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30/09/2013

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egm502 seafloor mapping

lecture 3 underwater acous8c wave propaga8on


lecture 3 underwater acoustic wave propagation

reading lurton 2010, chapter 2



This lecture

•  How does a signal propagate from one point to another underwater? •  What are the constraints? •  What transformations does it undergoes?

Acoustic (Sound) Waves

•  Sound is a disturbance of mechanical energy that propagates through matter as a wave.

•  Sound is characterized by the properties of sound waves which are frequency (f), wavelength (l), period (T), amplitude (γ) and velocity (v).



•  Noise and sound often mean the same thing; when they differ, a noise is an unwanted sound.

•  In science and engineering, noise is generally an undesirable component that obscures a signal (discussed at end of lecture).



•  Frequency (f) is the measurement of the number of times that a repeated event occurs per unit of time.

•  It is also defined as the rate of change of phase of a sinusoidal waveform.

•  To calculate the frequency of an event, the number of occurrences of the event within a fixed time interval are counted, and then divided by the length of the time interval.

•  In SI units, the result is measured in hertz (Hz), named after the German physicist Heinrich Rudolf Hertz.

•  1 Hz means that an event repeats once per second, 2 Hz is twice per second, and so on.

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•  An alternative method to calculate frequency is to measure the time between two consecutive occurrences of the event (the period) and then compute the frequency f as the reciprocal of this time:

where T is the period.

•  A more accurate measurement takes many cycles into account and averages the period between each.

f = 1 T



•  The wavelength is the distance between repeating units of a wave pattern.

•  It is commonly designated by the Greek letter lambda (λ).

•  In a sine wave, the wavelength is the distance between the midpoints of the wave:



•  Frequency has an inverse relationship to the wavelength.

•  The frequency f is equal to the velocity (v) of the wave divided by the wavelength (λ) of the wave:

f = v λ

or v = f λ

•  Sound propagates as waves of alternating pressure, causing local regions of compression and rarefaction.

•  Particles in the medium are displaced by the wave and oscillate.

•  The scientific study of sound is called acoustics.

•  In marine acoustics we employ acoustic waves to measure properties of the water column, seafloor and sub-surface.

•  Waves alternatively termed acoustic waves, sound waves, acoustic pulses, p-waves, longitudinal waves or compressional waves.



Time and Frequency Domains

•  We can specify a seismic waveform as a continuous graph of some variable as a function of time.

•  The waveform is then said to be defined in the time domain and is referred to as a time series.

am

plit

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time (s)

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•  An alternative and equivalent representation of the same information is to present these data in the frequency domain. •  The frequency domain relates to the Fourier transform or Fourier series by decomposing a function into an infinite or finite number of frequencies. •  This is based on the concept of fourier series which is that any waveform can be expressed as a sum of sinusoids



•  Names Chirp, boomer, pinger etc. reflective of the frequency content of the source signal. •  The usual domain for the interpretation of acoustic data is the time domain, whereas the usual domain for specification of acoustic instruments and filtering of acoustic data is the frequency domain.



Analogue and Digital Data •  Acoustic data is recorded either in analogue or in digital format. •  Digital revolution – practically all underwater signal (and noise) recorded digitally and the results and analysis are displayed on computers. •  The acoustician employs signal acquisition and digitizing equipment, signal processing algorithms and graphic display software.

•  The noisy detected recorded by the transceiver or hydrophone is an analogue signal, originally a mechanical wave, converted to an electrical voltage at the transceiver and expressed as a continuous function of time.



•  The analogue signal must be sampled to convert it from analogue to digital format in order to store it on a computer.

•  Analogue to Digital Converter used (ADC).

an

alo

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e

sam

ple

d

sam

ple

d

•  Signals must be sampled properly.

•  Is sampling rules are obeyed, the original signal can be recovered from the sampled signal.

•  If the rules are not obeyed, and sampling is too sparse, the original signal cannot be recovered.

•  Nyquist Frequency The sampling frequency must be greater than twice the highest frequency component in the signal.

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Principle of echo-sounding

sea-surface

seafloor

transceiver

1. transmits

2. reflects

3. receives

d = twt x V

2

where: •  twt = two-way-time •  V = p-wave velocity

V = p-wave velocity = speed of sound = 1,500 ms-1 salt water

V is variable.



•  1500ms-1 is used as a kind of standard speed of sound in water •  Equivalent to approx. 4.5 times the speed of sound in the atmosphere •  However - sound velocity in any kind of fluid depends on two physical quantities: density and compressibility

•  Density (symbol: ρ - Greek: rho) is a measure of mass per unit of volume.

•  The SI unit of density is the kilogram per cubic metre kgm-3

ρ = m / V,

where:

ρ is the object's density (measured in kilograms per cubic metre)

m is the object's total mass (measured in kilograms)

V is the object's total volume (measured in cubic metres)



•  Compressibility is a measure of the relative volume change of fluid or solid (sediment or rock) as a response to a pressure (or mean stress) change.

•  Rule: Increase in density and/or compressibility leads to a decrease in p-wave velocity.

•  The density and compressibility of sea-water are dependent on:

(a) the static pressure (or the water depth)

(b) the salinity

(c) the temperature



Wa

ter d

ep

th (

m)

Sound speed (ms-1)

1490ms-1 1500ms-1

100m

1000m

4000m

•  Since sound speed varies with temperature, pressure and salinity there are considerable variations in sound velocity both spatially (with depth / geographically) and temporally (daily / seasonally).

•  Horizontal variations in sound velocity are usually small due to small gradients in T, S and p. Exceptions might occur in estuaries or around oceanic frontal systems.

•  However, since vertical gradients in T, p and S are much larger vertical variations in sound velocity are much larger.

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Conductivity Temperature Depth measures (CTDs)

•  A CTD is an instrument cluster that measures conductivity (a measure of the salinity of ocean water), temperature and depth.



•  The predominantly horizontal layering of sound speed in the oceans (with T normally decreasing downwards and P always increasing downwards) affects sound propagation by refraction in two ways:

1.  Enables sound propagation in the horizontal along ocean-wide ranges (discussed next);

2.  Limits the effective swath width of acoustic imaging sources (discussed in later lecture on swath systems).



Enables sound propagation in the horizontal along ocean-wide ranges:

•  The SOFAR (SOund Fixing And Ranging) Channel - a deep water layer (approx. 1000m deep) where the speed of sound is at a minimum.

•  This minimum sound speed exists at the depth where the cumulative effect of water pressure, temperature, and salinity causes the water at this depth to be less dense than that of other parts of the water column.

The sound directed upward is refracted down by temperature gradients, and the sound directed downward is refracted up by pressure (depth).



•  Within the SOFAR channel, low frequency waves may travel thousands of km before dissipating. In temperate waters, this minimum sound depth is shallower, and it reaches the surface between about 60 degrees N or 60 degrees S.

•  Low-frequency sounds, attributed to humpbacks and other baleen whales, are a common occurrence here.

•  Humpback whales may dive down to this channel and "sing" to communicate with other humpback whales many kilometres away.

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Sound attenuation •  Attenuation is the reduction in amplitude and intensity of a signal with respect to distance travelled through a medium. •  Attenuation can also be understood to be the opposite of amplification.

distance

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Sound absorption

•  As the acoustic pulse propagates through the water column and sub-surface, some of the energy is simply absorbed by the medium due to frictional effects.

•  In general terms, the higher the frequency of the transmitted pulse, the higher the absorption rate.

•  Absorption is also significantly stronger in saline water than in fresh water.

•  Therefore - low frequency waves travel greater distances than high frequency waves.

•  Is the perfect solution to always transmit low frequency waves?



Sound attenuation

•  As the acoustic pulse is transmitted from the survey instrument, it spreads through spherical divergence – the distribution of wave energy on an increasing spherical surface during propagation.



•  The sonar transmits a fixed amount of energy into the water in the form of the acoustic pulse.

•  As the wave-front spreads in a spherical pattern, the intensity of the pulse falls with increasing distance (or range) from the source.

•  The energy returning to the sonar is also effected by spherical spreading.

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Earlier question Is the perfect solution to always transmit low frequency waves?

•  Low frequency waves travel long distances (long ranges)

•  High frequency waves travel short distances (short ranges)

f = v λ

•  High frequency sources (short wavelength) result in high resolution data

•  Low frequency sources (long wavelength) result in low resolution data

but

implies compromise



•  The optimum compromise between range and resolution depends on the application and is decisive for the frequency band of choice (horses for courses).

•  Some systems allow users to transmit swept frequency sources – combining high and low frequencies in one signal e.g. Chirp systems.

A linear chirp waverform - a sinusoidal wave that increases in frequency linearly over time.

An exponential chirp waveform - a sinusoidal wave that increases in frequency exponentially over time.

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