Energy deposition and Infrasonic measurement of

Bolides

P. BrownDept of Physics and Astronomy, Western University, London CANADA

Work sponsored by:NASA Meteoroid Environment Office (MEO)

Impact Frequency

2

Meter-sized Impactors@ 20 km/s (0.08 kT)@ 11 km/s (0.03 kT)@ 30 km/s (0.2 kT)Mass ~2 T

One such event globally every~week – ten days

Any one optical site on Earth can “see” a meter-sized impact once every ~two decades

Some large (D>5 m) impacts over the last two decades (having speed

and peak height)

3

Date Location a e inc q Q Energy D V HPeak

(AU) degs (AU) (AU) (kT) (m) km/s (km)

20130215 Chelyabinsk, Russia 1.71 0.56 4.1 0.753 2.67 500 19 19.0 29.5

20101225 Pacific Ocean (Japan) 1.01 0.39 16.4 0.611 1.40 33 7.5 18.5 26.0

20040903 Southern Ocean (Antarctica)0.86 0.18 12.2 0.710 1.02 13 6.9 13.0 25.0

20130430 Mid-Atlantic Ocean 1.07 0.12 7.2 0.936 1.20 10 6.6 12.3 21.2

19940201 S. Pacific (Kosrae Islands) 2.1 0.74 2.0 0.546 3.65 31 6.2 25.0 24.0

19990114S. Pacific Ocean 1.90 0.49 14.0 0.969 2.83 10 5.7 15.0 35.0

20091121 Botswana 0.84 0.59 56.4 0.346 1.33 18 5.2 32.0 38.0

20091008Indonesia (South Sulawesi) Gulf of Boni

1.20 0.55 14.1 0.541 1.85 33 5.2 22.0 19.1

20140823 Southern Ocean (Antarctica) 1.35 0.34 20.7 0.894 1.80 8 5.0 17.6 22.2

Observational data for meter-sized impactors

• Three Sources:– Ground-based fireball networks (European

Network, Prairie Network, MORP)• [6 meter-sized events]

– Fireball producing meteorites [23 to date] with instrumental flight data• [10 produced by >1m diameter]

– US Government (USG) sensor data • [>50 with speed and energy]

http://neo.jpl.nasa.gov/fireball/4

Impact Statistics

• SpeedMean = 18.5 ± 0.7 km/sMedian = 17.9 km/s

• Entry angle = 46◦ ± 3◦

• Mean height of peak brightness 33 km >90% lie between 20 – 40 km

5Height at peak brightness

20 30 40 50 60 70

Count

0

2

4

6

8

10

12

14

16

18

Orbital Characteristics:Meter-sized impactors

6

Semi-Major Axis (AU)

0.0

0

0.2

5

0.5

0

0.7

5

1.0

0

1.2

5

1.5

0

1.7

5

2.0

0

2.2

5

2.5

0

2.7

5

3.0

0

3.2

5

3.5

0

3.7

5

4.0

0

4.2

5

4.5

0

4.7

5

5.0

0

5.2

5

5.5

0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Eccentricity0.0 0.2 0.4 0.6 0.8 1.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Inclination0 10 20 30 40 50 60

Fra

ction

0.0

0.1

0.2

0.3

0.4

0.5

Fra

ction

Fra

ction

Semi-Major axis (AU)1 2 3 4

Eccen

tricity 0.0

0.2

0.4

0.6

0.8

1.0

Semi-Major axis (AU)

1 2 3 4

Inclin

ation

(deg

rees)

0

10

20

30

40

50

60

T=3

T=2

q=1.017

Q=0.983

q=

0.9

q=

0.5

Impact Statistics - II • Orbital origins

Source population mainly from ν6 (inner main-belt)

• 7% Halley Type Comet (HTC) orbits; similar fraction Jupiter-family comet (JFC) origin

• No trend in strength with size/energy

7

Log M(kg)

3.00 4.00 5.00 6.00 7.00 8.00

Hp

eak Pressu

re (MP

a)

0.01

0.10

1.00

10.00

100.00

Jupiter Family Comet (JFC)Outer Main-Belt (OB)3:1 MMR with Jupiter (P_31)Intermediate Mars Crossers (P_IMC)ν6 secular resonance (P_Nu6 )

Bottke et al (2002) Source Regions:

Meter-class impactors : Physical Characteristics

• Median energy = 0.4 kT

• Triggered Progressive Fragmentation Model (TPFM) [ReVelle 2005] used for comparison

8

Fireball Class

FragPres (Mpa)

ΔHfrag-peak

(km)

I 0.7 10-14

II 0.2 14-17

IIIa 0.01 17-19

IIIb 0.001 19-24 Velocity (km/s)

12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Height of P

eak Brightness (km

)

10

20

30

40

50

60

70

80Tj > 3

MeteoritesNetworks2<Tj<3

Tj<2

0.01 MPa

0.2 MPa

Type I

Type II

Type IIIa

Type IIIb

SM

M

B

PFBC

TL

KAS

C

0.7 MPa

AS – Almahata Sitta (Ure-Anom)K – Kosice (H5)TL – Tagish Lake (C2 ung)

BC– Buzzard Coulee (H4)C - Chelyabinsk (LL5)PF – Park Forest (L5)

B – Benesov (LL3.5, H5,Primitive Achondrite)SM – Sutter’s Mill (CM2)M – Mariboo (CM2)

Meteorites – individual symbols:

Energy Deposition

• Light curve ~ energy deposition

• Caveat: τ(m,h,v,comp)• Of 5m class events with

speeds LC only available for Chelyabinsk (top) and Feb 1, 1994 (bottom)

9

Height (km)

20253035404550

kt / k

m(h

eig

ht)

0

20

40

60

80

100

Brown et al (2013)

Tagliaferri et al (1995))

dtdV

MVdt

dM2

VI

2

W/s

ter

Detailed data (Borovicka and Spurny 1996) including light curve, fragmentation behavior, precise astrometry and spectra

Benesov meteorites recovered 2011 (Spurny et al 2014) – mixture of OC types?

Detailed model comparisons to Benesov observations by Borovicka and Popova (1998)

Benesov:V =21 km/s; Imax~ -19.5mag

Hpeak~24 kmMass estimates:3000-4000 kg (Borovicka et al.,1998) (ReVelle&Ceplecha, 2002)D ~ 1.3mE = 0.20 kT

Benesov (EN 070591) & Sumava (EN 041274)

Sumava:V =27 km/s; Imax~ -21.5mag

Hpeak~67 kmMass estimates:5000 kg (Borovicka& Spurny,1996) D ~ 3mE = 0.4 kT

Benesov spectra of final flares

Borovicka and Spurny (1996)

One model interpretation (Borovicka et al., 2013): Earliest fragmentation at ~45 km

altitude at P = 0.7 MPa Large scale disruption at 30 – 37 km

height with P= 1 – 5 MPa By 29 km object was ~20 boulders of

1-2m sizes based on changes in lightcurve

These boulders break again at 26 km under P~10 MPa

Lateral fragment speeds ~400 m/s

Another (bottom by Popova et al (2013))

Based on a number of plausible simulation realizations to encompass large parameter space of fragmentation behavior (in particular)

11

Chelyabinsk - Fragmentation

Borovicka et al (2013)

Popova et al (2013)

12

Kosice (H5)Fell Feb 28, 2010 – producing 11 kg of H5

meteorites in 200+ fragmentsDetailed data (Borovicka et al 2015)

including light curve, fragmentation behavior, precise astrometry

Very weak meteoroid – fragmented under < 0.1 MPa

Catastrophic disintegration at P ~ 1 MPa Infrasound constrained energy from I43

RU @ 1400 km range: Kosice:V =15 km/s; Imax~ -18mag

Hpeak~36 kmMass estimates:3500 kg (Borovicka et al.,2015D ~ 1.2mE=0.1- 0.2 kT

Pre

ssure

(Pa

)A

rriv

al A

zim

uth

Height (km)

57

39

29

22

V

c

MS

1sin

13Extreme meteoroid velocities between ~Mach 30 – 240 produce long, narrow shocks over very short time scales.

Characteristics (period and amplitude) of the shock wave are related to meteoroid energy deposition

Meteor generated infrasound provides another means of determining meteoroid MASS & KINETIC ENERGY

@ M = 30, β = 1.9° @ M = 240, β = 0.2°

β

2

1

)/

(o

O p

dLdER

R O

• Meteors (bolides/airbursts) produce low frequency sound when they detonate in the atmosphere

• Detectable at infrasound arrays at long distances due to low attenuation of sound and natural sound waveguides in atmosphere

MET

EORS!

Gra

vity

Waves

Infra

sou

nd

Au

dib

le

14

• Blast Radius dictates the frequency at which a meteor will produce its sound

• Small Ro: High Frequency / Large Ro: Low Frequency

• cm – m size objects Infrasound: 0.1 – 10 Hz• >10 m size (eg Chelyabinsk): < 0.1 Hz • As Frequency ↓ Attenuation ↓• Large, energetic sources produce IS which goes

further– Lower frequencies, lots of energy

Bolide Infrasound

15

o

Sm R

Cf

81.2(ReVelle 1974/1976)

Ground-level overpressure from cylindrical line source theory

• Numerical implementation of ReVelle (1974) meteor shock theory and comparison to observations of cm-sized meteoroids by Silber et al (2015)– Main finding – weak-shock to linear transition distance from source is

larger than originally assumed

• Crude rule of thumb – ΔP at the ground scales as ~E1/216

Application to Chelyabinsk• At Chelyabinsk, nuclear

airblast relations (Glasstone and Dolan, 1977) predict 5 – 10 kPa overpressure (0.5-1 MT)

• Cylindrical weak-shock theory predicts ~ 2-3 kPa

• Need more instrumental records of ground-level overpressure from large bolides

Cylindrical theory using lightcurve

1 MT Nuclear

0.5 MT Nuclear

International Monitoring System• 45/60 Stations Complete

(75%)• Stations are arrays

composed of 4 – 12 microbarometers

• Signals found through cross-correlation

• Arrival direction and steepness directly measureable

• Local wind noise and stratospheric wind system determines detection efficiency

• Varies with geography and time of year

181 km

IMS Bolide events : 2010 – mid 2014Removed auto detected IS events correlated with mining, rocket launches, volcanoes,

repeating sources etc. – Total events examined: 1462– Total number of potential airbursts : 69 (4% of 1462)– Expected number of meter-sized impacts from Brown et al (2002) : 29/yr (130 vs 69)– Expected number of kiloton (~2 m) class airbursts : 4/yr (18 vs 69)

2014 IMS event also detected by USG sensors

IMS bolide detection efficiency – Cued vs. “survey”

• Based on 2014 cued search with USG Sensors:– IMS identifies ~1/4 of all meter-sized

impacts– Approximately 3/4 of all such impacts

are detectable infrasonically– Cuing important!

• IMS raw (survey) detections (~15 /yr)

Implications • As a stand alone system, current IMS

system identifies minority (<0.5) of all meter-sized impactors

• Cued impacts from next Gen asteroid surveys (eg. ATLAS) should expect most impacts to be detectable by IMS– Will give an estimate of total energy and

geolocation

21

Airburst Energy Estimation : Period – Yield

• Source energy estimates based on periods/amplitudes calibrated to explosive sources

• Small events at short ranges usually better estimated with amplitudes (but need to include winds)

• Larger events show good agreement with ground-truth/USG energies (Ens et al., 2012) particularly by averaging periods across many stations

USG

Example: Regional Infrasound for the Chatham Island AirburstMay 16, 2014 @1242 UT (0.8 kT)

PaUSG Measurements:Energy = 0.8 kTMass ~ 25 TDiameter 2.5 – 3 mV = 16.5 km/sBurst altitude = 44 kmEntry Angle = 66 degs

Time (Sec) from12:45:15 UT May 16, 2014

20 40 60 80 100

Arrival A

zimuth

0

100

200

300

20 40 60 80 100

Arrival A

ngle (degrees)

0

10

20

30

40

50

60

70

Infra Measurements:End Height ~ 33 kmBegin Height ~ 69 kmBurst Height ~ 47 km

Infrasound cross-correlation in 15 sec windows with 80% overlap

12

3

4

1 2 3 4

Bolide Infrasound measurements

Pilger et al (2015)Chelyabinsk

Infrasound only estimated terminal burst altitude = 20 ± 4 km

Energy ~ 50 kt

Line source

Point source

US Government Sensor data (2014):Terminal burst altitude = 19 km

Energy ~ 33 kt

Silber et al (2011)Oct 8, 2009 - Indonesia

Future Research• Luminous efficiency – calibrate from different

techniques• Infrasound models for validation of cylindrical line

source overpressure estimates at the ground (particularly amplitude model constraints)– (Silber et al., 2015) applied to cm-sized meteoroids,

need to expand to meter-sizes– Search IMS for regional IS airburst detection and

apply/modify model– Adapt Whitham weak-shock theory to cylindrical

hypersonic sources (eg. Haynes and Millet, 2013)

24

General Observations• Meter-sized impactors begin fragmentation under 0.1 – 1

MPa ram pressure (Popova et al 2011)– peak luminosity is reached 1-2 scale heights lower

• Fragmentation is complex• Lightcurves are crucial to constraining atmospheric energy

deposition in individual cases– Not enough meter-class LCs available to make any generalizations

about fragmentation behavior

• Spectra very helpful, but rare• Recovered meteorites provide ground-truth• Multi-instrumental observations critical – each measurement

technique suffers different systematic biases

25

Need for Model validationModels have now incorporated very elaborate physics

BUT we have few constraints from observations to guide choices in a very large parameter space (Fragmentation!).

1. Compare various models (particularly fragmentation characteristics) to existing published/detailed large bolide measurements (Chelyabinsk, Benesov, Sumava, Moravka, Kosice)

2. Apply models to USG data for statistical studies

3. Process/extract existing but unpublished precise large fireball data and apply models (EN – eg. EN 171101)

26

Modeling Capabilities• FM ablation model (theoretical and observational fit to bolide

data) [Ceplecha and ReVelle 2005]• Triggered Progressive Fragmentation ablation model (TPFM)

[ReVelle 2007a]• Acoustic Gravity Wave production from bolides [ReVelle

2007b]• Numerical Bolide - cylindrical line source weak shock model

[Edwards et al., 2007]• Seismic hypocenter geolocation of bolide airbursts [Edwards

et al. 2004]• Infrasound bolide airwave measurement and empirical energy

estimation [Ens et al., 2012]• Monte Carlo Dark Flight model of meteorite fall ellipse

production [Brown et al., 2011]27

28

The End

Backup

The Cylindrical Blast Radius

30

R O

V

po

dE/dL

Meteor is effectively an oriented cylindrical line source. Shock propagation is approximately perpendicular from trajectory

Atmospheric pressure = Meteor energy loss/length

31

• IMS Network requires 1kt globally

• thresholds vary primarily with stratospheric seasonal wind pattern.

• NH Winter– Westerly NH– Easterly SH

• NH Summer– Easterly NH– Westerly SH

(Le Pichon 2009)

Source Energy Estimation• Source energy estimates for bolides from IS has much

interstation variability due to:– Unique characteristics: Line source + quasi-Point source– Wide range of source altitudes detected at different stations– Compounded by numerous phases & extreme distance

• Two approaches:

1. First principles: Weak shock model (Revelle, 1976) – works at short ranges (<250 km)

2. Empirical Energy/Attenuation Relations– Signal Periods, Amplitudes + USG data.– Now calibrated by multi-instrumental, well-characterized events

(Ens et al (2012)– Use existing explosion relations (eg. Clauter and Blandford

1998).

32

Schematic: Bolide Entry IS Propagation

Weak Shock Theory (ReVelle, 1974)

 

 

x = R/R0

 

 

 Weak shock regime

Linear regime  

Applicable for direct arrivals – short (<200 km) range Can be used to estimate overpressure at the ground

34

http://neo.jpl.nasa.gov/fireballs/

Source Information from Observations

• Single Station– Alternative data source required! (Optical/radar/eyewitness etc.)– If trajectory information available

• Travel time/Arrival modelling (met.data required): Source Altitude

• Forward theoretical modelling energetics• Multiple stations

– 0th order: Intersection of observed back-azimuths– 1st improvement: Intersection + travel-time fit phase ID– 2nd improvement: Intersection + tt + wind correction + source model– Empirical attenuation & period relationships energetics

• NOTE: Energetics will often represent meteor at source position!• The more observations the better for energetics – large

variation! 36

Cylindrical Blastwave Theory (ReVelle 1974/1977)

• Propagation from source to observer goes through 2-3 stages – Nonlinear: very high

overpressures, strong attenuation– Weakly Non-linear: high

overpressures & attenuation, lengthening period

– Linear: low overpressure & attenuation, stable period

37

Bla

st R

adiu

s

Ro

Weakl

y N

on-l

inear

Pro

pagati

on

Δp ≤

po :

Incr

easi

ng P

eri

od

Non-l

inear

Pro

pagati

on

~1

0 R

o:

Δp >

> p

o10 Ro

Linear

Pro

pagati

on

Δp <

< p

o :

Peri

od S

table

d′ < dLinear Transition

002

1

p

pc

dt

d

38

Meteor Propagating Northward (red line)

Source Altitudes100 – 70 km

Radiant Altitude

7°

30°

50°

Radiant Altitude: 30°

Radiant Altitude: 50°

e.g. Grazers, Genesis, Stardust, Hayabusa

Most meteors fit in these

categories

Steeper is lost to atmosphere via

refraction

Fireball Infrasound Range Discriminators

39

Modeling of Bolides as Infrasonic Sources: Hypersonic Aerodynamics

• Line source blast wave analogy: Hypersonic flow– Ma >> 1 and dV/dt 0; Very narrow Mach cone Nearly

cylindrical source symmetry

• Line source energy deposition: Nonlinear blast wave relaxation radius: Ro– Ro Square root of energy deposited per length/pressure

Ro Mach no. diameter (No fragmentation assumed)

– Detectable Ro and source energy, Es, ranges from:• ~10 m to > 6 km (Tunguska)• ~10-5 kt to > 10 Mt (Tunguska)

– Wave period Ro/(local thermodynamic sound speed): Near-field weak shock wave valid for distances > ~10Ro

• Modified line source effects (fragmentation): Larger Ro at the same size and speed 40

Part III: Detailed numerical models

IDG group – SOVA 3D are only radiation hydrocode to date

Lack of good observations to calibrate the high fidelity in the models for large objects

Some USG lightcurves, but often lacking kinematic information or heights (or both)

41

Fragmentation - Assumptions• Most models assume that stagnation pressure =

material strength is trigger for breakup– ie. Breakup occurs when ρv2=strength

• Need to account for dust and macroscopic fragments – dust important in light production

• If time between successive fragmentation epochs is short compared to separation timescale (big objects, weak objects etc.) details of individual fragmentation can be ignored (large bodies) treat material as liquid-like object with no material strength (SL9 – like)

• Standard assumption in many models is interaction of individual fragment shocks produces pressure gradient produces lateral fragment speeds of order

• This gives fragment separatiuon speeds of a few tens of meters per second for meter-tens of meter sized bolides

Passey and Melosh (1980)42

Bolide Fragmentation Modeling• Break-up schemes: {A (drag) = A (heat transfer) for the single-body model}

– Baldwin and Sheaffer (1971): Frontal area, A (drag) N^1/3, where N = number of fragments produced during the gross-fragmentation process

– Petrov and Stulov (1975), Padavet (1973; 1977; 1978): A (heat transfer) >> A (drag) due to turbulent mixing of air/ablated vapor

– Liu (1978): A (heat transfer) >> A (drag) due to meteoroid porosity effects– Grigoryan (1977, 1979): “Pancake” break-up process (no ablation case)

• Once impactor is heavily fragmented the pressure difference between the front and back of the body compresses the impactor and it if forced to “flow” out the sides expanding in area at a rapid rate (pancaking)

– Bess (1979): Break-up: Progressive fragmentation process– Zahnle (1992), Hills and Goda (1993), Chyba et. al. (1993), Bronshten (1994; 1995

{after Grigoryan (1976; 1979) including ablation}, Svetsov (1995), Lyne, Tauber and Fought (1996), Nemtchinov et. al. (1995, 1997), Stulov (1997): Airburst, “Pancake” model development, tests and applications

• Break-up mechanisms:– Thermal effects: Very inefficient (too long of a time delay is necessary)– Mechanical effects: 1-D stagnation pressure exceeds the bolide’s “strength”

Pancake model : Predictions• The pancake model makes a number of

predictions/assumptions - cf. Grigoryan (1979), Melosh (1981), Zahnle(1992), Chyba et al (1993); Hills and Goda (1993;1998)); Korycansky et al (2002) Bland and Artemieva (2004)

– Most of the airburst energy is released as a nearly point source (assumption when used to calculate ground damage) (H&G, 1998)

– Lateral fragment speeds are a few tens of m/s (prediction)– Mass surviving to the ground as >100g fragments is ~50% of initial

mass (prediction) (B&A, 2006)

44

Collins et al., (2005)

Bolide masses

• Dynamic vs photometric mass• Long standing issue as photometric mass

10-100x larger than dynamic masses for bolides (Ceplecha et al 1980)

• Root cause – fragmentation (Ceplecha and ReVelle 2005)

• Luminous efficiency depends on velocity, mass (and maybe height and composition)

45

Panchromatic Luminous Efficiency:

Near the End of the Entry (TPFM)

46

Radiation Efficiencies• Panchromatic efficiencies calibrated using Lost City

– 6% at 13 km/s (Ceplecha, 1996)

• Large uncertainty in extrapolating results – camera network bolides much smaller than satellite

events

• Calibrate satellite energies by – cross-fusion with other sensors – either ground-truthing

or infrasound (Brown et al 2002)– Using hydrodynamic models which treat complete

radiative aspects of entry (Nemtchinov et al., 1997)47

Filled Circle – Meteorite events where energy is known well from many other techniques

Open Circles – Energy determined from infrasound observations alone

Brown et al (2002)

48

Numerical modeling results from Nemtchinovet al. (1997)

Graph shows result from entry model for pure Irons and H-Chondrites

Equation (14) is solid line in graphEquation (15) is dashed line in graph

Much spread, but average η close to empirical result found by Brown et al (2002) at smaller energies

49

Optical Energy (kT)

10-5 10-4 10-3 10-2 10-1 100 101 102

inte

gra

l (%

)

1

10

100

Integral Bolometric Efficiency Based on Calibrated Satellite – Sensor Events(Brown et al 2002)

50

Masses and Sizes• Total energy is determined by taking the observed

optical yield (Er) and dividing by efficiency (η)– Et=Er/ η

• With total yield (=energy = kinetic energy of impactor) known, mass is found from Et=1/2mv2

– Assumes velocity is known

• Size is found using mass and assuming a spherical shape and bulk density– Bulk density can be determined if meteorites are found51

Video Calibrations – Chelyabinsk Lightcurve• Uses indirect scattered

light and corrected for autogain

• Calibrated using meteorite-dropping fireball events and radiant intensity from US Gov Sensors

• Total deposited energy assuming η = 17% is >471 kT

52

Time [s]

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Ab

solu

te Mag

nitu

de

-29

-27

-25

-23

-21

-19

-28

-26

-24

-22

-20

-18

Height (km)

20253035404550

kt / k

m(h

eig

ht)

0

20

40

60

80

100

Brown et al (2013))

Chelyabinsk : Shock wave – Cylindrical or Spherical?

• Shock wave causing damage was cylindrical not spherical

• Ray tracing establishes origin height – arrivals are from various heights, not a single point

• Secondary, weaker shocks after main arrival are spherical - from discrete fragmentation 53

Top-down Modelling• Now find the blast radius from photometric measurements and entry model

run weak shock model to obtain the predicted signal amplitude and period

𝒅𝑬𝒅𝑳

=( 𝒗𝟐

𝟐𝒅𝒎𝒅𝑳

+𝒎𝒗𝒅𝒗𝒅𝑳 ) 𝑹𝟎=(𝒅𝑬 /𝒅𝑳

𝒑𝟎)𝟏/𝟐

1) Meteoroid intersects Earth and “collides”• Typical velocity ~20 km/s (11.7 – 73 km/s)• Meteoroid size: 0.1 – 10 m

2) Around 80 – 100 km Meteor becomes luminous

3) Meteoroid produces shock wave• Line source sound produced ┴ to trajectory

4) 15 – 40 km: Fragmentation• Point source sound produced

5) Direct Acoustic heard, Seismic Detections ? Meteorites ? 6) Ducted sound “heard”

at microbarometer array

7) Hydroacoustic in ocean (impact or airwave)

56

cS RER

Theoretical work has shown range scales with energy in

a power law (use USG sensor energy here)

Apply wind correction of form AA kv

w 10 Apply a multivariate linear least

squares regression in log-log space

RESULT:

cc

b

c

kva

ARE1

10

kvEcRbaA )log()log()log(

Airburst Energy Estimation : Amplitude – Yield

Depends on knowing the wind well

Lots of scatter Amplitude not very

reliable at large ranges