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Fundamentals ofunderwater sound

Report No. 406

May 2008


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Fundamentals or underwater sound

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International Association o Oil & Gas Producers

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able o contents

1 Sound waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Sound levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 Measurement o sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Signal measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5 Comparison o measurements in air & in water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6 Sound propagation in water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

7 Special propagation modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

8 Fundamental sound summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18


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Fundamentals o underwater sound

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Sound waves are defined as compressional (or longitudinal) waves that have a requency that is within the audible spectrum. For humans this covers requencies rom 20 Hz to 20 kHz, but ormarine mammals and other species the audible spectrum can extend beyond the human hearing

range. Sounds outside the human hearing range are ofen reerred to as inrasound (below 20 Hz)and ultrasound (above 20 kHz).

Compressional waves are mechanical waves that propagate through the interior o the material as pressure fluctuations. A characteristic o longitudinal waves is that the motion o the particles goesback and orth along the same direction in which the wave travels. Te rate o change o these pres-sure fluctuations determines the requency o the wave.

Figure 1 illustrates the generation o sound waves, and shows how the pressure variations propagateaway rom the source with a velocity v. At the locations where the particles are shown close together,a pressure maximum in the sound wave is ound.

Figure 1: Illustrating the generation of sound waves.

v v

Partices o me ium

Tere are three other types o mechanical waves that will propagate through solid material: shear,Rayleigh and Lowe waves. In common with compressional waves, shear waves travel through theinterior o the material. Both are known as body waves. Rayleigh and Lowe waves travel along thesurace o a solid material. Shear waves depend on elastic deormation o the medium in a directionthat is perpendicular to propagation. Although most reflection surveys are based upon analysis o

pressure waves, seismic sources generate all types o waves in the seabed. Te various wave types areseparated by their differences in propagation velocity. Only compressional waves can travel through

water, and are thereore the only type o waves that needs to be considered in terms o possibleimpact on marine lie.

Fluids, such as air or water, cannot sustain a shear deormation; thereore there wil l only be compres-sional waves propagating through air or water. At the water/solid interace however, new wave types

will be generated through energy conversion, and shear and surace waves wil l be present in marineseismic surveys.

Depending on the conditions or generation o the sound wave, they can be either plane waves,spherical waves or something between. Plane waves propagate in an ideal medium with no loss oenergy in the direction o the wave propagation. Spherical waves, on the other hand, have an energydecay in the ideal medium that ollows a spherical law, that is the energy decreases with the inverseo the distance squared.

Depending on how they are generated and other local conditions, sound waves can also propagate ascylindrical waves, or with other decay actors.

I measurements o sound waves are taken very close to the source they are called near field measure-ments. Similarly, i taken urther away rom the source, they are called ar field measurements.

Te near field is defined as inside a distance r0, and is determined by the size o the source. For a

circular source o area A, the near field will extend to a distance determined by:

where fequency o the sound wave λ wavelength o the sound wave c propagation velocity o the sound wave

Seismic signals have a low requency, and although the “source area” can be significant, measure-ments made at distances o over 100 metre will be in the ar field. Tis is normal practice in thegeophysical industry.

1 Sound waves


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2 Sound levels

Te definition o sound level is not directly given by mathematical equations, but depends on anumber o actors, including the intensity o the sound wave, the requency and the length o thesound exposure, and whether the sound is propagating in air or in water.

2.1 Intensity

Te acoustic intensity, I , o a sound wave is defined as the average rate o flow o energy through aunit area normal to the direction o wave propagation. Te units or acoustic intensity are Joules persecond per square metre, which can also be expressed as Watts per square metre.

In some cases it has been stated that the loudness o the sound is determined by its intensity. Tis isnot true in the general case, or loudness and intensity are not synonymous. Te loudness o a soundis subjective, and the loudness is in all cases a combined unction o both intensity and requency.

2.2 Pressure

Sound waves are pressure fluctuations, compression and rareaction o the molecules in the mediumthrough which the sound waves propagate. Te unit or pressure is Pascal, equal to Newton persquare metre.

Te pressure can be measured with a pressure sensitive device such as a microphone (or measure-ments in air) or a hydrophone (or measurements in water).

Intensity and sound pressure (P) in a plane wave are related through the equation:

[Watt/m

]where ρ0 specific density o the medium through which the sound propagates c propagation speed o sound in the medium

Te instantaneous particle velocity, U , within the plane wave can be related to the sound wave pres-sure through the equation:

[metre/second]

Te displacement amplitude A , or particle motion, o a sound wave can be related to its pressure andrequency through the equation:

[metre]where ω = 2π, and is the fequency o the wave

Te above ormulae hold or both plane and spherical waves when the distance to the source is morethan a wavelength at the lowest requency, ofen called the ar field. I the measurements are taken insmall enclosures, it might be difficult to obtain accurate measurements o the sound pressure due tothe many reflections rom the enclosure walls. In this case the relation between pressure and inten-sity can only be estimated. However, the relationship between pressure and displacement amplitude

will be accurate.

Te pressure that represents the lower limit o human hearing (20.4 μPa, corresponding to an inten-sity o 10-12 Watt/m2, as will be discussed later) will cause a displacement o the eardrum that is inthe order o 10-9cm at a requency o 1000 Hz. Tis is approximately one-tenth the diameter o a

hydrogen molecule.

In many papers on biological acoustics, there seems to be a belie that pressure and particle motionare separate physical phenomena. As shown above, the pressure and the displacement amplitude, or

particle motion, in the ar field are directly proportional.


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2.3 Acoustic impedance

Te actor ρ0c is called the acoustic impedance, and describes the conditions or sound propagation

through the medium. Te unit or acoustic impedance is rayl, equal to Pascal second per metre orkilogramme per square metre second. As seen above, the acoustic impedance is the ratio between the

pressure and the instantaneous particle velocity (ρ0c=P/U).

Te acoustic impedance is an important actor in all evaluations o sound waves, especially whencomparing sound measurements in air and in water. For such evaluations, it is customary to speciythe characteristic acoustic impedance as ollows:

Air: 415 rayl = 20°C and standard atmospheric pressureWater: 1 480 000 rayl Distilled water at 20°C.

Te similarity between Ohm’s law or electrical computations and the above equations, where Inten-sity represents power (Watt), Pressure represents voltage (volt) and acoustic impedance representsresistance (ohm) is a useul consideration or the understanding o acoustic calculations.

2.4 Attenuation factors

Te amplitude o seismic waves generally declines with distance rom the source. Tis weakeningo the seismic signal with distance is requency dependent, with stronger attenuation o higher re-quencies with increasing distance rom the source.

Te main actors determining the amount o weakening o the seismic signal with distance are:

2.4.1 Geometrical spreading

From a point source, the sound waves will propagate as spherical waves, the energy o which willdecay at a rate proportional with the inverse o distance squared. Many geometrical conditions willcause the waves to propagate with a different decay rate, the other extreme being plane waves wherethere is no geometrical spreading loss. Cylindrical waves have characteristics that are between thoseo the plane wave and the spherical wave.

2.4.2 Transmission/Reflection

Te pressure waves will be transmitted into the sea bottom and be reflected rom the geologicalboundaries. Te transmitted/reflected signals will in some cases have a higher amplitude than the

primary signal transmitted only in the water, but due to different propagation paths, the transmit-ted/reflected signal will not have the same characteristics as a pulse close to the signal source. Anelongated pulse rom seismic sources at great distances is ofen the result o a transmission/reflection

process.

Due to the attenuation o low requency sound waves in the water, at great distances the pressure pulse transmitted through the strata below the sea-bottom is ofen stronger than that travellingthrough the water. Te majority o models that estimate sound levels at distances rom a sourceocus on propagation and attenuation within the water column only. I these models are comparedto measured data and used to estimate propagation rates and attenuation actors in water columnalone, the results are likely to be in error. Tis is area that requires urther attention in many o thestudies that estimates environmental impact rom strong sound sources.

2.4.3 Absorption

Te transmission loss due to rictional dissipation and heat is an exponential unction o distance.Normally, this process is weak in seawater and will only contribute significantly to the losses whenseismic waves are propagating within the seafloor and underlying material.


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2.4.4 Scattering

Reflection, reraction and diffraction rom inhomogeneities in the propagating medium cause an

apparent transmission loss. Frequency dependence due to destructive intererence orms an impor-tant part o this weakening o the seismic signal. Since the inhomogeneities in water are very smallcompared to the wavelength o the signal, this attenuation-effect will mostly contribute when thesignals propagate through the sea floor and the subsurace.

2.5 Characteristic differences between air and water

Due to the difference in acoustic impedance, a sound wave that has the same intensity in air and in water, will in water have a pressure that is 60 times larger than that in air, while the displacementamplitude will be 60 times less.

I the pressure is kept the same, the displacement amplitude in water will be 3580 times less than inair.

Another characteristic phenomena o the differences in acoustic impedance are that the air/waterinterace will act as a very good reflector, the so-called Lloyd mirror. Tereore very little energy will

pass this reflector, meaning that sound generated in the water will not pass over to the air, and vice versa.

One important aspect o the air/water interace is that sound waves in the water will be reflected with an opposite polarity o the original wave. Tis means that a compression will be returned as arareaction, and a rareaction returned as a compression. As will be seen later, this is o importanceor the evaluation o sound propagation rom seismic sources.


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3 Measurements o sound

Te characteristics o a seismic signal are described by a variety o parametres, both in the time andrequency domain. In the literature, the qualities o geophysical sources (airguns in particular) as

well as the impact on marine organisms are defined in terms o these measures.

Te main eatures o a seismic pulse are presented in figure 2. Perhaps the most undamental meas-ure is the pressure amplitude o the initial pulse. Tis is commonly reported as the peak-to-peakamplitude A1, and given in barm (ie the pressure in bars that would be measured at a distance o1 metre rom the equivalent point source).

Figure 2: The seismic pulse

A1

A2

Following the initial pressure pulse, there will be a “bubble” signal, A2, originating rom the volumeo air released into the water. Te bubble signal is unwanted, and special efforts are taken to reduce

this part o the pulse to a minimum.

3.1 The dB scale

Due to the wide range o pressures and intensities encountered in measurements o sound, it is cus-tomary to describe these through the use o a logarithmic scale. Te most generally used logarithmicscale or describing sound is the decibel scale (dB).

Te intensity level, IL, o a sound o intensity I is defined as:

where I 1 measured intensity level (Watt/m 2 )

I 0 reerence intensity level (Watt/m 2 )

log logarithm with base 10

Since intensity is proportional to pressure squared, the decibel expression or sound pressure level(SPL) becomes:

log logSPLP P

P P

10 200

2

1

2

01

= =

where P 1 measured pressure level (Pascal) P 0 reerence pressure level (Pascal)

It is very important to note that the decibel scale is a relative measure, and not a unit or measuring

sound. Tereore other units o measurement and reerence level can be used instead o the stand-ards indicated above.


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3.1.1 Reference levels

For the reerence level I 0 or P

0 , different values are used or measurements in air and in water.

For measurements o sound in air, the reerence level o I0 = 10–12 Watt/m2 is used or intensity.Tis corresponds to the lower limit o human hearing at 1000 Hz. Converted to pressure, this cor-responds to an effective (root-mean square) sound pressure level o:

P 0 (air) = 20.4μPa (or 0.0002μbar)

For sound measurements in water, the pressure reerence level is set as:

P 0 (water) = 1μPa (or 0.000001μbar)

It is important to note the different reerence levels between measurements made in air and in water.Te difference between the two is 26dB.

Given a dB value, there is no standard nomenclature that will say whether a measurement is madein air or in water. Tereore, any reerence to a dB-value must be careully checked in order to deter-

mine where the measurement is taken, and what reerence level is used.As stated in section 2.5 there is a physical difference between sound in air and in water, and a differ-ent reerence level is used as stated above. Tereore, in comparisons o sound pressure measurementsmade in air and in water, a correction actor o 62dB must be added to the air measurements.


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4 Signal measurements

Sound levels are measured in many ways, and the abundant amount o research literature on theimpact o noise on marine lie (fish and mammals) presents data in a variety o ways.

4.1 Spectral analysis

Measurements made or noise studies or the analysis o human hearing are most ofen carried outin the spectral domain. Tis implies that the data are transormed rom the time domain to therequency domain, and the results displayed as a unction o requency. Tese transormationscan either be done in processing, or by use o filters. In the latter case, octave-bands are most ofenused, either 1-octave or ⅓-octave. I data are transormed in data processing, a 1Hz band is mostcommon.

Figure 3: Human audiogram in air (after Kinsler and Frey)

Frequency in Hz

S o u n

d

p r e s s u r e

l e v e

l ( d B

r e

2 0

µ P a )

120

100

80

60

40

20

0

20 50 100 200 500 1000 2000 5000 10000 20000

Figure 4: Lower limit of human audiogram in water (after Parvin and Nedwell)

Frequency in Hz

S o u n

d

p r e s s u r e

l e v e

l ( d B

r e

2 0

µ P a )

120

100

80

60

40

20

0

20 50 100 200 500 1000 2000 5000 10000 20000

Figre 3 presents a human audiogram in air, and indicates the lower threshold o human hearing.Figure 4 gives the lower limit o human hearing in water. It is important to note that the lower limito human hearing under water is only 6dB less than in air. Te apparent larger difference shown inthe figure is due to the acoustic impedance o water. It is also worth noting that the high-requencyhearing o humans is considerably reduced underwater.


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Spectral analyses are ofen done in data processing, using the Fourier ransorm method. Tis tech-nique uses the act that any signal can separated into a series o sine waves with different requen-cies.

Te Fourier transorm o a real, continuous-time signal x(t) is a complex-valued unction definedby:

where ω real variable (w=2π, angular fequency given in radians/second) & j=√–1.

Te inverse transorm is likewise defined as:

It should be noted that continuous signals will give a line spectrum with a discrete number o re-quency components, whereas a transient signal (or a single pulse) will result in a continuous re-quency spectrum.

An important parametre o the Fourier analysis is the total energy in a time unction x(t), definedas:

and the total energy in the requency domain defined as:

In studies o underwater sound it is most common to give pressure as a unction o requency inspectral analysis.

Parceval’s theorem states a very important aspect o these two ways o defining total energy,namely:

4.2 Broadband analysis

Explosions and most seismic sources are impulsive sources. Tey are characterised by having a tran-sient output signals, which is a signal with zero power and finite energy. For such signals, it is mostsuitable to use broadband analysis.

Broadband analyses, as opposed to spectral analysis, are taken over a wider band o requencies. Inthe definition o a sound level taken as a broadband analysis, the bandwidth over which the analysisis based should be stated.


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Figure 5: SEG standard for seismic pulse definition

4

3

2

1

0

-1

-2

-3

212

209

-3dB

10Hz 90Hz

206

203

200

197

194

191-4

0 Time (ms)

Pa Primary pulse

Pb Secondary pulse

Pa (Mpa@1 meter) andPa/Pb specified with nolow-cut filter and a 2msantialias high-cut filter

Variation

Nominal

Frequency (Hz)40 80 120 160 200 240 50 100 150 200

Broadband analysis can be undertaken in a number o ways, either as direct measurement o theamplitudes in the time signal, or as a value related to the time signal using a conversion ormula.

Impulsive sound, o very short duration, can be given as 0-peak or as peak-peak levels. Te firstis used in the study o underwater detonation o explosives, and the latter or defining the sourcestrength o seismic sources.

I the positive and negative part o a signal have the same value, the difference between 0-peak and peak-peak measurements will be 6dB.

Te Society o Exploration Geophysicists (SEG) has issued standards or the specification o marine

seismic energy sources, and Figure 5 gives the parametres that define the source level.

Te use o the so-called rms (root mean square) notation has gained considerable interest in describingthe pressures associated with sound waves. Te basis or this notation is measurements o alternating

voltages in electrical circuits, but the concept is equally applicable to sound pressure measurements.It should be noted, however, that the rms notation is only valid or continuous signals, and the timegate or analysis should be equal to a ull period o the lowest requency in the signal.

Energy is defined as power times the duration o the signal. Te time is easy to measure, whereas the power needs definition, as the analysis may be dependent on the time duration o the signal.

Continuous signals may be analysed using the ollowing ormula or the power (as in computationo electrical signals):

[Watt]

where V oltage in olts I current in Amperes R resistance in Ohms

I the voltage is alternating, it is possible to compute an effective voltage, equal to a fixed voltage thatover the time will give the same energy. For a continuous signal, the mean power can be computedrom the ollowing ormula:

[Watt]

where time or one period o the lowest fequency in the signal x(t) sample values describing the signal


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From the Mean Power it is possible to define the corresponding effective voltage as:

[volt]

V eff

is ofen reerred to as the root mean square (rms) value o the signal.

Te ratio between the maximum amplitude ( peak level) and the root-mean-square value (rms level)defines the crest actor or the signal.

As an example, a sinusoidal signal with peak amplitude o 1 (over a resistance R=1) is shown infigure 6:

Figure 6 Illustration of sinusoidal waveforms

T

Since the signal x(t) = sin(t) is repeating with period , the signal squared will repeat at an intervalo /₂(rom 0 to π), and the effective voltage or this signal becomes:

Tis shows that the crest actor or a sinusoidal signal is:

or in decibels the crest actor is 3dB.

I the same sinusoidal signal is rectified (ie the negative part o the signal is removed) the waveorm will be as shown in figure 7:

Figure 7 Illustration of rectified sinusoidal waveforms

T

Te signal will now repeat at a period o , but only one hal o the period have values that are differ-ent rom zero. Te analysis must, however, be taken over the whole period, as shown in the ollowingormula:

Te crest actor o the rectified sinusoidal signal then becomes:

or in decibels the crest actor in this example is 6dB.


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Te above analysis can be developed urther, and it should be obvious that i the non-zero part o therepetition period becomes small, so will the V

rms become very small. For single impulses the V

rms will

be undefined, and this type o analysis cannot be used or single pulses.

Description o non-sinusoidal signals can be more difficult, as the effective voltage will depend onthe duration o the signal as well as the statistical distribution o amplitudes.

Te ormula or computing the rms value o a statistical varying signal is:

where x sample values o the signal, and p(x) amplitude density (probability or the amount o samples with values between a

value x and x+∆x when ∆x approaches zero). duration o the signal analysis window (the signal is assumed to be continuous).

Random noise (white noise, containing all requencies) will have an amplitude density that can be

described with the normal distribution unction (Gaussian distribution), and the rms value o thesignal can be computed as:

It should be noted that the crest actor or a random signal does not exist, since a true random signal will have amplitudes that approaches infinity.

A popular method or computing the rms-level o signals is to make a histogram o the accumulatedamplitudes squared, and define the time in the above ormula as the time between 5% and 95% othe histogram. Tis is a urther approximation to the assumption o random signals, and may leadto gross errors in the analysis.

Furthermore, the method described above is only useul or stationary signals. Impulsive signals,such as airgun pulses, have short duration, and errors in the time estimate may give large errors inthis type o calculation o rms levels. Figure 8 illustrates the use o this method on airgun pulses:

Figure 8 Illustration of airgun pulse (left) and resultant “waveform” (right) assumed in computing a “Vrms

” value withthe 5-95 % method.

It should be obvious that the 5-95% method leads to rms-levels that are much higher than the actualsignal generated by the airguns.


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4.3 Energy flux calculations

Te problems in defining sound exposure levels with rms-levels have been widely recognised, and the

use o energy flux is gaining much interest. Te relationship between rms and energy flux are givenby the ollowing equations:

Hence it is easy to compute one rom the other by the simple relationship

Computing energy flux in the way described above does not overcome the problems associated withcomputations o V

rms. I continuous signals are being analysed the method is usable, but or pulsed

signals it becomes very misleading. For single impulses, V rms

is undefined and energy flux calculationsas shown above become meaningless. I a series o pulses is analysed the repetition rate is the timeseparation between the pulses, and this must be the basis or the calculations.

Standards or damage risk criteria (DRC) rom repeated exposure o impulsive noises sources usethe peak pressure as the basis or evaluation. It is most probable that the zero-peak sound pressurelevel will be the best or assessing direct physical damage, and it is recommended that this be used inevaluation o possible impact rom impulsive sources like airguns.

In some special cases, the total acoustic energy in a pulse can be an indication o “perceived noisi-ness”, and are thereore used in some studies o the impact rom seismic surveys on marine mam-

mals.

Te acoustic energy in the pulse can be approximated by the equation:

[Watt×s/m]

where P 2 average pressure squared time duration o the pulse

For practical purposes, the time duration is ofen taken as the time the pulse has a pressure that is5% above the ambient noise level.

It must be stressed that measurements o total acoustic energy are very sensitive to the determinationo the time , and are also dependent on the requency bandwidth used in the analysis. Tereore itmay be difficult to compare the dB values obtained rom one study directly with those rom otherstudies.


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I a spectral analysis is undertaken with 1 Hz bands used as a basis, an equivalent broadband pres-sure level can be computed by the equation:

PL = SPL + 40 log W

where PL = broadband pressure level SPL = spectrum pressure level W = effective bandwidth

With the understanding o the dB levels, and the various ways o measuring sound pressure levels,it is possible to establish a table or comparison o the most requent measurements in air and in

water. Te ollowing table gives corresponding values or air and water having the same intensitiesat a requency o 1 kHz:

Pressure in air re 20μPa/Hz Pressure in water re 1μPa/Hz Comments from Kinsler & Frey:Fundamentals of Acoustics

0 62 lower limit of human hearing

60 122120 182 threshold of hearing

140 202 threshold of pain

160 222 threshold of direct damage

(the comments quoted fom Kinsler & Frey: Fundamentals o Acoustics, 2nd edition, John Wiley & Sons,

1962, page 392, are given as rms-levels or pure tones).

Assuming that the lower limit o human hearing is connected to the pressure o the sound wave,the table shows that in water the lower limit should be approximately 62dB. Te direct connectionbetween intensity and pressure allows us to use both when discussing the lower limit o hearing.

With reerence to figures 3 and 4, this compares well with test-results showing that the limit is41dB re 20μPa, or 67dB re 1μPa, or an 800Hz signal. (S.J. Parvin and J.R. Nedwell: Underwater

Sound Perception and the Development o an Underwater Noise Weighting Scale, Underwater ech-nology, Summer 1995).

At the higher end o the table, the pain/damage level or pure tones in a ir o 140/160dB (re 20μPa)corresponds to a level in water o around 202/222dB rms (re 1μPa). Tis corresponds very well withmany experiments where is has been shown that physical damage occur to fish (eggs, larvae and ry,as well as larger fish) when the sound pressure level is higher than 230dB peak-to-peak (re 1μPa).It should be noted that at these high-pressure levels non-linear effects occur, and the differencebetween broadband signals and single requencies becomes much less than at lower levels. Further-more, these sound levels are only ound in very close proximity to the airguns, and other mechanicalactors resulting rom the release o high-pressure air, may well have a much larger impact than thedirect sound pressure waves.

5 Comparison o measurementsin air & in water


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As stated in the introduction, the intensity o spherical waves will be proportional to the inverse othe squared distance rom the source. From the relationship between intensity and pressure, i ol-lows that the pressure will be proportional to the inverse o the distance. In practice, the decay rate

o a sound wave will be dependent on the requency, the local conditions such as water temperature, water depth and bottom conditions as well as the depth at which the signal is generated.

6.1 Propagation models

Te studies o sound propagation in var ying local conditions have been given considerable attentionor a long time, and a number o papers have been published on the subject. A thorough treatment isgiven in Urick: Principles o Underwater Sound, 3rd edition, Peninsula Publishing, 1983.

Te propagation o sound in the ocean will always be dependent on the requency o the signal.Most models are developed or high requency sound, rom several kHz and upward. Low requency

sound generated near the sea surace will penetrate into the sea floor, and in practice the conditions will be very similar to spherical spreading. Tis is o special importance when evaluating the impacto marine seismic surveys. Te act that seismic surveys use the signals reflected rom geologicalboundaries in the sub-surace, indicates that a significant amount o energy has penetrated the seabottom.

Te use o sophisticated models designed or high requency applications can give misleading resultsi used to estimate the propagation characteristics o seismic signals, due to limited knowledge othe subsurace conditions. Simplified models o the earth used in combination with techniques ortracing o the sound propagation (ray tracing) might well give a better estimate o the variation inseismic signal strength with distance in may cases. An even more practical method, an possible su-ficiently accurate in most cases, is given by the ollowing ormulae:

SL = A log (r)–B.r–CWhere SL received pressure level at distance r fom the source A wave mode coefficient; or spherical waves A equals 20. B attenuation actor that is dependent on water depth and sea bottom conditions. C fixed attenuation due to acoustic screening; in open water this will be 0. r distance over which the sound has propagated.

In the above equation, the actor C is included or evaluations o sound wave pressure in coastalareas, where it is shown that sound might also be present even i there are small islands in the direct

propagation path. In these cases, all sound will travel through the bedrock. In deep water areas theactor C can be set to zero.

For high requency signals, higher than around 1 kHz, more elaborate propagation models must

be used.

6.2 Importance of water depth

Variations in water depth will influence the propagation o seismic signals, but to a much lesserdegree than the impact on sound waves with higher requencies.

In publications it has been discussed whether seismic signals in shallow water will ollow a cylindri-cal decay law, which can be expressed as:

SL = 10 log (r)

Tis might be correct or high requency signals, but the low requency nature o the seismic signal

will cause it to travel through the rocks beneath the sea, and thereore attain a decay rate that ismuch closer to the deep-water conditions; ie a spherical decay law or even stronger attenuation.

6 Sound propagation in water


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6.3 Sea floor conditions

In areas with a very strong acoustic contrast at the sea floor, much o the seismic signals will be

reflected back into the water column, and not penetrate into the bedrock. In such cases there mightbe a lower decay with distance than normally predicted.

It should be noted that seismic surveys carried out in order to map the sedimentary structure underthe sea, and thereore, in most cases, the sea floor conditions will be acoustically transparent to thelow requency seismic signals.

It is thereore sae to assume that in most cases seismic signals will penetrate well into the sea floor,and that variations in sea floor conditions will not have a significant impact on sound propagationrom seismic surveys.

6.4 “Ghost” reflectionsTe sea surace acts as a very good “mirror” or the sound waves (the Lloyd mirror effect). Tis meansthat the seismic source will have a mirror image, placed at a position that is as much above the seasurace as the source is below. Te signal coming rom the mirror images will be o opposite polarityto the real source, due to the negative reflection coefficient at the sea surace.

O the many characteristics o the ghost reflections, the most characteristic is that the primarysource and the mirror image will cancel each other at the sea surace, resulting in a rapid decay o the

waterborne seismic signal. All observations o seismic energy at significant distances rom the soundsource must thereore come rom reflections, either at the sea floor or in the sediments below. Dueto reflection loss, these signals wil l always have a higher attenuation than would have been estimatedrom strict propagation modelling o high requency sound.


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Seismic signals will propagate through the rocks below the sea floor in many different ways. As theenergy hits a geological boundary, new wave phenomena such as shear waves and surace waves willbe set up. Tese will propagate away rom the source, and will be the origin o new pressure waves

that can be detected in the water column.

All these mode conversions will mean that the seismic signal loses energy, resulting in stronger atten-uation o the signal over distance. However, some conditions might also cause the signal to havelower energy decay, and most noticeable o these are sound channels. It is known that sound maybe trapped in the interval between geological layers, and propagate with lower attenuation or greatdistances. But these conditions in the subsurace are rare, and will not account or stronger seismicsignals over distance in the general case.

7.1 Sound channels

In the sea a phenomenon called sound channels requently occurs. Changes in sound propagation velocity due to temperature and pressure, will orm these sound channels at varying depths and with varying thickness. Both these actors wil l influence how seismic signals are transmitted throughsound channels.

Sound channels act like ducts that tend to ocus the sound energy, and attenuation in these ductscan be significantly less that normal spherical spreading. Trough this mechanism sound can travelover considerable distances.

Figure 9 Mixed layer sound channel (near surface)

Velocity

D e p t h

Range

Shadow zone

Sound channels are ofen named afer their placement in the water column, such as deep sea soundchannels, shallow water sound channels and mixed-layer sound channels.

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Sound channels will not transmit all requencies in the same manner. Depending on the thicknesso the channel, there will be a cut-off requency, and sound energy with a lower requency will notbe affected by the channel. Te lower cut-off requency or a near surace sound channel can be esti-

mated by the equation:

[Hz]

Using this ormula, one finds that a channel thickness o 145m is needed or a requency o 100 Hzto be transmitted through the channel.

I the sound waves are generated outside the channel, much less energy will enter into this low-attenuation environment, significantly reducing the distance that the sound can travel.

Under conditions when sound channels can orm, this wil l have significant impact on sound propa-gation. Sound can travel great distances, but there will also be areas in the vicinity o the soundsource that little or no sound will reach. Figure 8 illustrates the conditions in a mixed-layer soundchannel, clearly showing the “no-sound” areas.

Te seismic source will be placed very close to the sea surace, thereore only mixed-layer- and shallow water sound channels can be considered as alternatives or long-range propagation o seismic sound.Tese channels ofen have a thickness that prevents low requency signals rom being transmittedthrough them. With the low requency characteristics o the seismic source, it is clear that soundchannels wil l not play an important part in the propagation o seismic sound. Tis is confirmed bothby actual modelling and measurements. It should also be noted that most o the energy rom theseismic source will travel through the geologic strata below the sea floor, and this must be taken intoaccount when evaluations o signals rom a seismic source is measured at some distance.


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8 Fundamentals o sound summary

Sound rom seismic sources can be recorded over great distances. However, the sound pressure levelsare strongly attenuated as the distance rom the source increases. Sound pressure levels that maycause physical damage can only be observed within a ew metres o the source, but the annoyance

level may extend much urther.

At distances over 1000 m, the seismic sound reaching the sea surace is dominated by energy thathas travelled through the sea floor. Tis energy has a stronger attenuation than comparable high-requency signals would have i they travelled in the water-column only.

It is easy to misuse the many different notations o underwater sound, and make comparisons basedon dB values that are inconsistent. Great care must be taken in any reerence to inerred sound pres-sure levels based on the source strength and the distance between the source and the observation.


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About IAGCThe International Association of Geophysical Contractors

(IAGC) is the international trade association representing

the industry that provides geophysical services (geophysical

data acquisition, seismic data ownership and licensing, geo-

physical data processing and interpretation, and associated

service and product providers) to the oil and gas industry.

IAGC members provides services to the oil and gas indus-

try throughout the world; both onshore and offshore.

About OGPThe International Association of Oil & Gas Producers

(OGP) encompasses most of the world’s leading publicly

traded, private and state-owned oil & gas companies, oil

& gas associations and major upstream service companies.

OGP members operate in more than 80 different countries

and produce more than half the world’s oil and about one

third of its gas.

The association was formed in 1974 to develop effective

communications between the upstream industry and an

increasingly complex network of international regulators.

OGP works with its members to achieve continuous

improvement in safety, health and environmental perform-ance, and in the engineering and operation of upstream

ventures.


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OGP, 209-215 Blackfriars Road,

London, SE1 8NL, UK

Tel +44(0)20 7633 0272

www ogp org uk

IAGC, 2550 North Loop West. Suite 104,

Houston, Texas 77092, USA

Tel +1 713 957 8080

www iagc org

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