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

Principles of Underwater Acoustics – sea acoustics 2

© 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

Principles of Underwater Acoustics – sea acoustics 3

© Henryk Lasota 2005/06 - 2015/16

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

Principles of Underwater Acoustics – sea acoustics 4

© Henryk Lasota 2005/06 - 2015/16

Propagation conditions (2)

• absorbtion

• scattering (reverberation)

• high level of noise

– natural

– of civilization origin

Principles of Underwater Acoustics – sea acoustics 5

© Henryk Lasota 2005/06 - 2015/16

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.

Principles of Underwater Acoustics – sea acoustics 6

© Henryk Lasota 2005/06 - 2015/16

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).

Principles of Underwater Acoustics – sea acoustics 7

© Henryk Lasota 2005/06 - 2015/16

Sound modes 2

Principles of Underwater Acoustics – sea acoustics 8

© Henryk Lasota 2005/06 - 2015/16

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)

Principles of Underwater Acoustics – sea acoustics 9

© Henryk Lasota 2005/06 - 2015/16

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]

Principles of Underwater Acoustics – sea acoustics 10

© Henryk Lasota 2005/06 - 2015/16

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

Principles of Underwater Acoustics – sea acoustics 11

© Henryk Lasota 2005/06 - 2015/16

Sound rays 2

Snell’s law

a

izc

i

zc

)(

sin

)(

sin

cos

dzds

cos)()( zc

dz

zc

dsdt

dztgdr

Principles of Underwater Acoustics – sea acoustics 12

© Henryk Lasota 2005/06 - 2015/16

Sound rays 3

Radius of ray path:

czgradbdz

zcd

)]([

abr /1

sin

cz

grad

cr

Principles of Underwater Acoustics – sea acoustics 13

© Henryk Lasota 2005/06 - 2015/16

Sound rays 4

Positive and negative curvature radius

Principles of Underwater Acoustics – sea acoustics 14

© Henryk Lasota 2005/06 - 2015/16

Sound rays 5

Shadow zones

Principles of Underwater Acoustics – sea acoustics 15

© Henryk Lasota 2005/06 - 2015/16

Refraction

Principles of Underwater Acoustics – sea acoustics 16

© Henryk Lasota 2005/06 - 2015/16

Principles of Underwater Acoustics – sea acoustics 17

© Henryk Lasota 2005/06 - 2015/16

Layered structure of oceanic waters

Principles of Underwater Acoustics – sea acoustics 18

© Henryk Lasota 2005/06 - 2015/16

Oceanic sound channel (dukt akustyczny) 1

Principles of Underwater Acoustics – sea acoustics 19

© Henryk Lasota 2005/06 - 2015/16

Oceanic sound channel 2

Sound velocity distribution in deep (?) oceanic waters has a minimum favoring cylindrical energy spread

Principles of Underwater Acoustics – sea acoustics 20

© Henryk Lasota 2005/06 - 2015/16

Deepwater sound channel 3 – SOSUS

Principles of Underwater Acoustics – sea acoustics 21

© Henryk Lasota 2005/06 - 2015/16

Sound attenuation in water 1

Fresh water

Principles of Underwater Acoustics – sea acoustics 22

© Henryk Lasota 2005/06 - 2015/16

Sound attenuation in water 2

Sea water

Principles of Underwater Acoustics – sea acoustics 23

© Henryk Lasota 2005/06 - 2015/16

Sound attenuation in water 3

Principles of Underwater Acoustics – sea acoustics 24

© Henryk Lasota 2005/06 - 2015/16

Sound attenuation in water 4

A reminder:

Principles of Underwater Acoustics – sea acoustics 25

© Henryk Lasota 2005/06 - 2015/16

Sea noise

Principles of Underwater Acoustics – sea acoustics 26

© Henryk Lasota 2005/06 - 2015/16

Sea noise

Knudsen curves

• wind, f > 500 Hz - 5 dB/frequ. oct. + 5 dB/v doubling

• thermal noise f > 50 kHz + 6 dB/oct.

Principles of Underwater Acoustics – sea acoustics 27

© 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

Principles of Underwater Acoustics – sea acoustics 28

© Henryk Lasota 2005/06 - 2015/16

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

Principles of Underwater Acoustics – sea acoustics 29

© Henryk Lasota 2005/06 - 2015/16

Equiphase surfaces and sound rays

a b

Principles of Underwater Acoustics – sea acoustics 30

© Henryk Lasota 2005/06 - 2015/16

Sound rays due to positive velocity gradient

Principles of Underwater Acoustics – sea acoustics 31

© Henryk Lasota 2005/06 - 2015/16

Sound rays proper to negative velocity gradient

Principles of Underwater Acoustics – sea acoustics 32

© Henryk Lasota 2005/06 - 2015/16

Surface channel

Principles of Underwater Acoustics – sea acoustics 33

© Henryk Lasota 2005/06 - 2015/16

Acoustic channel

Principles of Underwater Acoustics – sea acoustics 34

© Henryk Lasota 2005/06 - 2015/16

Sound intensity distribution

Principles of Underwater Acoustics – sea acoustics 35

© Henryk Lasota 2005/06 - 2015/16

Depth distributions of sound velocity: left chart – Wdzydze lake, spring season, right chart - Baltic Sea, summer season.

Principles of Underwater Acoustics – sea acoustics 36

© Henryk Lasota 2005/06 - 2015/16

Sound intensity distribution in Wdzydze lake

Principles of Underwater Acoustics – sea acoustics 37

© Henryk Lasota 2005/06 - 2015/16

Acoustic channel in Southern Baltic

Principles of Underwater Acoustics – sea acoustics 38

© Henryk Lasota 2005/06 - 2015/16

Intensity distribution of the wave emitted by an antenna of defined directivity pattern

under a negative gradient of sound speed