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Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620

www.elsevier.com/locate/jastp

Acoustic analysis of shock production by very high-altitudemeteors—I: infrasonic observations, dynamics and luminosity

P.G. Browna,�, W.N. Edwardsb, D.O. ReVellec, P. Spurnyd

aCanada Research Chair in Meteor Science, Department of Physics and Astronomy, University of Western Ontario,

London, Ont., Canada N6A 3K7bDepartment of Earth Sciences, University of Western Ontario, London, Ont., Canada N6A 5B7

cLos Alamos National Laboratory, Los Alamos, NM 87545, USAdAcademy of Sciences, Astronomical Institute, Ondrejov Observatory, 25165 Ondrejov, Czech Republic

Received 24 May 2006; received in revised form 16 October 2006; accepted 20 October 2006

Available online 18 December 2006

Abstract

Four very high-velocity and high-altitude meteors (a Leonid, two Perseids and a high-speed sporadic fireball) have been

unambiguously detected at the ground both optically using precision all-sky cameras and acoustically via infrasound and

seismic signals. Infrasound arriving from altitudes of over 100 km is not very common, but has been previously observed

for re-entering spacecraft. This, however, is the first reported detection of such high-altitude infrasound unambiguously

from meteors to our knowledge. These fragile meteoroids were found to generate acoustic waves at source heights ranging

from 80 to 110 km, with most acoustic energy being generated near the lowest heights. Time residuals between observed

acoustic onset and model predictions based on ray-tracing points along the photographically determined trajectories

indicate that the upper winds given by the UK meteorological office (UKMO) model systematically produce lower

residuals for first arrivals than those from the Naval Research Laboratory Horizontal Wind Model (HWM). Average

source energies for three of the four events from acoustic data alone are found to be in the range of 2� 108�9 J. One event,

EN010803, had unusually favorable geometry for acoustic detection at the ground and therefore has the smallest

photometric source energy (10�5 kt; 6� 107 J) of any meteor detected infrasonically. When compared to the total optical

radiation recorded by film, the results for the three events produce equivalent integral panchromatic luminous efficiencies

of 3–7%, within a factor of two of the values proposed by Ceplecha and McCrosky [1976. Fireball end heights—a

diagnostic for the structure of meteoric material. Journal of Geophysical Research 81, 6257–6275] for the velocity range

(55–70 km s�1) appropriate to our events. Application of these findings to meteor showers in general suggest that the

Geminid shower should be the most prolific producer of infrasound detectable meteors at the ground of all the major

showers, with one Geminid fireball producing detectable infrasound from a given location every �400 h of observation.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Infrasound; Meteors; Fireballs; Meteor shower

e front matter r 2006 Elsevier Ltd. All rights reserved

stp.2006.10.011

ing author. Tel.: +1 519 661 2111;

4085.

ess: pbrown@uwo.ca (P.G. Brown).

1. Introduction and overview

Infrasonic signals generated by meteors have beendetected frequently, since the first recordings were

.

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made almost a century ago (cf. Whipple, 1930).Most meteor infrasound is generated by largefireballs penetrating deep into the atmosphere, withassociated acoustic energy often concentrated atlower frequencies. Such low-frequency meteorinfrasound may propagate and be detected forthousands of kilometers (ReVelle, 1976). Lesscommon are acoustic detections of smaller meteorsmade at short (�100 km) ranges. In the fewinstances where short-range meteor infrasound hasbeen clearly detected (cf. Le Pichon et al., 2002), themeteors have been deeply penetrating and usually ofmodest energy. Meteor infrasound is distinct fromthe other type of sound occasionally associated withbright meteors, namely electrophonic or simulta-neous sound (Keay, 1980). Electrophonic soundoccurs simultaneously with the appearance of ameteor (unlike infrasound which propagates atacoustic velocities) and is believed to be related toemission of very low-frequency electromagneticwaves from very bright meteors (Keay and Ceple-cha, 1994). Throughout our discussion when we usethe term ‘‘sound’’ we are referring to acousticwaves, not electrophonic sound.

Generally, shower meteors associated with thePerseids of August or the Leonids of November, donot produce sounds at the ground. They are usuallynot energetic enough and (most importantly) ablatetoo high due to their fragile physical structure toeasily produce the type of audible phenomenausually associated with larger meteorite-producingevents. A key limitation to the detection ofinfrasound from such high-altitude meteors is theheavy attenuation (associated with absorptive lossesfrom viscosity, heat conduction, turbulence andmolecular relaxation) experienced by acoustic wavesof high frequency (associated with smaller events) atlarge heights (ReVelle, 1976).

Despite this limitation, two cases of probableinfrasound from shower meteors have been reportedin the literature. In 1974, the infrasonic signal of aGeminid fireball observed by radar was veryprobably detected (McIntosh et al., 1976). In thiscase, an absolute correspondence between theacoustic signal and radar record was not possibledue to the lack of a means of measuring thecomplete trajectory and position from the radarrecord (which provided range only). The mostconvincing case of a shower meteor-producinginfrasound was reported by ReVelle and Whitaker(1999) associated with a Leonid fireball in 1998. Inthis case, a clear infrasound signal of high frequency

and short duration was detected after a brightLeonid fireball was recorded visually, with CCDcameras and probed by LIDAR (Zinn et al., 1999).While a general trajectory was determined in theatmosphere, the event did not have multi-stationinstrumental optical records to provide a completepath/lightcurve for reference in the infrasoundanalysis, limiting any numerical ray tracing. Never-theless, it is certainly clear that the infrasound signaldetected was associated with this exceptionallybright Leonid fireball, the infrasound having beengenerated at a height of 9177 km, and representsthe first time an unambiguous acoustic signal hasbeen detected from a shower meteor. Although thissignal was brief, it demonstrated the result knownfrom work done years ago that small sources can bedetected at high altitudes if the surface winds arerelatively low in speed. For example, during theNASA rocket grenade experiments in the1960–1970s (e.g. Stroud et al., 1960), routinedetection of 2–4 lb ‘‘point’’ source grenades at theground became almost commonplace. These datawere subsequently used to infer atmosphere tem-perature and horizontal wind structure in theatmosphere. This is equivalent to point sourceenergies of 10�6–10�5 kt, very similar to the recentlyquoted minimum expected to produce detectableinfrasonic signals at the ground by ReVelle (2005) (1kiloton TNT ¼ 1 kt ¼ 4.185� 1012 J).

Motivated by this Leonid detection, we began toinvestigate the possibility of obtaining infrasonicdetections of other bright high-altitude (shower)meteors. The goals of this study were to

1.

Determine the expected frequency that shower(high-altitude) meteors produce infrasonic sig-nals at the ground (for a particular station).

2.

Refine from observations and theory the mini-mum energy needed to produce infrasonic signalsat the ground from small-meteor events buildingon the early estimates of ReVelle (1976) andReVelle (2005).

3.

Use high-precision photographic trajectoriestogether with ray tracing to ground-truth testseveral modern atmospheric models to highaltitudes by comparing expected and observedacoustic arrivals from these high-altitudemeteors.

4.

Better understand the shock-generation mechan-ism producing shower infrasound signals at theground by performing ray tracing from the high-precision trajectory measurements.

ARTICLE IN PRESSP.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620602

5.

Make direct estimates of integral luminousefficiency for bright shower meteors by usingvarious theoretical formulations of expected totalsource energy based on acoustic measurementsand comparing these to the total panchromaticradiation emitted.

6.

Compare theoretical models of entry to observeddynamic, photometric and acoustic measure-ments for large shower meteoroids to validatethese models and estimate the best ablationmodel parameters for cm to tens of cm-sizedparticles.

7.

Examine the seismo-acoustic coupling of air-waves from these small events.

The site chosen for the infrasonic part of theinvestigation was I26DE (Freyung) (48.91N, 13.71E)since it is an infrasonically quiet site well suited todetection of very low-amplitude infrasound signals.Additionally, it is located close to the southern edgeof the European Fireball Network (EFN) (cf.Spurny, 1997), a network of cameras designed tomeasure the precise trajectory and brightness profileof cm-sized (and larger) meteoroids ablating in theatmosphere.

During the interval 2000–2005, we systematicallysearched infrasound records at I26DE for 34European network fireballs, which had accuratelymeasured photographic trajectories/lightcurves andoccurred relatively close to I26DE (within�300 km). Almost half of these events (16) weredetected infrasonically at I26DE. In particular, 11of these 34 events had very high ending heights(above 70 km) and of these, four were detected atI26DE. It is the infrasound from these four events(and corresponding seismic records), which consti-tute the material for our study.

In this first paper, we present and discuss theobservational data for these four exceptionally high-altitude events based on multi-station photographicrecords of their flight including their trajectorysolutions and photometric behavior. We alsopresent and discuss the observed infrasound signals.Additionally, we will examine the acoustic sourcelocations along the trajectories of the infrasoundfrom ray tracing, make simple source energyestimates from the acoustic signals using existingrelations, which have been developed and presentedin other work (e.g. ReVelle and Whitaker, 1999) andestablish the probable shock source mechanism(ballistic or ablational) based on ray deviationsfrom idealized cylindrical line-source blast theory.

These acoustically derived energies are compared tothe photometric lightcurves to establish among thefirst independent estimates for integral luminousefficiency. Finally, we conclude by examining theimplications for the frequency of infrasound detec-tion of other meteors associated with major meteorshowers based on our results.

A second paper in this study will focus on anenergetics analysis of these events together withnumerical modeling of the blast waves, overpressuredecay and meteor entry. A third and final paper willfocus on the seismic recordings of the airwave fromthese four events and determine probable seismo-acoustic coupling efficiencies of the acoustic wavesfrom a simple half-space model of the ground nearI26DE.

2. Optical observations

A summary of the four high-altitude events thathave both infrasound and ground-based photo-metric recordings (and in some cases spectra andseismic recordings) are shown in Table 1. Opticalobservations of the four high-altitude meteors weremade as part of the routine operation of the EFNwhich employs all sky cameras equipped with fisheye lenses operating in both fixed and guided modesto record meteor activity in central Europe(cf. Spurny, 1997 for more details of networkoperations, goals and data reduction methods).Spectral response for the panchromatic photo-graphic emulsion of these systems lies in the360–675 nm wavelength band. Unless otherwisenoted, all magnitude estimates refer to the panchro-matic passband. Additionally, in all cases, ground-based radiometers were able to record the bright-ness of the meteors, within a much wider400–1200 nm (silicon) wavelength band with atemporal sampling resolution of 1ms. In additionto providing a precise measure of relative brightnessin the silicon passband, these radiometers establishthe absolute timing of each event with highprecision, an essential element in linking the atmo-spheric trajectories to the observed airwave throughray tracings. In all four of the following cases allgeodetic position, altitude, time, intensity andorbital information are derived from optical ob-servations by the EFN.

A general property of all four events is their highvelocity (greater than 60 km s�1), high begin andend heights (ranging from 116 to 69 km altitude)and fragile physical structure. All four move on

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Table 1

Basic atmospheric trajectory data, apparent and geocentric radiants and orbital elements (J2000.0) of four bright EN meteors with high

altitude infrasound registrations from all-sky photographic cameras

Meteor EN130801 EN151101A EN010803 EN030804

Date 13.8.2001 15.11.2001 1.8.2003 3.8.2004

Time (UT) 23h29m45.0s70.3s 1h32m30.0s70.3s 22h18m54.0s70.3s 23h10m22.6s70.3s

Hb (km) 111.4370.03 115.8670.01 109.5470.04 112.3770.02

lB (deg) 11.922870.0006 13.658570.0001 13.862070.0003 13.2722570.00004

jB (deg) 49.367370.0004 49.810370.0001 48.860870.0003 49.0127470.00002

HE (km) 68.68070.010 80.8670.03 83.9170.06 75.8170.02

lE (deg) 11.4935470.00015 12.999870.0004 13.057770.0005 12.8584070.00004

jE (deg) 49.0742670.00010 49.851370.0003 48.528270.0005 48.7876370.00002

Hmax (km) 75.5 82.2 96.1 80.9

lmax (deg) 11.562 13.026 13.444 12.917

jmax (deg) 49.121 49.850 48.689 48.820

L (km) 62.66 59.72 75.36 54.13

t (s) 1.06 0.84 1.09 0.90

Slope (deg) 43.0370.03 35.8870.04 19.8870.05 42.4970.02

straj (m) 23 11 15 9

MPmax �13.3 �14.9 �8.1 �12.5

Mass (g) 600 800 24 370

logR

I dt (kt) �5.25 �4.54 �6.54 �5.34

LogE (kt) �3.63 �3.31 �4.88 �3.84

PE �5.24 �6.02 �5.27 �5.61

Type II or IIIA IIIB IIIA IIIA or IIIB

RAapp (deg) 51.3770.07 152.1570.03 38.8870.06 33.5670.03

DEapp (deg) 59.4670.03 23.4770.04 35.7470.05 54.5970.02

VN (km s�1) 59.8970.13 71.3070.11 68.7870.10 60.870.2

RAg (deg) 52.0870.07 152.3070.03 39.4070.06 34.1470.03

DEg (deg) 59.5170.03 23.3070.04 35.5070.05 54.6270.02

Vg (km s�1) 58.6970.13 70.1870.11 67.6370.10 59.670.2

a (AU) 26 8.470.7 40 24

e 0.96570.010 0.88370.010 0.97670.009 0.96070.014

q (AU) 0.933370.0007 0.9814970.00018 0.957670.0008 0.966870.0005

o (deg) 147.170.2 169.5570.14 152.370.2 154.770.2

O (deg) 141.2477570.00001 232.7339670.00001 129.2099270.00001 131.1646470.00001

i (deg) 111.4370.10 160.6870.07 146.7470.08 114.1870.11

Shower Perseid Leonid Sporadic Perseid

P.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620 603

retrograde orbits of the Halley-family-type cometsand are therefore unambiguously of cometaryorigin. Following the physical classification schemeof Ceplecha and McCrosky (1976), the mechanicalproperties of the fireballs can be described via thePE criterion. In the case of all four fireballs, thecharacteristics are those of group III (A or B); thismeasure establishes the meteoroids as likely havingquite low bulk densities (below 1000 kgm�3) andhigh ablation abilities (cf. Ceplecha et al., 1998 for adiscussion), again consistent with a cometary origin.This fragility together with their high entry velocityis the underlying cause of their particularly highend-heights.

In what follows we provide a brief set ofcomments relating to each of the four meteors,

beginning with the available photographic andphotometric data and then presenting the associatedinfrasound signals for each event.

1. EN130801: August 13, 2001 Perseid Fireball:On August 13, 2001 a bright Perseid meteor(EN130801) was observed by the EFN at23:29:45UT, at its brightest the meteor reached amaximum magnitude of �13.3 (Figs. 1 and 2).Travelling initially at a velocity of 58.7 km s�1,the photometric mass (using the differentialpanchromatic efficiency values from Ceplechaand McCrosky (1976)) was determined to be0.60 kg, corresponding to an initial kineticenergy of 0.247 ton TNT. The visible trajectoryof the Perseid meteor as detected by the photo-graphic cameras had a beginning height of 111.4 km

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Fig. 1. European fireball network images of the four high-altitude meteors from which infrasound has also been recorded.

Fig. 2. Panchromatic lightcurves of all four infrasonically detected fireballs. These lightcurves were derived from densitometery

measurements of the original film records following the standard technique as described in Ceplecha (1987).

P.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620604

and penetrated down to an end height of 69 km.In addition, records from low-light level TV(LLLTV) systems recorded the very earliest portion

of the visible trajectory, beginning at 161 kmaltitude. The infrasound signal (described later) isclearly linked to this meteor and is the first time

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Fig. 3. The array layout for the I26DE (Freyung) infrasound

station.

P.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620 605

infrasound from a Perseid meteor has beenreported.

2. EN151101A: November 15, 2001 Leonid Fire-

ball: At 01:32:30UT on November 15, 2001 theEFN detected a very bright Leonid meteor travelingwestwards at a heading of 275.421 and entry angleof 35.81. Observations were made by several all-skycameras, fixed and guided cameras (Fig. 1), aground-based radiometer, and by spectrographiccameras at the Ondrejov observatory where adetailed meteor spectrum was obtained. The Leonidreached an absolute brightness of �14.5 (Fig. 2)during its visible descent from 120 to 81 km altitude;the event is comparable to or slightly larger inenergy than the first Leonid reported infrasonicallyby ReVelle and Whitaker (1999). It should be notedthat the extreme brightness of this event requires alarge extrapolation from the brightness/density ofreference stellar sources on the photograph leadingto an uncertainty in the peak panchromaticmagnitude of �1.5 magnitudes.

3. EN010803: August 1, 2003 Sporadic Meteor:This bolide event was caught on three EFN camerason August 1, 2003 at 22:18:54UT. With a radiantnot associated with any specific major shower, it isconsidered a true sporadic (random) meteor. With amaximum visual magnitude of �8.1 and an initialvelocity of 68.8 km s�1, this sporadic meteor wasfound to have a photometric mass of 0.024 kgcorresponding to an initial kinetic energy of 0.0136 tTNT (10�5 kt) and is currently the lowest massmeteoroid yet recorded with an infrasound signal atground level. One reason for this sensitive infrasonicdetection is the particular observing geometry; thevisible trajectory having passed almost directlyoverhead of the I26DE array. In addition tothese photographic data, the event was recordedby two sensitive LLLTV cameras beginning at143 km altitude. Fig. 2 shows the panchromaticlight curve.

4. EN030804: August 3, 2004 Perseid Fireball: Thefinal high-altitude bolide event was a second Perseidmeteor detected on August 3, 2004 at 23:10:23UTand having a maximum absolute magnitude of�12.5. It had an initial photometric mass of0.370 kg and an entry velocity of 60.8 km s�1,corresponding to an initial kinetic energy of0.163 t of TNT. Its beginning height was firstobserved at 114.3 km and it subsequently penetrateddownward to an end height of 75.8 km. In this case,the meteor was photographed by guided and fixedall-sky cameras at EFN station 4 Churanov as close

as �30 km from the I26DE (Freyung) InfrasoundArray.

3. Infrasound observations

The infrasound records associated with eachof the four high-altitude meteor events describedhere are analyzed using standard techniques(cf. Evers and Haak, 2001; Edwards et al., 2006).All data were processed using the analysis packageMatSeis 1.7 (Harris and Young, 1997) (availablefrom http://www.nemre.nnsa.doe.gov/cgi-bin/prod/nemre/matseis.cgi). These measurements produceangle of arrival for the coherent infrasonicwavetrain in selected bandpasses (both backazi-muth and angle of incidence or trace velocity) aswell as amplitude, duration and signal cross-correlation across the array. Total signal energyis also computed, based on squaring and thensumming each sample of the filtered, optimumwaveform over the entire duration of the signal.More details of the methodology can be found inEdwards et al. (2006).

The I26DE infrasound array consists of fiveseparate microbarographs (MB2000 units whichmeasure absolute pressure changes) separated byspacings typically of order 1 km. Fig. 3 shows thelayout of the I26DE array. Here, we briefly describethe salient features of each meteor-associatedinfrasound signal and summarize these propertiesin Table 2.

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Table 2

Observed and computed infrasound signal properties for the four high altitude bolides as recorded at I26DE

Meteor EN151101A EN130801 EN010803 EN030804

Arrival time (UT) 01:40:20 23:39:32 22:24:26 23:16:03

Delay time to initial arrival (s) 470 587 332 340

Signal duration (s) �3 �24 �28 �37

Trace velocity (km s�1) 0.395 0.341–0.357 0.734–1.53 0.433–0.563

Arrival azimuth (degrees) 349.51 2791–2871 2181–2421 2681–2851

Ground range to fireball (km) 118 164 36 59

Mean signal speed (km s�1) 0.315 0.303 0.301 0.294

Slant range to fireball (km) 148 178 100 100

Peak to peak amplitude (Pa) 0.4370.16 0.2470.04 0.2070.11 0.1570.05

Period at maximum amplitude (s) 1.7970.23 1.4570.1 3.0170.11 2.5470.06

Integrated signal to noise ratio 3672 6476 32715 4578

Maximum cross-correlation value 0.82 0.78 0.74 0.68

Computed source height (km) 87–89 �70–95 �84–100 78–100

Blast wave radius R0 (m) 25.0 19.6 7.7 16.8

Local air temperature (K) 272.4 303.2 303.3 302

Sound speed at ground (km s�1) 0.331 0.349 0.349 0.348

Observed signal incidence angle 331 �01 771–391 521–361

All measurements were made over the bandpass 0.3–9.5Hz.

Fig. 4. Trajectories and detection geometry for the four high

altitude meteors in relation to I26DE. (a) Meteors and the

observing station, (b) same, with the range of observed infrasonic

backazimuths for each meteor indicated. Prevailing winds for

each observation were from easterly directions, except

EN151101A, which were westerly.

P.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620606

1. EN130801: August 13, 2001 Perseid Fireball:Infrasound from this event first arrived at thewestern element of I26DE starting at23:39:32.0UT on August 13, 2001 with a totalcoherent signal duration of 24 s. Observed infra-sound back azimuths systematically changed from2791 to 2871 during the course of the signal andare consistent with acoustic radiation emanatingfrom the region that surrounds the flare near theend of the trail (Fig. 4). The waveform (Fig. 5)shows three distinct arrivals—an initial pressuredecrease followed 5 s later by a shocky blast-wave signature and then a final pressure dropanother 4 s later. The individual features (labeled1, 2 and 3 in Fig. 5) have arrival azimuths of 284.51,290.71 and 290.81, respectively, indicating theendpoint detonation may be related to theinitial pressure drop (which also has the smallestacoustic distance to the station). The propaga-tion is all counter-wind based on our bestmodel estimates (see later) and is associatedwith an average signal speed of 0.303 km s�1.The trace speed also indicates the acoustic signalwas traveling nearly parallel to the ground; pre-suming the signal comes largely from the detonationnear the endpoint (consistent with the azimutharrival estimates) the apparent elevation above theground of the fireball terminal point as seen fromI26DE was only 231 elevation, confirming thisinterpretation (see details in section on ray-traceresults).

2. EN151101A: November 15, 2001 Leonid Fire-

ball: The acoustic signal from this energetic eventbegins at 01:40:2071UT, some �8min after theoptical registration of the fireball. The brief blast-wave infrasonic signal was recorded at I26DE andlasted only �3 s (Fig. 5). Despite the brief duration,

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Fig. 5. (A) (TOP) Infrasonic pressure waves as recorded by the I26DE microbarometers (channel 2): (a) EN130801, (b) EN151101A, (c)

EN010803 and (d) EN030804. (B) (BOTTOM) Infrasound analysis for the EN151101A meteor. Shown are (top) the unbounded F-statistic

which measures coherency of the waveform across the receivers (cf. Evers and Haak, 2003), apparent trace velocity of signal across the

array (middle) and the dominant arrival azimuth for signals in each of the 10 s bin windows. The solid vertical line indicates the timing of

the signal arrival.

P.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620 607

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Fig. 5. (Continued)

P.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620608

the signal amplitude is the largest of the four eventsin this study with a backazimuth of 349721 and atrace velocity of 0.395 km s�1 corresponding to an

arrival angle of 331 from the horizontal. Forcomparison, the apparent angular altitude of thefireball endpoint as seen from I26DE was also 331.

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The straight-line backazimuth projection intersectsthe trajectory at a height of �100 km, though thisdoes not take into account changes due to winds(Fig. 4). The average signal speed was 0.315 km s�1.The signal characteristics, including duration, fre-quency content and pulse shape are very similar tothe infrasonic signal for the bright Leonid reportedby ReVelle and Whitaker (1999) and are summar-ized in Table 2.

3. EN010803: August 1, 2003 Sporadic Meteor:Infrasound from this meteor first arrived at I26DEat 22:24:26UT, some 332 s after the optical eventand displayed an initial arrival back azimuthsstarting near 2181 increasing to 2301. The arrivaltrace velocities ranged from 0.734 to 0.951 km s�1,corresponding to very steep airwave arrivals. This isall consistent with a line source passing nearlydirectly over the station as indicated by the opticalrecord, which has the meteor at an altitude near105 km when passing closest to the station. Thearrival directions further suggest I26DE detectedonly acoustic radiation from the last �10 to 15 kmof the path. Fig. 4 shows the arrival azimuth rangeand direction relative to the meteor ground path.The initial shocky N wave is consistent with thenotion that this is the detonation point/deepestterminal point, while the signal just a few secondsafter this point is very low in amplitude as might beexpected for acoustic signals having been generatedat 4100 km altitude. Time delays of some of theweaker features after the main signal are consistentwith arrival azimuths of �2301, indicating poten-tially slightly higher source altitudes than the firstarrivals.

4. EN030804: August 3, 2004 Perseid Fireball:This event showed a signal at I26DE beginning at23:16:03UT with a corresponding signal duration of37 s. Initial arrival backazimuths start in the range262–2681 while the final values at the end of thewavetrain are close to 2851. The trace velocitysystematically increases across the signal, startingnear 0.433 km s�1 and ending close to 0.56 km s�1

corresponding to arrival angles of �40–501 from thehorizontal. The endpoint occurs near an apparentangular altitude of 451 as seen from I26DE,consistent with the acoustic arrival angles. Thedetection geometry, timing, trail orientation andrelative wind system are almost identical to that ofEN130801 (see Tables 1, 2 for comparisons of thetwo cases). Of particular interest to this study, thelower-frequency content of this signal (and loweramplitudes) near the end of the acoustic signal

produce back azimuths consistent with shockgeneration in regions on the meteor’s trail wherethe altitudes are greater then 100 km. Fig. 4 showsthe detection geometry relative to the groundprojection of the trail.

The infrasonically observed characteristics of allfour events are summarized in Table 2 and thefiltered waveforms are shown in Fig. 5. Fig. 4summarizes the relative geometry and detectionazimuths of each meteor path relative to I26DE.

4. Ray-tracing determination of acoustic source

regions

Using the infrasonic observations of arrival timeand duration along with position and timinginformation for each meteor as summarized inTable 1 we performed ray tracings from source toreceiver. As each meteor had very high-precisiontrajectory data (standard deviations of the trajec-tory solution are typically o20m—see Table 1) thegoal was to establish the portions of each trailgenerating acoustic signals detected at I26DE, usingthe photographic trajectories as the assumed start-ing conditions. The robustness of the source regionfit was found by comparing arrival times, arrivalazimuths and elevations from various heightsagainst observed quantities at I26DE. Each of thesemeasures is an independent check on the solution.

Once the height interval producing acousticsignals at I26DE is established for each event inthis manner, it then becomes possible to find thedeviation of the original acoustic radiation frompure ballistic shock (which is perpendicular to themeteor trajectory in the idealized case) and con-strain whether or not the source behaves as a quasi-spherical moving point source (ablational shock).Additionally, it becomes possible to test variousupper wind/atmospheric models by comparingarrival times with the predicted residuals. Theraytracing was performed using both the InfraMAPsoftware (Gibson et al, 1999) and Supracenter(Edwards and Hildebrand, 2004) software, todelimit the source regions and geometry of theobserved airwaves. In general, we found almost nodifference in the predicted arrival times using thesetwo different software tools—in what follows weshow only the Supracenter solution, noting that theInfraMAP solutions are virtually identical.

Using the measured position at each shutterbreak along each meteor’s trajectory, rays werelaunched towards I26DE; those rays passing within

ARTICLE IN PRESSP.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620610

�2 km of the station were accepted as detectableand their traveltimes and launch conditionsrecorded. Initially, model atmospheres were con-structed using nearby radiosonde releases near thetime of each event (providing temperature and winddata to �30 km altitude), supplemented with NASAand Naval Research Labs MSIS-E00 and Horizon-tal Wind Models (HWM) (Hedin, 1991; Hedin etal., 1996). Using these models, however, it wasfound that for nearly all events (except EN151101A)it was impossible to match the arrival timing of theI26DE observations. After removing all windinformation, rays were again launched; however,poor timing agreement remained for three of thefour events. This problem coupled with the pooragreement when winds were added, suggestedpotentially poor modeling of upper atmosphericwinds by HWM. Indeed HWM modelled strato-spheric winds in each case exceeded 80m s�1 at�65 km altitude. As these winds are easterly duringthe summer, the effect was to shift all predictedarrivals to later times, effectively over-correctingarrivals for the presence of winds as compared tothe observed travel times exactly as observed.

In an attempt to obtain a better estimate for thestratospheric winds present during these events, weexamined the UK meteorological office (UKMO)stratospheric assimilated data set which providedmeasurements (as taken by the UARS satellite) toan altitude of �60 km of the temperature and windconditions for the days in question (Swinbank andO’Neill, 1994). Satellite profiles were compared toradiosonde measurements and were found to be inexcellent agreement, providing confidence for mea-surements at higher altitudes. Interestingly, UKMOmeasured wind values were approximately half ofthose provided by HWM at stratospheric altitudes.Thus UKMO satellite measurements were mergedwith MSIS-E00 and HWM model values at �60 kmand a third set of ray tracings were performed,which provided the consistently best timing fit to theobservations at I26DE than either the no-wind caseof the HWM modelled wind case.

Fig. 6 shows the arrival time curves for each ofthe four events for all three-ray tracings (no windcase, HWM and UKMO (merged with HWMabove 60 km)). The differences between HWM andUKMO are significant for all events butEN151101A. In particular, HWM shows firstarrivals between 15 and 30 s too late in all three ofthe remaining cases (reflecting the overestimation ofthe stratospheric winds), while the UKMO solutions

are consistent typically to within 5 s in the startresiduals for these events. Given the time delays, the5 s differences reflect average sound speeds in theUKMO data set accurate to �1%. In what followsall timing solutions are assumed to be thosesolutions found using the UKMO wind data atstratospheric altitudes.

From the infrasonic signal residual times alone,as derived from the optically observed meteortrajectories, acoustic source regions for the fourmeteors tended to lie at altitudes 480 km. ForEN151101A (Leonid) this region was found to be at89–93 km, for EN130801 and EN030804 the sourceregions are more extended between �80 and100 km, while due to degeneracy the EN010803(sporadic) meteor may have had contributions fromheights between its terminal points at 84 km altitudeup to nearly 110 km.

To refine these solutions, the ray-trace resultswere further examined to estimate arrival azimuthsand arrival elevations as seen from I26DE. Theseresults are shown in Fig. 7 (arrival azimuths) andFig. 8 (arrival elevations).

The time residual solution for EN151101A, whichpredicts source heights of 89–93 km, is very con-sistent with the modelled azimuth and elevationarrivals, which supports the source height lyingbetween 88 and 90 km, respectively. On this basis wesuggest the best-fit source height for EN151101A is89 km, with a potential range of 88–94 km (mostlikely near the low end of this range), lendingconfidence to the original source height identifica-tion from timing alone.

For EN130801, the modelled arrival elevationsare near zero (horizontal) making precise determi-nation of the best-fit height intervals problematic.Nevertheless, the modelled elevations are consistentwith a first arrival from roughly near the endpointand extending to 100 km height. The arrivalazimuths are most consistent with first arrival fromthe endpoint near 70 km height and ending near100 km height. Assuming the UKMO data haveslightly underestimated the wind field in thiscounter-wind return, the timing difference of �5 sbetween the modelled and observed first arrivalswould suggest an overall best-fit source height from70 to 95 km altitude.

Timing solutions for EN030804 using nominalUKMO wind parameters suggest first arrivals fromnear 80 km altitude. However, the presence of viableacoustic ray paths from the endpoint of thisdetonating fireball 2 km lower (with timing residuals

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Fig. 6. Computed arrival times for acoustic rays from measured points along their respective trails for the four high altitude meteor

events. Delay times bounded by gray lines indicate onset and duration of the observed infrasound at I26DE in Freyung, Germany.

P.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620 611

of order 10 s) hints again at a possible slightunderestimation of the windfield. In this case,however, the primary detonation of the fireballwas observed at 81 km height, so whether themodelled winds are in error is unclear. The arrivalazimuths and elevations are most consistent withfirst arrivals from 78 km height extending to�100 km altitude.

Solutions for EN010803 are the most challengingdue to the geometry of the trail; the meteoroidpassed almost directly overhead at I26DE. Theminimum in the timing model suggests first arrivalsfrom heights near 93 km; however, the elevationarrivals are more consistent with first arrivals fromnear the endpoint at 84 km. Modelled azimutharrivals show less than 11 variation from 84 to100 km height and therefore are not diagnostic. Ifthe elevation solutions are forced to match theobserved elevation at the endpoint, all three-modelsignal metrics (timing, elevation and azimuth) are

consistent with the acoustic signal beginning at105 km height.

These source height estimates/ranges are sum-marized in Table 2.

5. Shock mechanism identification and non-linear

refraction effects

Here we present a general, approximate methodto determine the refractive angle with respect to anideal cylindrical line source (ballistic wave). This isimportant as it provides a semi-quantitative meansof distinguishing terminal/fragmentation-type shockproduction (which is quasi-spherical) from cylind-rical line source shock production (produced alongthe entire path by the body entry), which producesacoustic radiation roughly perpendicular to themeteor trajectory. Bronsthen (1983) refers to thesetwo different shock types as ablational shocks (fromfragmentation effects) and ballistic shocks. Ballistic

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Fig. 7. Computed arrival azimuths for acoustic rays from measured points along their respective trails for the four high altitude meteor

events. The range of observed arrival azimuths are shown bounded by gray lines as observed at I26DE in Freyung, Germany.

P.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620612

shocks produce expanding cylindrical shock frontsand therefore lead to a more confined region on theground where acoustic radiation is detectable.

From hydrodynamic calculations with respect tothe very high temperature, non-linear region (whichfor the line source explosion geometry lies inside oneblast radius), we have extracted the computedtemperatures at the radial distance where linearityapproximately begins, namely at one blast radii.Interior to this distance, extreme non-linear effectsdominate, though from more detailed simulationsrelated to point source explosions, refraction is notsignificant in this region. We note that downwardpropagating rays will more quickly become lineardue to the increase in air density; as these are mosttypically the ones observed at the ground, theanalysis below should is applicable to these and notto upward propagating rays.

We make use of the numerical results of Plooster(1968) to compute the refraction at two fixed

times (which can be readily converted intothe adiabatic thermodynamic sound speed assum-ing the fluid is well mixed and behaves as an idealgas) at one blast radii from the center of the linesource.

Specific values at a fixed distance of one blastradius from Plooster’s (1968) work can be summar-ized as follows:

Tpeak ¼ 350K, Tmin ¼ 292K (assuming 300Kambient background).

Cpeak ¼ 375m s�1, Cmin ¼ 343m s�1.Cylindrical distance from the blast maximum to

minimum (for our smallest R0 ¼ 7.7m) ¼ 4.6m.Thus, we can obtain an estimate of {1/cs}qcs/qz,

where z represents the vertical direction, using theabsolute value of the blast radius which measuredthe rate at which the sound speed varies as afunction of distance—if this value is close to or inexcess of unity (highly non-linear), then Snell’s lawis not applicable.

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Fig. 8. Computed arrival elevations for acoustic rays from measured points along their respective trails for the four high altitude meteor

events. The range of observed arrival elevations are shown bounded by gray lines as observed at I26DE in Freyung, Germany.

P.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620 613

Moreover we may write that cs(z)/cos(y) ¼ con-stant. This statement assumes that a linearizedSnell’s law in integral form is an adequate approx-imation for the subsequent refraction angles. Forthe earliest linear part of the downward propagationusing the above numerical values withcs(z1) ¼ 375m s�1 and cs (z2) ¼ 292m s�1;z2�z1 ¼ 4.6m and y (launched from the ideal linesource) ¼ 01 (i.e. perpendicular to the trail), we havethat the angular deviation is 241 while (1/cs) � qcs/qz

is 0.02m�1. This is near the limit of the applicabilityof the linearity approximation which requires thegradient normalized to the sound speed to be stillslowly varying and 51. For events with larger R0,the linearity approximation will be more valid andthe angle smaller.

Thus as dcs or dT-0, ynew-y goes to y ¼ 01(perpendicular to the trail), but it is not bounded asthe gradients increase; we note that in reality thegradients are bounded by the possible radiation

hydrodynamics ignored in the treatment of Plooster(1968).

Applying this result to our data, the initialdeviations of the modelled ray paths from eachmeteor trajectory were computed in order todifferentiate between the two main source mechan-isms of meteor infrasound; ballistic shock andfragmentation. As a result of the non-linearpropagation of the initial shock rays may not beperfectly perpendicular to a meteor’s trail, thus raydeviations tending to lie within �251 of perpendi-cular (65–1151) were characterized as consistentwith a ballistic shock source pattern from our earlieranalysis.

Fig. 9 shows each individual ray-tracing point,which emanate from heights consistent with arrivaltimes observed at I26DE. Examining the deviationsfor each meteor it is found that all airwave solutionsare consistent with a ballistic shock radiationpattern. Only for EN030804 are the deviations

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Fig. 9. Deviations of computed acoustic rays from their

trajectories for those rays which arrive within the observed

infrasonic signal time window. Arrival angles of 901 correspond

to travel perpendicular to the meteor trajectory.

P.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620614

sufficiently close to the maximum expected andconsistently away from the perpendicular early inthe trail to suggest that a moving point sourcemechanism, such as fragmentation, may be a betterdescriptor of the airwave geometry. Even in thiscase, however, if the acoustic radiation is confinedto the end of the trail and/or the non-linear effectsslightly higher than assumed here it is entirelypossible to reconcile the deviations with a ballisticsolution.

6. Acoustic source energy estimation techniques:

analytical/empirical approach and luminous

efficiencies

The approaches which have been previously usedin estimation of meteor source energies fromacoustic measurements alone are summarized inReVelle (1976), Ceplecha et al. (1998) and mostrecently Edwards et al. (2006). Using these pre-viously employed analytical expressions estimates ofsource energy from acoustic signals alone arepossible. By comparing these total acoustic energieswith optical radiation emission, an independentestimate of the luminous panchromatic efficiencyfor each event becomes possible. As will be shown inthe second paper in this series, the acoustic waves atthe receiver are propagating as linear waves (havingjust transitioned from weak-shocks). As a result,

while the weak-shock source energy formulationsderived in ReVelle (1976) are not strictly applicableto the events discussed here, the resulting energyestimates are still expected to be very close to theactual values as most of the propagation in eachcase occurs with the wave as a weak shock.

Valid in the weak shock regime, using observedacoustic wave period and amplitude for line sources(Ceplecha et al., 1998) leads to

Es ¼ 11:5prmR03 Dpffiffiffiffiffiffiffiffiffi

pspgp

!4c3sV, (1)

where the variables are defined below. Equivalently,the wave period method for line sources, wherelinear propagation is assumed after an initial weakshock phase (Ceplecha et al., 1998) produces:

Es ¼p12

rmt

1:579

� �4 c7sV

R0�1, (2)

where Es bolide source energy (J); rm, density of themeteor (kgm�3), here taken to be 1000 kgm�3 asappropriate to group III fireballs; Dp, observedsignal overpressure (zero to peak) (Pa); pg, ambientpressure at the ground (Pa); ps, ambient pressure atthe source altitude (Pa); cs, average acoustic soundspeed (m s�1); V, meteor velocity (m s�1); t,observed period of signal at maximum amplitude(s); R0, total slant range from receiver to source (m).

In addition to these purely theoretical sourceenergy estimators, we make use of two differentempirical energy estimates.

Using a data set containing a wide variety of highexplosive yields (in the hundreds of tons TNT andsmaller) as observed by the Los Alamos NationalLabs’ infrasound network, Whitaker (1995) foundthat more generally:

log Es ¼ 1:47 log Pc þ 2 log R� 4:96, (3)

where Pc is wind corrected amplitude (Davidsonand Whitaker, 1992), R is the ground range (in km)and the source energy, Es, is in kilotons of TNTequivalent explosive energy. As with our events, thisrelation was constructed from experiments whereinfrasound readings were performed at relativelysmall range (few hundred km range) and withenergies only one to two orders of magnitude largerthan our bolide events. The primary differencebetween this empirical yield formulation and ourdata set is the point-source nature of the HEexplosion data and the fact that the detonationsoccurred at ground level rather than at high altitude

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Fig. 10. The measured peak-to-peak amplitude (top) and period

at maximum amplitude (bottom) as a function of lower cut-off

frequency for the infrasound signal from EN130801. In each case

measurements are made on the best-beam waveform, which is

created by phase aligning all five microbarometer signals (see

Edwards et al., 2006 for more details of the procedure).

P.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620 615

(cf. ReVelle, 1976 for more discussion on thedifferent acoustic signals expected between point-source and cylindrical line explosions).

Finally, we also make use of empirical relationsderived from actual bolide acoustic signals asdescribed in Edwards et al. (2006). These relationshave the advantage of being most applicable tobolides (albeit generally of much larger energy thanis the case for our study) and hence height of burstcorrections should be smaller than is the case forEq. (2). The primary disadvantage is that all eventsin the Edwards et al. (2006) study were selectedbased on minimum range from source to receiver of4250 km, which is comparable to or larger thanmost of our total slant ranges in this study. Hence,application of these relations to our events doesrequire extrapolation and likely source energyestimation uncertainties of factors of several.

These yield equations have the form:

Es ¼ 10�ð5:50þ0:01vhÞR3DP1:71, (4)

Es ¼ 10�ð8:58þ0:02vhÞR3SNR2:08, (5)

where Es is the bolide’s yield (initial kinetic energy)expressed in tons (2000 lb) of equivalent TNT, R isthe total slant range to the bolide in kilometers, DP

is the maximum signal envelope amplitude (Pa), vhis the horizontal wind between source and receiverand SNR is the integrated signal to noise ratio ofthe entire bolide airwave signal. More details can befound in Edwards et al. (2006).

Application of Eqs. (1)–(5) depends on measuredproperties of the infrasound signal, most notablysignal amplitude (overpressure), the period atmaximum amplitude and the integrated signal tonoise ratio of the entire airwave. In general, thesevalues will depend on the bandpass chosen formeasurement and may show variation across thearray due to local deviations in noise or micro-barometer differences. Note that the observedwaveforms are transformed according to the pro-vided microbarometer transfer function (one trans-fer function assumed to apply to all fivemicrobarometers at I26DE). There will also bequantitative differences in a particular bandpassdepending on the mode of analysis chosen; if all fivesignals are combined in a best-beam waveform andmeasurements then made, these will differ modestlyfrom values obtained by measuring all five wave-forms separately and then combining the result inan arithmetic average together with a standarddeviation.

Fig. 10 shows an example of the effects ofchanging the lower-frequency cutoff in the filtering.As the lower frequency is moved higher, thecontamination from microbaroms lessens, but somesignal energy is removed and as the cutoff movesupward eventually a large portion of the signal itselfis removed. The inflection in the period measure-ment in Fig. 10 near 0.3Hz is due in this case to acombination of both of these effects. In this case atrue period of 1.4570.05 s is adopted as this is mostconsistent with measurements across the lowerbandpasses, before the linear decrease in period isseen above 0.35Hz cutoff due to increasing removalof the actual signal energy. While the formal error isonly 0.05Hz, we adopt 0.1Hz as the true physicalerror reflecting the uncertainty in the change inperiod as a function of bandpass. In practice, thislevel of error in period is physically insignificant in

ARTICLE IN PRESSP.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620616

terms of final energy estimations relative to ourother uncertainties.

A similar, though less dramatic change, is seen inthe peak-to-peak amplitude. With an adoptedbandpass near 0.3Hz, the amplitude is measuredto be 0.2470.04 Pa. This generally reflects well therange of amplitudes over most of the chosenbandpasses. For comparison, the average amplitudeof the five individual channels was found to be0.2970.04 Pa. For all four-meteor events it wasfound that the variation in amplitude with band-pass, while noticeable, was not large enough togenerally be outside the range of the variationbetween microbarometer elements using the best-beam waveform.

The final adopted values for amplitude andperiod (and their respective errors) are shown inTable 2. Note that the final analysis for all acousticmeasurements was performed over the bandpass0.3–9.5Hz.

Table 3 summarizes the resulting equivalentsource energies found from application of Eqs.(1)–(5) with the values from Table 2. There is asubstantial range (often two orders of magnitude ormore) separating these various energy estimates perevent. This reflects the extrapolation of all relationsused here outside their normal ranges as well assimplifications in the models which do not accountfor dispersion, caustics, and turbulence (cf. ReVelle,1974 for a detailed discussion of these effects).Similar large variability has been found for sourceenergy estimates based on direct meteor acousticarrivals in the past (cf. ReVelle and Whitaker(1999)). In the second paper in this series weattempt to address this shortcoming of previoustreatments by performing direct numerical compu-

Table 3

Summary of infrasonic energy evaluations for four high altitude me

(4.185� 109 J)

Type of approach EN130801

Photographic energy (panchromatic emission ONLY) 0.0056

Davidson and Whitaker (1992)—ANFO tests—

Amplitude and winds (Eq. (3))

4371

Line source (wave period): Es (�) (Eq. (2)) 1.170.3

Line source (wave amplitude): Es (�) (Eq. (1)) 0.04570.025

Line source (wave period and amplitude): source height

Empirical relation (Edwards et al., 2006)—Peak-to-

peak amplitude (Eq. (4))

2.870.6

Empirical relation (Edwards et al., 2006)—Int SNR

(Eq. (5))

220070.5

tation of source energies from acoustic signalparameters via application of a full ablation modelwith more complete incorporation of real-worldeffects such as signal attenuation due to non-lineareffects. Note that for the cases of EN130801 andEN030804 the initial acoustic arrivals associatedwith period at maximum amplitude and theamplitude are from near the endpoint; as a resultthe energy estimates using Eqs. (1) and (2) are lowerlimits, these energies referring to the energydeposited per unit length at the point in the trailwhere the acoustic emission occurs.

As a final comparison, we use the total opticalradiation for each event (given by log integral I dt inTable 1) and compare to our average acousticalsource energy (using all five approaches) per event.The resulting average values (with ranges inbrackets) are:

tL (integral) EN151101A ¼ 4.3% (0.7–19%),tL (integral) EN010803 ¼ 0.01% (0.001–0.02%),tL (integral) EN130801 ¼ 2.6% (0.003–12%),tL (integral) EN030804 ¼ 7.1% (0.01–35%).For comparison, the often used panchromatic

efficiency introduced in Ceplecha and McCrosky(1976) predicts efficiencies between 1.75% and 2.2%over the velocity range (57–71 km s�1) covered byour study. From a similar detailed analysis of abright Leonid detected infrasonically during the1998 shower, ReVelle and Whitaker (1999) esti-mated an integral luminous efficiency between0.47% and 5.3% while Borovicka and Betlem(1997) based on spectral observations estimate aluminous efficiency value near 2% for two brightPerseid meteors of similar velocity/mass to ourfireballs. These are all in remarkably good agree-ment with the average of three of the four events;

teors: all values are in units of tons of TNT equivalent energy

EN151101A EN010803 EN030804

0.0257 0.00029 0.0046

4.772.6 1.9 71.5 6.470.3

3.071.5 2774 1471

3:9þ8:4�3:2 4:1þ6:0�3:00.01370.010

0.1470.07 1.170.5 0.6870.5

4.070.4 1077 35712

ARTICLE IN PRESSP.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620 617

for EN010803 the unusual geometry of the detec-tion and the erratic acoustic waveform may be theproblem in producing such discordant results.

7. Lower-energy limit for meteor infrasonic

detection: theory and observation

Starting from an expression relating the sourcekinetic energy (at any height from which theinfrasound is arriving) to the non-linear line sourceblast wave relaxation radius of the entry, we canwrite the following explicit relationship for sourceenergy (with no fragmentation effects explicitlyincluded and a shape factor (Ceplecha et al., 1998)of Sf ¼ 1.209):

Es ¼ ðp=12Þ � rm � R30 � fc

3s=Vg. (6)

Or more generally written as (ReVelle, 2005):

Es ¼ 1=2m� V 2 ¼ ½ðp3=2=2Þ � ð1=f8k3gÞ

� ð1=S3=2f Þ� � ½rm � R3

0 � fc3s=Vg�, ð7Þ

where Sf, Shape factor which reduces for a sphere(Sf ¼ 1.209) Projected area/Volume2/3; k, constantrepresenting fragmentation effects (taken to be0.29164); m, instantaneous meteor mass; V, instan-taneous meteor velocity; R0, instantaneous linesource relaxation (blast) radius; Cs, instantaneouslocal adiabatic sound speed.

Application of these formulations assume that thepropagation is still weak-shock, which may not becorrect in some cases (see discussion in paper II),but serves as a useful approximation for our generaldiscussion.

Observationally, Kraemer and Bartman (1981),have shown that they could readily detect a USPrairie Network bolide (P.N. no., 42556) infrasoni-cally at the ground (at 130 km range) whose kineticenergy has been deduced from photographic data tobe 1.55� 10�5 kt with a corresponding blast waverelaxation radius of �3.45m. This bolide had anentry velocity ¼ 16.5 km s�1 with a photometricmass of about 320 g and a maximum recordedmagnitude of �5.1. The infrasonic signals had�0.21 s period with an amplitude ¼ 2.3 mbar(0.23 Pa), and �5 s signal duration. Reverse raytracing missed the photographed trajectory byo410m (with the location results triangulated fromtwo ground-based cameras). The energy for thisevent is only slightly larger than our estimate for theEN010803 fireball, confirming that under excep-

tional conditions, bolides of this energy producedetectable infrasound at the ground.

From theoretical considerations, ReVelle (1976)found the minimum ground, detectable blast radiusto be R0 (ffiMad)ffi10m. The lower limit here isdue to atmospheric absorption losses at higherfrequency, i.e. bolide sources with smaller Ro do notproduce enough low-frequency waves to be detect-able at ground level.

As shown in (6) and (7) above, the kinetic energyof the bolide is proportional to R0 to the thirdpower and inversely proportional to the velocity.For a spherical, cometary-type bolide withV ¼ 30 km s�1, R0 ¼ 10m and a bulk density ¼1000 kgm�3, a minimum kinetic energy ¼ 6.2�10�5 kt is predicted using k ¼ 1 in Eq. (6). As willbe shown from the entry dynamics solutions inpaper II, most meteor sources with energies lessthan �10�6 kt cannot penetrate deeply enoughto produce a line source blast wave (requiringcontinuum flow conditions to be met) to be detectedat the ground and typical shower meteors (withvisual magnitudes of +2) have kinetic energiesmore than 108 times smaller. Only exceptionalmeteor shower fireballs may be expected to exceedthis minimum energy criterion.

8. Frequency of infrasound from meteor shower

bolides

We have shown that it is possible under nearlyideal observing conditions to detect bright(Mvo�6) shower meteors infrasonically even iftheir source altitudes approach 100 km. Such brightshower meteors do not occur very often, but whenthey do, if the acoustic observing conditions arequite good, based on our study we may expectinfrasonic arrivals at the ground as long as the entryangle is not too steep. More precisely, we maycompute the approximate recurrence frequency formeteor shower infrasound from our results. Usingour earlier result of �6� 10�5 kt as the approximatetheoretical lower limit for meteor source energy toproduce infrasound observable at the ground(noting that EN010803 was a factor of 6 smallerthan this value, but exceptional in many respects)we can derive equivalent minimum masses requiredfor various major showers to typically produceinfrasound at the ground.

Table 4 summarizes the result of these calcula-tions. In the table, the population index is a measureof the relative number of meteors of magnitude

ARTICLE IN PRESSTable

4

Frequency

ofshower

infrasound

Shower

Date

of

maxim

um

Velocity

(kms�

1)

Population

index

Mlim(kg)

MVlim

Flux6.5

(�10�6km�2s)

Fluxinfra

(�10�6km�2s�

1)

Frequency

(h�1)

Hours

per

event

Quadrantid

3January

41

2.1

0.30

�8.2

8.4

1.54E�10

5.55E�03

180

Lyrid

22April

48

2.9

0.22

�8.6

4.6

4.79E�13

1.73E�05

57963

Z-Aquarid

5May

65

2.4

0.12

�9.2

6.4

6.87E�12

2.47E�04

4044

Sd-Aquarid

28July

41

3.2

0.30

�8.2

6.2

2.33E�13

8.38E�06

119402

Perseid

12August

60

2.1

0.14

�9.1

65.64E�11

2.03E�03

492

Orionid

21October

66

2.4

0.12

�9.3

2.2

2.16E�12

7.79E�05

12841

STaurid

5Novem

ber

27

2.3

0.69

�7.3

11.02E�11

3.67E�04

2726

NTaurid

12Novem

ber

29

2.3

0.60

�7.4

1.4

1.31E�11

4.73E�04

2116

Leonid

17Novem

ber

71

2.5

0.10

�9.4

1.9

8.94E�13

3.22E�05

31059

Gem

inid

14Decem

ber

35

2.3

0.41

�7.9

11

6.80E�11

2.45E�03

408

Theshower

values

are

derived

from

thecompilationin

Campbell-BrownandBrown(2005).Shownisthenameoftheshower,itsapproxim

ate

calendardate

ofmaxim

um

andentry

velocity

(kms�

1).More

detailsare

given

inthetext.

P.G. Brown et al. / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 600–620618

M+1 to those of magnitude M. Based on theassumed minimum energy of 6� 10�5 kt required toproduce a detectable infrasound signal at theground, a minimum mass is given for each shower.Similarly, an approximate peak absolute magnitudebased on the mass–magnitude–velocity relationfrom Jacchia et al. (1967) is shown. The showerflux at the peak of activity to a limiting magnitudeof +6.5 is also given and assuming the populationindex remains fixed from +6.5 to the limitinginfrasonic magnitude an equivalent flux for largerpotentially infrasound-producing fireballs in eachstream is computed in the Flux_infra column.Finally, the two last columns show the expectedfrequency of infrasound detections from any onelocation (assuming a collecting area out to 100 kmrange) and the number of hours between infra-sound-producing fireballs from a particular showerat one location. Note that the frequency is an upperlimit as it assumes the flux at the time of the peak,whereas most locations see a somewhat lower flux asa result of radiant geometry (the radiant is rarelyoverhead at the precise time of the shower).Additionally, this figure makes no allowance foracoustic detectability at the ground due to raypropagation. As a result, in practice the frequency islikely a factor of �5 lower on the peak night of anygiven shower than shown in the table. The valuesquoted are for the time of maximum activity of eachstream (which may be just a few hours as with theQuadrantids, to �day for the Perseids/Geminids).

The table suggests that of the annual showers, theGeminids and Perseids are most prolific at produ-cing infrasonic signals detectable at the groundamongst the major meteor showers. This result isfurther strengthened by the fact that both of theseshowers have long-lived periods of strong activity(several days above 1/2 strength). The peak rate ishighest for the Quadrantid shower of January, butits very short duration implies that the practicaldetection rate is more than one order of magnitudelower than shown integrated over the entire day ofthe maximum.

As a final remark, it is notable that the verybrightest shower meteors on record have masses oforder a few kilograms and peak magnitudes nearMv ¼ �15, these belonging to the Leonids (cf.Spurny et al., 2000). However, at the high altitudesof ablation for such Leonids fireballs (extreme endheights no lower than 70 km; Spurny et al. (2000))all high frequency (420Hz-audible) acoustic sig-nals will be removed through absorption before

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reaching the ground (cf. Temkin, 1981). Thus, it iscertainly not possible to detect audibly the sonicboom from even the brightest Leonid fireballs.Similar considerations apply to other fast group IIImeteor showers for which similar large endingheights apply (Perseids, Eta Aquarids, Orionidsetc.). However, for slower showers with among thestrongest (highest density) meteoroids such as theGeminids (group I; Spurny, 1993) which have beenrecorded with masses approaching 10 kg, there arecases of bright events penetrating as deep as40–50 km altitude (Halliday et al., 1996). For theserare shower events, it is possible that weakly audiblesonic booms might be heard at the surface of theEarth under ideal conditions.

9. Summary and conclusions

We have shown in this paper that acousticalpropagation of waves emanating from brightmeteors ablating at altitudes close to 100 km ispossible provided the source is large enough (andthus has a sufficiently low-peak wave frequency).The minimum detected source energy of our fourhigh-altitude bolides was E ¼ 10�5 kt, though thiswas possible probably due only to unusual obser-ving geometry; in practice we suggest the minimumdetectable meteor energy is closer to 6� 10�5 kt.Shower meteors may produce such bright eventsroughly once per 400 h (such as the Geminids)referenced to their peak activity. In most casesaudible sonic booms will not be heard from even thebrightest shower meteors (due to their high ablationaltitudes). The possible exception is the Geminids,where low-end heights and large initial massesmay produce weakly audible sounds under idealconditions.

A comparison of the arrival times for each eventwith ray-trace modeling consistently shows largerresiduals when the HWM stratospheric atmosphericmodel winds are used as compared to UKMOwinds. From this work, we suggest that themagnitude of the stratospheric winds, in particular,are too high in HWM (nearly double the valuesfound in the UKMO model).

For all four high-altitude events, the character ofthe shock production is consistent with a ballistic(cylindrical) shock as opposed to the quasi-sphericalacoustic radiation expected for fragmentation-typeshock production. This is unsurprising given therelatively small mass (o1 kg) of the fireballsstudied.

Integral luminous efficiencies were independentlycomputed by comparing the total panchromaticradiation emitted by each event with the averageacoustic source energies determined by severalindependent methods. This results in values between2 and 7%, approximately a factor of two within thebounds adopted by Ceplecha and McCrosky (1976)who derived luminous efficiencies through compar-ison of dynamic and photometric masses.

A detailed application of an entry model andincorporation of non-linear propagation effects tobetter relate source energies to observed acousticmetrics is the subject of the second paper in thisstudy series. A final paper will examine in detail theseismo-acoustic coupling of the airwaves from eachmeteor event.

Acknowledgments

We thank Dr. Jiri Borovicka of the OndrejovObservatory for providing additional informationfor the 11/15/2001 Leonid fireball. D.O.R. thanksthe US DOE (NA-22) for providing continualfunding for the infrasound program at Los Alamos.We also thank the British Atmospheric Data centerfor providing use of UKMO weather data. PGBacknowledges Natural Resources Canada, theCanada Research Chair program and the NaturalSciences and Engineering Research Council ofCanada for funding support. PS was supported byGA CR Grant 205/03/1404 while long-term ob-servations of the Czech part of the EFN weresupported by the AV CR Project K3012103.

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