Infrasonic Technology Workshop
November 3-7, 2008, Bermuda, U.K.
Session 5: Detection, Propagation and Modeling
Oral Presentation:
Acoustic-Gravity Waves from Meteor Entry as
well as from Rockets and Missiles
D.O. ReVelle
EES-17, Geophysics Group
Los Alamos National Laboratory
Los Alamos, New Mexico 87545 USA
Summary of Presentation
• Introduction, Overview and Motivations:
 Limitations of the PPK Normal Mode Code
• AGW’s from very rapidly moving, impulsive sources:
 Atmospheric source model: Dirac Delta function type source
• Weak shock wave propagation from bolides and rockets:
Direct and indirect arrivals
• Lamb-edge wave formation: Dispersion and Airy functions
• Acoustic wave dispersion: Dispersion and Bessel functions
• Ducted acoustic waves: Sound speed and horizontal wind
speed sensitivity using Gaussian beam theory “miss”
distances, near integral number of hops, etc.
• Total signal construction as a function of range, source size, etc.
• Applications: The Carancas meteorite fall/crater: 09/15/2007
• Summary and Conclusions
The Pierce-Posey-Kinney (PPK)
Normal Mode Code
• Motivation- New AGW Code work due to significant PPK Code
Limitations:
 PPK: Designed for stationary point “bomb” sources: Small
source limit (Rs << H) and scaling at relatively low heights
 Limitations: Relatively large sources at great ranges/long times
 Significant sensitivity to upper boundary conditions at ~150 km
(where the atmosphere is most poorly known and with highly
non-steady conditions AND with an unmixed diffusive
separation of light constituents resident on top of heavier ones)
 Leaky modes not allowed (Only discrete modes included)
 Exclusively linear, but full wave theory (No changes of behavior
are predicted at caustics, etc.)
 A code was needed for meteors/bolides (small sources at close
range and large sources at great range and intermediate
ranges, etc.) as well as for rockets and missile sources.
Examples: Bolide entry and
Second stage ignition sequence
Specific Source Examples:
• On the next slide, we have plotted the predicted line source
cylindrical blast wave pressure amplitude time series (at the
altitude corresponding to the maximum blast wave relaxation
radius conditions using ReVelle’s TPFM entry modeling) for:
 The Revelstoke Meteorite Fall of March 31, 1965 (Canada)
 The Carancas Meteorite Fall of September 15, 2007 (Peru)
• On the next slide, we have also indicated a conceptual view of two
possible source mechanisms for the generation of infrasound from
very rapidly moving rocket and missile sources
• On the next slide we present a conceptual view of the construction
of a energetics-based, self-consistent solution for AGW from
bolides as well as form rockets and missiles
Blast Wave Signatures:
Revelstoke and Carancas Meteorite Falls
14.3 km source
altitude assumed:
Based upon TPFM
Modeling
65 km source
altitude assumed:
Matching of
Peru and Paraguay
infrasound signal
amplitudes
Rocket Infrasound:
Conceptual View
Leading
shock front
Rocket motion
Main rocket body
Trailing shock front
High temperature Engine
Mach 3 plume with
wake turbulence
generated “noise” ,
i.e., acousticgravity wavesAGW
Supersonic/hypersonic
shock front regime:
 Mach 10-20 for
steady state
aerodynamic flight
Nonlinear atmospheric
refraction and heating
regime at close range
Two-Dimensional Source Modeling
Model Atmosphere: Horizontally stratified, range
independent, steady state, hydrostatic model
atmosphere (including seasonal detailed properties
and horizontal atmospheric winds, etc.)
Geopotential
altitude, z
Intermediate range:
Range ~ O({Ro, R1})
Bolide source
Ray-mode skip distance of
the ducted wave paths:
Internal wave
generation
region
Ducted Stratoand Thermospheric arrivals
Lamb wave
formation
Weak shock/linear wave arrivals
Duct height
Observer
Lamb edge wave guided arrivals
+x direction
Overview:Wave Solutions Expected
• Starting from a very narrow short period blast wave pulse whose
attributes depend on the source properties (energy, altitude, etc.):
• Internal Gravity Waves are launched; Lamb-edge wave solutions
(Lowest order gravity wave mode at low frequency) expressed as
an Airy function with longer periods traveling faster and arriving
earlier than higher frequencies: Normal dispersion- The final
shape is a function of range and source energy (Gill, 1982).
• Internal Acoustical Waves are launched: Bessel function solutions
with shorter frequencies traveling faster and arriving earlier than
lower frequencies: Inverse dispersion (Tolstoy, 1973).
• Ducted Acoustical Waves (trapped in a waveguide) whose
amplitude and wave period are a function of the source properties
and whose behavior is critically dependent upon the mean and
perturbed atmospheric sound speed and wind speed structure.
• Weak shock waves: Direct/indirect arrivals at sufficiently close
range whose properties depend on the properties of the source
Lamb wave (LW) Analyses
A.D. Pierce, J.A.S.A., 1963: Isothermal, hydrostatic atmosphere ()
• R0 = {/(B2)}h = Lamb Wave (LW) formation distance
• R1 = {(2 2/(23))h2exp[2B2h]}1/3 = LW dominance distance
 R2 = {2/(B2 )}h; R3 = {(2)1/2 /}h
where
• h = zs /Hp = Dimensionless height of the source
• B2 = (2 - )/(2)  0.2143 ;  = 1.40= Ratio of specific heats for air
• 2 = 2 - A2 ; 2 = 2 – ¼ ; A2 = ( - 1)/ 2  0.2041
• 2  ( + i) = Scaled wave frequency squared including losses
•   o/(cs/Hp) = Non-dimensional (scaled) wave frequency
• cs2 = gHp = Adiabatic thermodynamic sound speed squared
• Hp = Atmospheric pressure scale height
(): Lamb waves can still exist below non-isothermal inversion
conditions as shown previously by Kulichkov and ReVelle (2002).
LW Analysis Procedure
• Using the following set of inequalities we can completely describe
the AGW solutions as a function of the horizontal range R:
• A. R < {R0 , R1}: Weak shock/quasi-linear acoustic waves only
• B. R ~ O{R0 , R1}: Weak shocks/linear and Lamb waves present
• C. R > {R0 , R1}: Lamb wave solutions dominate the response
• {R0 , R1}: Explicit horizontal length scales developed by A.D.
Pierce (1963) for the prediction of the presence and dominance of
the Lamb wave after a small explosion (Ro(z) << H(z) ), where
Ro(z) = Blast wave relaxation radius and H(z) = Density scale
height of the atmosphere ~ 10 km {H(z) = - //z}.
Lamb Formation and Dominance
Distances: Source altitude = 20 km
Using a Rayleigh
friction viscous
decay formalism
Lamb Wave Dominance Distance versus
Wave period and Geopotential height
Airy function & its large argument behavior
Tunguska bolide
observation conditions in
Great Britain (June, 1908)
Dirac Delta function source:
Acoustic, Bessel function solution
Summary: Guided Internal Wave
Propagation Characteristics
• Three AGW propagation schemes have been employed:
 Downwind- Stratospheric and Thermospheric returns
 Upwind- Thermospheric returns only (Diffracted Stratospheric
returns were neglected due to small expected amplitudes)
 Crosswind- Thermospheric returns only expected
• Signal velocities computed internally for the US Standard
Atmosphere (1976) model:
 csig-Stratospheric (downwind) = 0.2945 km/s
 csig-Thermospheric (up-wind) = 0.2667 km/s
 csig-Cross-wind = 0.268-0.293 km/s (depending on the phase angle)
• Number of hops, slant range and travel time (ducted internal
waves) were computed/compared to the horizontal range and
travel time for the Lamb wave.
• Time delay (internal waves) used to control internal wave onset.
Ducted Wave Characteristics
•
The procedure used to determine if these waves could be ducted
was treated “exactly” for an idealized waveguide assuming:

Angle of incidence = Angle of reflection at both the upper
and lower duct interfacial boundaries (ignores the detailed
bottom topography, especially at the shorter wavelengths).

The vertical gradient of the wave amplitude was assumed to
be zero so that the wave frequency and amplitude were
unchanged upon reflection at both the upper and lower
waveguide boundaries.

A near-integer number of hops, n, must exist between the
source and observer. Also if the number of hops < some
small limiting value (~0), these solutions were also rejected.

A “miss” distance was computed for each of these “rays”
that satisfied the above conditions. The miss distance value
was further assigned on the basis of the computed e-folding
widths of Gaussian beams (Porter and Bucker, JASA, 1987,
etc.) as a function of horizontal range.
Summary of predicted ducted wave arrivals
vs the integral mode number (range = 1620 km)
Miss distance = 20 km, Integral no. of hops +/- 0.20
Return type
1- Strato
Integral
atmospheric
mode number
3
Computed
number of
hops
0.882
Computed
miss distance:
km
2.449
1- Strato
4
1.178
4.362
1- Strato
7
2.073
13.471
2- Thermo
13
0.805
9.644
2- Thermo
14
0.867
11.201
2- Thermo
15
0.930
12.878
2- Thermo
16
0.994
14.677
2- Thermo
17
1.057
16.598
2- Thermo
18
1.120
18.643
AGW Signal Construction
• Combined AGW Pressure Amplitude Response: Using separation of variables, we
have constructed amplitude predictions as a function of the blast radius, source
height and source energy, etc. in the form (neglecting, a ground reflection factor):
• pL(x, z, r, t) = psrc (Ro, z)L (x,t)ZL (z)XL (r) = Lamb wave amplitude
• piw(x, z, r, t) = psrc(Ro, z)iw(x,t)Ziw (z)Xiw(r) = Internal wave amplitude
• pws(x, z, r, t) = psrc(Ro, z)ws(x,t)Zws(z)Xws(r) = Weak shock wave amplitude
• ptL(x, z, r, t) = pi = pL(x, z, r, t) + piw(x, z, r, t) = Total amplitude; r > {R0 ,R1}
• ptws(x, z, r, t) = pi = pws(x, z, r, t) + piw(x, z, r, t) = Total amplitude; r < {R0 ,R1}
where
psrc(Ro, z) = Blast wave source amplitude at x = 10 via results in ReVelle (2005).
i(x,t) = Wave shape function (normalized between -1 and 1)
Zi(z) = Kinetic energy density conservation (inviscid fluid approximation)
Xi(r) = Geometrical wave spreading function for a two-dimensional waveguide
Xi(r) = {r/Ro}-;  = Geometric spreading decay factor (constant); ½    ¾
{R0, R1} = Distance scale over which the Lamb wave signals develop
Carancas Peru Meteorite Fall- 09/17/2007:
Basic Observations
• Visual eyewitness accounts: Region of very high altitude (see
below) and very rugged terrain in northeastern Peru
• Ancillary Observations:
Local sounds heard, broken bull’s horn, etc.
• 13.6 m diameter crater produced at 3826 m elevation (!)
• No satellite data available for this event
• Infrasonic wave data recorded at two IMS (International
Monitoring System) arrays:
 In Bolivia (I08BO) with a large signal/noise ratio (S/N)
 In Paraguay (I41PY) with a very small S/N.
• Seismic wave data (at several IMS stations) such as LPAZ (LaPaz,
Bolivia), UBINS, etc. including direct crater impact arrivals.
Carancas: Key Input
Direct Entry Modeling Parameters
•
•
•
•
•
•
•
•
•
•
•
0.79
12.6
30.0
16.0
1.209
0.6667
4.605
1.0
1.0
0.0
1.0
R
Initial bolide radius (m) [.000001 - 1000.0]
V
Initial velocity (km/s) [11.2 - 73.0]
ZR
Angle of entry with respect to the vertical (deg) [0.0 - 80.0]
NMax Maximum number of pieces of fragmentation [1 - 1000]
Sf Shape factor (area/volume2/3 ) 1.209 = sphere [1.209 - 2.0]

Shape change factor 2/3 = no change [- 3 to - 0.6667]
D
Kinetic energy at end height [2.303 - 4.605] i.e. [10% - 1%]
BRKTST Allow breakup 0 = no; 1 = yes [0 or 1]
FRAGTST Fragments in wake 0 = remain; 1 = Stay with body [0 or 1]
PORTST Allow porous materials 0 = no-porosity; 1 = porous [0 or 1]
POR Porosity or Fireball group [0 to 1 or 0.0 - 5.0 (uniform bodies)
• Initial entry mass = 7.641103 kg
• Initial entry kinetic energy = 0.1449 kt = 6.06571011 Joules
• Line source blast radius: Top of the atmosphere (initial) value= 61.47 m;
Maximum radius value = 156.9 m; Minimum radius value = 27.76 m
• Predicted maximum wave period (at x = 10) = 1.469 s
• AFTAC source energy (observed maximum 0.62 s wave period)  0.533 t
Carancas: Direct Entry Modeling Results
Inverse Entry Modeling Summary
Predicting the Nominal
Hypersonic boom Corridor
• Line source wave normal ray tracing procedure through a
specific atmospheric model as a function of geopotential
altitude (steady state, hydrostatic and range-invariant)
 Assume instantaneous energy release for uniform phase
 Specify/measure the adiabatic, thermodynamic sound
speed and the mean horizontal winds as a function of
height
 Specify the entry angle and the azimuth heading angle of
the bolide
 Specify a fixed entry velocity and predict the cone half
angle at al heights and times
 Predict the characteristic velocity (Snell’s law constant
of Geometrical Acoustics) and wave normal paths valid if
R < 2H2/ (H = Vertical duct height; = wavelength)
 Predict the arrival timing and arrival angles of the
waveforms
Temperature/sound speed
and wind speed profiles- LaPaz, Bolivia
BEST Solution: View Overhead and
from the West:  = 262 and  = 62
OVERHEAD
Hypersonic
Boom
Corridor
WEST
Theory and Observations: Infrasound at I08BO:
Bolivia
Predicted AGW
solution: Propagation
delay time ~ 287 s
Best entry time solution =
16:40:10 UT +/- 5s
P.Brown- personal comm.
I08BO infrasound arrived
at ~ 16:44:20 UT
Inferred time delay ~ 250s
Carancas: Paraguay Observations
and Simulation of Arrivals
Downwind propagation conditions
Thermo
Strato
Pa
Observed arrivals
Time with respect to 1800 UT
Summary and Conclusions-I
• We have developed a very general computer code in order to
calculate the properties of acoustic-gravity wave (AGW) signals
from bolides or rockets and missiles as a function of:
 Range (and scaled range)
 Source energy
 Source height
 Atmospheric temperature & horizontal wind-Vertical structure
• The model incorporates four types of atmospheric responses:
 Lamb edge-waves
 Internal acoustic waves
 Ducted acoustic waves (whose properties depend on the source)
 Weak shock waves: Direct (and indirect) arrivals at sufficiently
close range
Summary and Conclusions-II
• The Carancas meteorite impacted in the high mountains of Peru
on September 15, 2007. We have since determined that:
 No satellite observations are available for this event
 Inverse entry modeling (bottom-up) produced only a limited
range of size, velocity and angles of entry for an impact at
3826 m  500 m above sea-level (height error assigned). This
was also found consistent with a crater diameter= 13.6 m  2 m.
Our best, self-consistent modeling result assumed a meteorite
density= 3300 kg/m3 and a target “soil” density= 2000 kg/m3.
 Direct entry modeling (top-down) produced results that are
self-consistent with the inverse (bottom-up) modeling result.
 The deduced nominal hypersonic boom corridor is also
consistent with existing near-field observations of both
infrasonic as well as seismic waves.
 Long range modeling of acoustic-gravity wave signals has also
been found consistent with the details of the source as discerned
by other complimentary approaches.