Acoustic Signal Computations in
the Mediterranean Sea
ARENA 2006, Newcastle
V. Bertin, V. Niess
CPPM - IN2P3/CNRS - U. Méditerranée – France
27-30 June 2006
V. Bertin, V. Niess- ARENA 2006 - Newcastle
1
General Context
•PhD work at CPPM ( September 2002September 2005 )
Dedicated Acoustic ‘team’
at CPPM ( 2002-2005 )
With Engineers &
Physicists, mostly
involved in ANTARES
http://marwww.in2p3.fr/~niess/these.pdf (in French)
astro-ph/0511617 ( to be published in Astroparticle Physics )
See i.e. :
•Stanford Workshop 2003
•ICRC 2005, Pune
This Presentation Focuses on Acoustic Signal Computations
27-30 June 2006
V. Bertin, V. Niess- ARENA 2006 - Newcastle
2
A Brief Reminding
Thermo-acoustic coupling mechanism
( Askaryian, 1957 ; Sulak et al., 1978 )
3) Output :
Pressure signal
( Transduction … )
 1 
1  p
 q
  ( p)  2 2  

cs t
C p t 2
2
2) Propagation :
Vertically stratified medium
( Refraction )
27-30 June 2006
2
1) Input :
Energy density
( UHE Particle
showers )
Thermodynamic factor
Constant here
( Mediterranean Sea,
1 km depth )
V. Bertin, V. Niess- ARENA 2006 - Newcastle
3
Modelling Energy Deposition
Deep Inelastic Scattering
Cross sections from :
Gandhi et al.
Phys. Rev. D58, 093009 (1998)
n, l
n
W,Z
N
hadrons
hadrons
hadronic and
electromagnetic showers
27-30 June 2006
•Thermo-Acoustic emission :
Efficiency increases with energy density
Showers required
Considering :
J. Alvarez-Muniz, E. Zas
Phys. Lett. B 441 (1997) 218
Phys. Lett. B 434 (1998) 396
Focus on 2 limit cases :
• ne charged current ( CC ) :
because 100 % of ne energy goes into showers
but strong LPM spread …
 dedicated Monte carlo
• nL neutral current ( NC ) :
because it is presumed giving compact showers
but only ~20 % of the nL energy
 Parametrisation ( GEANT 4/ EAS data )
V. Bertin, V. Niess- ARENA 2006 - Newcastle
4
GEANT4 : Longitudinal Profile
E0 (bt ) a 1 exp( bt )
z
f z (t 
)
b
X0
X0
( a )
Extensive Air Showers, from
M. Nagano and A. Watson
Rev. Mod. Phys., Vol 72, No. 3, July 2000
GEANT 4, QGSP
In a water box
LPM ??
ELPM
Depth of maximum ( g/cm2 )
Depth of maximum ( X0 )
‘PDG Parameterisation’ : Good agreement
Geant 4, p
GEANT 4 results are consistent with Extensive Air Showers
But LPM is a Matter effect …
27-30 June 2006
V. Bertin, V. Niess- ARENA 2006 - Newcastle
5
GEANT 4 : Lateral Distribution
Power law behaviour
GEANT 4
Lateral exponents
E  50 TeV
/rm
Sustained by
Microscopic observation of
~ 100 GeV e-showers in Lead
plate/Emulsion
N. Hotta et al.
Phys. Rev. D, Vol 22, No. 1, July 1980
Core exponent ( ~10 %
agreement with EAS)
z/zmax
Exponents vary mostly with depth
little with primary nature and energy
( @ 50+ TeV )
27-30 June 2006
V. Bertin, V. Niess- ARENA 2006 - Newcastle
5·10-4 rm
6
Electromagnetic LPM : Scheme
Use a dedicated 2 steps scheme :
1. Randomize the high energy part of shower ( LPM fluctuations )
2. Reconstruct : Filter with average parametrisations for secondary showers
primary
Monte-Carlo
(Metropolis)
(FIR algorithms)
1D
2D
Migdal’s cross sections for LPM : Not constrained experimentally in the strong
suppression regime we are concerned with
27-30 June 2006
V. Bertin, V. Niess- ARENA 2006 - Newcastle
7
Electromagnetic LPM : Results
LPM ‘tail’
hadronic
g(
5·1013
eV )
ne ( 1019 eV )
Parametrisation extends up to 1017 eV
Longitudinal profiles of energy deposition
Depth of the maximum
LPM cascades
stochastic
zmax ( X0 )
LPM
L  E ,   0.5
GEANT4
log10( E / 1 GeV )
Depth [ z ] (m)
27-30 June 2006
V. Bertin, V. Niess- ARENA 2006 - Newcastle
8
Acoustic Signal Computation
•Approximate Green function : No (de)-focusing ( ~ few % )
 

   (t   (r , r ' ))  3 
p(r , t ) 
q( r ' ) d r '
 

4pC p t
r r'
Propagation time :
Ray tracing model
Strength of signal = time/spatial coherence : This is where to play …
•Reduce integral to 1D with causality/symmetries :
Sum over 2 acoustic rays
Transform of lateral distribution
  2 p /2
p(  , z, t ) 
f z ( zi )Gz (   0 , zi )d


4pC p t i 1 0
Longitudinal density
27-30 June 2006
Observer point, Time
& Ray structure
V. Bertin, V. Niess- ARENA 2006 - Newcastle
9
Propagation Loss
Signal Strongly modelled by Absorption
Viscosity
1/f2
Phase dependent model
Driven by :
L. Liebermann
Phys. Rev. 76(10), November 1949
With ‘modern’ input from :
R.E. Francois and G.R. Garrison
J. Acoust. Soc.Am. 72(6), 1982
B(OH)3
Transition from MgSO4
Delayed Impulse response
MgSO4
Frequency ( kHz )
27-30 June 2006
Time ( scaled )
V. Bertin, V. Niess- ARENA 2006 - Newcastle
10
Near Field/ Far Field
Pressure field ( mPa )
ne CC, En = 125 EeV, 10 km distance
L2
Transition : r 
 [0.5;100] km
2
Cylindrical wave-front
( near field )
*
Angular aperture
( NC compact cascades )
LPM
Fuzzy image
Longitudinal density
Compact cascades :
Rigorous far field conditions
achieved only at ~10 km
Spherical wave-front
( far field )
27-30 June 2006
V. Bertin, V. Niess- ARENA 2006 - Newcastle
11
Signal Shape
R/C versus Dt diagram
Signal characterised by :
•Duration : Dt
•Symmetry ratio : R/C
Signal more asymmetric than
previous studies
Get insight on source nature, extension ( R/C ), distance ( Dt )
27-30 June 2006
V. Bertin, V. Niess- ARENA 2006 - Newcastle
12
Mediterranean Sea Refraction
Pressure field ( mPa )
@ 1 km from the source
Mediterranean Sea
Linear sound velocity profile
Below 100 m
Deflection
Amplitude
is little affected
Amplitude ( mPa )
27-30 June 2006
Dcs
 1.65 cm/s/m
Dz
Global deflection
given by a ray tracing model
z(m)
z(m)
kc 
Time ( ms )
V. Bertin, V. Niess- ARENA 2006 - Newcastle
Directivity
only depends
on q
q
q
Effect is mostly native :
Local sound velocity variation
on energy deposition area
Not ray structure
13
Effective Volume
Signal threshold levels : 1 to 10 mPa
Energies : 1018 to 1020 eV
Model driven extrapolation
Sonic Volume ( dB ref 1 km3 )
Signal amplitude ( dB ref 1 mPa )
1 km
Range ( dB ref 1 m )
27-30 June 2006
1 km3
Near field, CC ne
Far field, NC nL
Model Parameters :
Range max, Effective length Leff,
effective angular aperture Dqeff
Amplitude ( dB ref 1 mPa )
V. Bertin, V. Niess- ARENA 2006 - Newcastle
14
Boundary effects
Water extension is vertically limited
zi = H/2
Source
Hypothesis : Direct detection
At long range
Detection limited
Close to vertical cascades
Mean geometric efficiency ( % )
Shadowing from the sea bed ( Refraction )
Shadow
Zone
Shadow Factor : Efficiency = 1 - F
Pure Monte-Carlo
Analytical &
Monte-Carlo
H = 2500 m depth
Receiver zi =448 m
above sea bed
max/( H/2 )
27-30 June 2006
V. Bertin, V. Niess- ARENA 2006 - Newcastle
15
Benchmark Sensitivity Estimates
1018 eV
1020 eV
Sea Noise 1-10 mPa in B = 100 khz
( Ceramic eq. ~ 2-6 mPa )
1 evt/decade/year
1/E2 Flux  1 an
E2 ~10-6 GeV·cm-2 · sr-1 · s-1
Flattening due to
boundaries
Mediterranean Sea
2500 m depth
(ANTARES like)
27-30 June 2006
V. Bertin, V. Niess- ARENA 2006 - Newcastle
16