictions of cylindrical-line sourceairblast theory applied to meteor entry13 are also shown. The airblastoverpressure in Chelyabinsk from window breakage measurements is3.2 6 0.6 kPa (see Supplementary Information for details). We notethe overestimation of overpressure using the nuclear blast relations7,an effect others have suggested in connection with airbursts4. Giventhat nuclear explosions release half their energy as radiation7, thusreducing the effective yield of airblast energy, the nuclear curve inFig. 2a that is most appropriate to Chelyabinsk is about 1 Mt.

To examine whether a fragmentation model14 is consistent with theobserved data and estimated object size, we have applied an entrycode based on a progressive fragmentation model of the initial object.Assuming an initial meteoroid of diameter 19 m and a tensile strengthat first fragmentation of 0.7 MPa (ref. 10), with ablation ending at about27 km once most of the energy has been lost, we find a reasonablematch to both the light curve and early dynamics. The final mainfragmentations in this model occur near 4 MPa, very similar to thoseobserved (1–5 MPa) in the most severe fragmentation portion of theairburst10. The dynamics and light production from the model are notrealistic near the terminal phase of the airburst because the modelassumes that all fragments split identically at each fragmentationepoch. This is in contrast to observations at the end of the airburstwhere one leading fragment was observed10 (as opposed to dozens ofidentically sized individuals).

To further define the nature of the shock, we have used the wellknown CTH simulation framework used for the Tunguska15 airburstand impactors1 comparable to the asteroid causing the Chelyabinskairburst. The simulation used all the observed trajectory parameters10

and the observed energy as a function of height (Fig. 1b) to mimic theentry process by creating an instantaneous energy release in a sequenceof momentum-preserving air cylinders along the airburst path, scaledsuch that the total integrated energy is 500 kt. Figure 2c and d showsthe result of this simulation and comparison to a video record of thedust cloud generated by the airburst at a similar time. The notablecharacteristics are that the primary shock is cylindrical, in contrast topoint-source energy release airburst models4–6, which have a strongspherical shock component. Instabilities that result from fast-risingbuoyant air in the simulation produce similar structures to those seenin videos of the dust cloud.

Model overpressures for central Chelyabinsk are found to be 3 kPa,consistent with observations. Our estimates of overpressure are basedon window breakage (see Supplementary Fig. 5) confined to a smallregion in Chelyabinsk. The CTH simulations were run for more thanthree minutes after the airburst, producing model variations of over-pressure across the entire city of Chelyabinsk which were smaller thanthe differences produced by local effects, such as shock reflections frombuildings, numerical uncertainty in the simulation and our generally

small number statistics. This limits our ability to validate the simulatedCTH overpressure spatially.

Using our best estimate for the Chelyabinsk airburst energy, ofabout 500 kt, we have estimated the bolide flux at the Earth over theperiod from 1994 to mid-2013. This estimate is based on 20 years oftotal global coverage by the US government or infrasound sensors,more than doubling the earlier time coverage16,17. All events with esti-mated yields in excess of 1 kt are included. Figure 3 shows that thisbolide flux at small sizes (less than 5 m in diameter) is in agreementwithin uncertainties with telescopic8 data and earlier infrasonic18

influx estimates. However, at larger diameters (15–30 m), both thebolide and infrasound18 flux curves show an apparent impact rate atthe Earth an order of magnitude larger than either that estimated by

Bolide energy (kt)

Cum

ulat

ive

num

ber i

mpa

ctin

g th

e Ea

rth

per y

ear

102

101

100

10–1

10–2

10–3

10–4

10–5

10210110010–110–2 103 104 105

Equivalent diameter (m)1 10 100

Lunar craters (ref. 9) NEAT (ref. 27)Spacewatch (ref. 27)Infrasound bolide flux (ref. 18)Power-law fit to ref. 16Ref. 8Bolide flux 1994–2013Bolide flux 1994–2013 fit

Tunguska

Figure 3 | The estimated cumulative flux of impactors at the Earth. Thebolide impactor flux at the Earth (bolide flux 1994–2013; black circles) is basedon about 20 years of global observations from US government sensors andinfrasound airwave data. Global coverage averages 80% among a total of 58observed bolides with E . 1 kt and includes the Chelyabinsk bolide (rightmostblack circle). This coverage correction is approximate and the bolide flux curveis probably a lower limit. The brown line represents an earlier power-law fitfrom a smaller data set for bolides 1–8 m in diameter16. Error bars representcounting statistics only. For comparison, we plot de-biased estimates of thenear-Earth-asteroid impact frequency based on all asteroid survey telescopicsearch data until mid-2012 (green squares)8 and other earlier independentlyanalysed telescopic data sets27 including the NEAT discoveries (pink squares)and the Spacewatch survey (blue squares), where diameters are determinedassuming an albedo of 0.1. From the telescopically determined number of near-Earth asteroids and their typical orbits we can compute the average intervalbetween Earth impactors of a given energy. Energy for telescopic data wascomputed assuming a mean bulk density of 3,000 kg m23 and average impactvelocity of 20.3 km s21. The intrinsic impact frequency for these telescopic datawas found using an average probability of impact for near-Earth asteroids of2 3 1029 per year for the entire population of asteroids. Lunar crater countsconverted to equivalent impactor flux and assuming a geometric albedo of0.25 (grey solid line) are shown for comparison9, although we note thatcontamination by secondary craters and modern estimates of the near-Earth-asteroid population that suggest lower albedos will tend to shift this curve to theright and downwards. Finally, we show the estimated influx from globalairwave measurements conducted from 1960 to 1974, which detected larger(5–20 m) bolide impactors (red triangles)18 using an improved method forenergy estimation compared to earlier interpretations of the same data.

RESEARCH LETTER

2 4 0 | N A T U R E | V O L 5 0 3 | 1 4 N O V E M B E R 2 0 1 3

Macmillan Publishers Limited. All rights reserved©2013

n(M) / M�3.5

Infrasound Propagation

While these chemical and nuclear explosions are analogues ofmeteors, it is not clear that meteors should result in identicalenergy scaling relations, as they occur both at higher altitudesand display directional sound generation due to the ballisticshock geometry (see Fig. 1(a)). These two characteristics aloneimply in some cases that sound generated from a range of heightsalong the meteor’s trail may be received simultaneously at anyone station. It is desirable, therefore, to independently generate aset of empirical relations between infrasonic signal properties andenergy for a suite of large meteors (bolides) having independentenergy estimates.

Such a study was undertaken by Edwards et al. (2006) andEdwards (2007). In order to do this, however, a means of ground-truth is required to calibrate meteor source energies since this isunknown for most meteor events. This was first accomplished inBrown et al. (2002a) using optical sensor satellite observations ofmeteors in the atmosphere to estimate total radiated energy. Anempirical wind correction factor was then introduced to take theeffects of atmospheric winds into account, following the proce-dure used in Mutschlecner and Whitaker (2009). The final rela-tions derived in that earlier (Edwards, 2007) study were

log W ¼3bða#kvÞþ3 log R#

3b

log A ð9Þ

a¼ 3:3670:60, b¼#1:7470:24, k¼#0:0177 s=m for Wo7 kt

a¼ 2:5870:41, b¼#1:3570:18, k¼#0:0018 s=m for W47 kt

where a and b are regression coefficients, k is an empirical wind-correction constant and v is the average component of the windvelocity in m/s along the source to receiver wave propagationdirection in the stratospheric duct. Here A is the maximumobserved peak to peak amplitude of the wave. Similar resultswere obtained for maximum amplitude, integrated energy andsignal to noise ratios (see Fig. 4 for a comparison of the variousamplitude–energy relations discussed). The present study builds

on this earlier work adding many more events and recordedwaveforms worldwide for analysis as well as optimizing themethods of analysis used.

As can be seen in all the above equations (Fig. 4), theserelations have a similar form; however, the exact values of theconstants vary between them for many complex reasons (seeReed, 1972 for a discussion of the need to rely on empirical, ratherthan purely theoretical approaches for long range amplitudedecay relations). Since these equations are linear in log-spacerather than linear space a small difference in a constant cantranslate into a large uncertainty in energy, so they must beapplied with care to obtain reliable information. In particular, thedetails of the fits (and weightings used) to establish the aboverelations are poorly documented and uncertainty bounds are notdefined.

The present work expands on Edwards (2007) by includinga larger dataset of satellite–infrasound bolide events (63 totalcompared to 31 total from Edwards, 2007) and employing a newapproach for objectively establishing the appropriate frequencybandpass to use for infrasound measurement. Further, it is knownthat since the atmosphere is a moving medium, waves travelingthrough it will be Doppler shifted (Morse and Ingard, 1987) so acorrection will be applied to determine whether this has asignificant effect on period measurements, a correction notexamined in Edwards (2007). The effects of wind on amplitudewill also be taken into account. Detailed uncertainty bounds forour relations using a multi-variate covariance approach to our fitswill be established. We will also examine the empirical characterof the frequency roll-off with distance and yield for bolide eventsto provide a discrimination tool for bolide infrasound signalassociation for those instances where range constraints areavailable. Finally, we examine the possibility of using a normal-mode approach to estimate bolide source heights, the remainingmajor uncertainty in bolide infrasound production, for individualbolide events under the assumption that most large bolides havedominant infrasound produced from fragmentation events occur-ring at discrete heights.

3. Theory and background

The detailed physics of the entry and ablation of largemeteoroids into planetary atmospheres is a complex topic wellcovered in the literature and will not be repeated in detail here.The interested reader is referred to Ceplecha et al. (1998) (andreferences therein) for more details. We briefly summarize onlythe major concepts pertinent to the present work.

As the meteoroid interacts with gas molecules in the Earth’satmosphere, energy and momentum is transferred between themeteoroid and atmosphere leading to light emission. It is nor-mally assumed that the luminosity associated with a meteor isproportional to the meteoroid kinetic energy-loss. The observedluminosity of the meteor as a function of time is known as thelight curve of the meteor and can be converted into a measure-ment of the source energy if the fraction of the total kineticenergy lost at any instant and radiated into the passband ofinterest is known (the luminous efficiency). For satellite measure-ments, the radiation efficiency (the fraction of the total energywhich is radiated across all frequencies, assumed to be in theform of a 6000 K blackbody) is given by Brown et al. (2002a)

tI ¼ 0:1212E0:115opt ð10Þ

where tI is the radiation efficiency and Eopt is the total radiatedenergy over the entire duration of the bolide event in kt of TNTequivalent. Eopt is found by integrating the light curve of themeteor (i.e. its radiant intensity as a function of time). Fig. 5

1000

100

10

1

0.1

0.01100 1000 10000

Range (km)Stevens et al. (2006)-CrosswindStevens et al. (2006)-DownwindANSI (1983)Blanc et al. (1997)Edwards (2007)Mutschlecner & Whitaker (2009)Clauter & Blandford (1998)

Ampl

itude

(pa)

Fig. 4. Comparison of AFTAC, French Nuclear, ANSI, Los Alamos HE and boliderelations from Edwards (2007) showing observed infrasound amplitude withrange for an explosion of 1 kt yield (4.185&1012 J).

T.A. Ens et al. / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 208–229 211

azimuth (the azimuthal angle of the arrival of the signal) andtrace velocity (the apparent velocity at which the wave propa-gates across the array). Further, two or more arrays detecting acommon signal may utilize cross-azimuth bearings for simplegeo-location (Brown et al., 2002b). As well, the range to infrasonicsources may also be broadly constrained from a single array usingstatistical estimates of the expected frequency content as afunction of range (Brachet et al., 2009).

The Comprehensive Nuclear Test Ban Treaty Organisation(CTBTO), an international organization set up to monitor fornuclear explosions world-wide, has implemented a worldwidemonitoring network, the International Monitoring System (IMS).The system comprises four technologies: seismic, hydroacoustic,infrasonic and radionuclide monitoring. The infrasonic portion of thesystem includes a proposed worldwide network of 60 infrasoundarrays, 43 of which are currently (as of early 2011) certified andoperational, located in countries around the world (see Fig. 2).

The network is designed to have at least two-station detectioncapabilities globally for a 1 kt TNT equivalent atmospheric nuclearexplosion (Christie and Campus, 2009). Due to the close analogbetween nuclear explosions and meteor events, this system iscapable of globally detecting large meteors, and currently providesmulti-station detections of most sizable bolides. As such, the IMS isan ideal source of infrasonic meteor data and allows a large datasetof energetic bolide events to be identified and analyzed as a singlepopulation for the first time.

With this in mind, in an earlier work, Edwards (2007) identi-fied bolide infrasound signals from IMS stations which were thencorrelated with satellite bolide detection, providing an indepen-dent estimate for source location and total energy. In whatfollows we build on this earlier work. Our goals are similar tothose of Edwards (2007), namely to establish empirical relationsbetween infrasound signal properties and bolide source charac-teristics, particularly yield.

2. Previous yield relations

There have been a number of empirical studies which havedeveloped relations between explosive yield and infrasonicamplitude and period using known explosive sources for calibra-tion. It is well known from blast theory (Sakurai, 1965) that forexplosions in the atmosphere, the amplitude derived yield scaleswith range following a power law of the form ! 1

2 or ! 13 power

depending on whether the wavefront is cylindrical or sphericalrespectively. These earlier studies have assumed such a powerlaw range dependence and then computed the relationshipbetween explosions of known yield and measured infrasonicwave properties (such as period or amplitude).

A commonly used empirical energy relation, the AFTAC (U.S.Air Force Technical Applications Center) period–yield relation,was developed from measurements of the dominant infrasoundperiod produced by ground-level nuclear explosions at rangesfrom 1300rRr8500 km. The regression to these data are givenby ReVelle (1997)

logW2¼ 3:34 log t!2:58,

W2

r100 kt ð1Þ

logW2¼ 4:14 log t!3:61,

W2

Z40 kt ð2Þ

where W is the source yield in kt of equivalent TNT ð1 kt TNT¼4:185% 1012 JÞ and t is the period in seconds of the observedinfrasonic signal at maximum amplitude (Fig. 3 displays theserelations).

Similar relations were found from AFTAC nuclear explosiondata relating source yield W, to infrasonic signal amplitude P(measured in Pa) for a distance D, the range from source toreceiver in degrees (Clauter and Blandford, 1998)

log W ¼ 2 log Pþ2:94 log D!1:84 ð3Þ

Blanc et al. (1997) performed a comparable analysis on Frenchnuclear tests, resulting in the following relation between source-receiver range (R in km), yield (W in kt TNT) and signal amplitudeP (in Pa):

log W ¼ 2 log Pþ3:52 log R!10:62 ð4Þ

Similar empirical energy relations were derived using Sovietatmospheric nuclear explosion infrasound recordings from theInstitute for the Dynamics of the Geospheres in Moscow, Russia(Stevens et al., 2006). Here the dataset was split into downwindand crosswind returns with separate yield relations given by

log W ¼ 3:03 log Pþ3:03 log R!9:09 Crosswind ð5Þ

log W ¼ 3:03 log Pþ3:03 log R!10 Downwind ð6Þ

Another commonly used relation between yield, range andinfrasonic amplitude was developed using known explosionyields of ammonium nitrate fuel oil (ANFO) rather than nuclearmaterials (Mutschlecner and Whitaker, 2009). In this study itwas recognized that since infrasonic waves propagate through amoving medium, a correction must be applied based on windspeed. This produced

log W ¼ 1:49 log Awþ2:00 log R!4:18 ð7Þ

where W is the source yield in tons of ANFO equivalent, Aw is thewind corrected amplitude in microbars and R is the range in km.

The standard overpressure–distance curves for nuclear and highexplosive yields at low amplitudes suggested by the AmericanNational Standards Institute are (Eq. (6) in ANSI (1983))

Dp¼ 6:526W0:3667A R!1:1 p

p0

! "0:6333

ð8Þ

where Dp is the overpressure in Pa, WA is the yield in kt of TNTequivalent, R is the range in km, p0 is the air pressure at the point ofobservation and p is the ambient atmospheric air pressure at thesource, both in Pa.

1000

100

10

1

0.1

0.01

0.0011 2 3 4 5 6 7 8 910 20 30 40

Period (s)

Ener

gy (K

iloto

ns o

f TN

T Eq

uiva

lent

)

AFTAC(E<200kt)AFTAC(E<80kt)

Fig. 3. The empirical AFTAC period–yield relation relates the dominant observedinfrasonic period with source yield.

T.A. Ens et al. / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 208–229210