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Principles of Underwater Acoustics – sea acoustics 1
© Henryk Lasota 2005/06 - 2015/16
Henryk Lasota
Department of Marine Electronics Systems Faculty of Electronics, Telecommunications, and Informatics
Gdańsk University of Technology
Principles of Underwater Acoustics
excerpt VI of the course:
Undersea acoustics
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© Henryk Lasota 2005/06 - 2015/16
Operating environment of hydroacoustic systems
• type of reservoir
– inland
• lake
• river
– sea • offshore
• continental shelf (depth up to 200 m)
• deep ocean
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Propagation conditions (1)
• refraction
– „curvilinear” propagation:
• shadow zones
• propagation channels
• rebound (reflection/scattering) from the bottom and water surface
– multiple paths of wave/signal propagation
– water surface motion (waves, ripples) causing fast signal fluctuations:
• deep changes in signal level - destructive interference
• change of signal - the Doppler effect by reflection
– daily volatility of propagation properties - extremely low frequency fluctuations,
– internal waves – relating to weather
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Propagation conditions (2)
• absorbtion
• scattering (reverberation)
• high level of noise
– natural
– of civilization origin
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Water reservoirs as (hydro)acoustic waveguides
The reservoir, as a medium of acoustic wave propagation in infrasound, sound, and ultrasound range, can be treated as a waveguide with a very heterogeneous "filler". The main phenomena affecting the wave wandering in it are:
– reflection / scattering – at medium borders,
– refraction – deflection on the heterogeneity of distribution of sound velocity - in the sense of changing the direction of the wave front of plane waves,
– attenuation - the effect of shear and volume viscosity of water and the relaxation of magnesium ions contained in MgSO4 (frm = 59.2 kHz) and boron ions contained in boron acids (frb = 0.9 kHz),
– dispersion - on small heterogeneity of the medium, in terms of different acoustic characteristic impedance, suspended in the depths.
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Sound modes 1
Shallow reservoir (relatively!) as a waveguide:
– wave equation for steady states (Helmholtz equation),
– harmonic sollutions are assumed, with separable dependence on r and z,
– boundary conditions are introduced (surface, bottom).
The solutions are waves (propagation modes) with „periodic" amplitude distributions between boundaries and different phase and group velocities!
Modes are also called specific values of the problem (eigenvalues).
Mode propagation concerns low frequencies (depth comparable to the wavelength).
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Sound modes 2
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Refraction
The speed of sound in water depends on:
– temperature T
– salinity S
– pressure/depth Ph / z
These parameters are different in different places:
- the type of water reservoir (lake, river, sea, ocean)
- climate zone
In given waters the distribution of T and S it is heterogeneous and varies in long, medium and short-terms (eg. internal waves):
- season of the year (seasonal changes),
- time of the day (diel - 24 h) [diurnal, nocturnal],
- phase of tides (tidal – 12.5 h)
- https://en.wikipedia.org/wiki/Tide
- https://pl.wikipedia.org/wiki/Pływy_morskie
- weather (wind, insolation)
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Propagation velocity
Empiric formula [Medwin]
c = 1449,2 + 4,6 T – 0,55 T2 +0,00029 T3 +
+ (1,34 – 0,010 T)•(S – 35) + 1,58•10-6 Ph
where:
c – sound velocity in water [m/s]
T – temperature [º C]
S – salinity [ppt = 10-3]
Ph – hydrostatic pressure [N/m2]
Approximate formula
c =1449 + 4,6 T + (1,34 – 0,01 T)(S – 35) + 0.016 z
where:
z – depth [m]
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Sound rays 1
Geometric approach – rays
Assumptions:
– channel dimensions are significant in relation to the wavelength
and furthermore, in the wavelength scale:
– the speed of sound propagation can be considered constant (not changing significantly)
– the wave intensity changes are also negligible
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Sound rays 2
Snell’s law
a
izc
i
zc
)(
sin
)(
sin
cos
dzds
cos)()( zc
dz
zc
dsdt
dztgdr
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Sound rays 3
Radius of ray path:
czgradbdz
zcd
)]([
abr /1
sin
cz
grad
cr
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Sound rays 4
Positive and negative curvature radius
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Sound rays 5
Shadow zones
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Refraction
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Layered structure of oceanic waters
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Oceanic sound channel (dukt akustyczny) 1
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Oceanic sound channel 2
Sound velocity distribution in deep (?) oceanic waters has a minimum favoring cylindrical energy spread
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Deepwater sound channel 3 – SOSUS
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Sound attenuation in water 1
Fresh water
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Sound attenuation in water 2
Sea water
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Sound attenuation in water 3
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Sound attenuation in water 4
A reminder:
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Sea noise
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Sea noise
Knudsen curves
• wind, f > 500 Hz - 5 dB/frequ. oct. + 5 dB/v doubling
• thermal noise f > 50 kHz + 6 dB/oct.
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© Henryk Lasota 2005/06 - 2015/16
Roman Salamon Department of Marine Electronics Systems
Faculty of Electronics, Telecommunications, and Informatics Gdańsk University of Technology
Sonar systems or personal/copyright use of
acoustic wave propagation in natural waters
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Typical profile of acoustic wave velocity in ocean [30]
0.016 1/s
1470 1480 1500 1490
z [km] c [m/s]
0.5
1
1.5
2
2.5
warstwa izotermiczna
termoklina główna
warstwa powierzchniowa
termoklina sezonowa
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Equiphase surfaces and sound rays
a b
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Sound rays due to positive velocity gradient
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Sound rays proper to negative velocity gradient
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Surface channel
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Acoustic channel
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Sound intensity distribution
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Depth distributions of sound velocity: left chart – Wdzydze lake, spring season, right chart - Baltic Sea, summer season.
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Sound intensity distribution in Wdzydze lake
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Acoustic channel in Southern Baltic
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Intensity distribution of the wave emitted by an antenna of defined directivity pattern
under a negative gradient of sound speed