underwater acoustics

C H A P T E R 9

UNDERWATER ACOUSTICS

Robert E. Randall

Ocean Engineering Program Civil Engineering Department

Texas A&M University College Station, Texas, USA

CONTENTS

INTRODUCTION, 383

Early History, 383

Underwater Acoustic System Categories, 385

Underwater Sound Fundamentals, 387

Decibel Scales, 388

SONAR EQUATIONS, 389

Active Sonar Equation, 390

Passive Sonar Equation, 391

Transient Form of the Sonar Equations, 392

PROPERTIES OF TRANSDUCER ARRAYS, 394

Array Gain, 395

Receiving Directivity Index, 397

Transducer Responses, 398

Beam Pattern, 399

Special Arrays, 401

UNDERWATER SOUND PROJECTOR, 403

Explosives as Sound Projectors, 405

UNDERWATER SOUND PROPAGATION, 408

Spreading Laws, 409

Cylindrical Spreading, 409

Multiple Constant-Gradient Layers, 422

TRANSMISSION LOSS MODELS, 426

Transmission Loss for Ray Diagrams, 426

Sea Surface and Bottom Loss, 427

382

Underwater Acoustics 383

Transmission Loss Model for Mixed Layer Sound Channel, 428

Deep Sound Channel Transmission Loss Model, 428

Arctic Propagation, 429

Transmission Loss Models for Shallow Water, 429

AMBIENT NOISE, 430

SCA'I~ERING AND REVERBERATION LEVEL, 434

TARGET STRENGTH, 439

RADIATED NOISE LEVELS, 440

SELF NOISE LEVELS, 443

Sources of Self Noise, 443

Flow Noise, 446

DETECTION THRESHOLD, 447

UNDERWATER ACOUSTIC APPLICATIONS, 449

Seismic Exploration, 449

Analysis of Seismic Reflection Data, 450

Acoustic Position Reference System for Offshore Dynamic Positioning, 452

Short Baseline System, 455

Acoustic Depth Sounders, 457

Side-Scan Sonar, 459

Subbottom Profiling, 465

Acoustic Positioning and Navigation, 466

Acoustic Doppler Measurements, 467

REFERENCES, 468

Introduction

Early History

In the 15th century, Leonardo da Vinci stated that if a ship is stopped and a person places one end of a long tube in the water and places the other end to the ear, then the person can hear other ships at a great distance. Placing a second tube similarly to the other ear provided the opportunity to estimate the direction to the ship. The first mathematical treatment of sound theory was completed by Newton in 1687, and it related the propagation of sound in fluids to physical properties of density and elasticity. Bernoulli, Euler, LaGrange, d'Alembert, and Fourier all contributed to the theory of sound during the 18th and 19th centuries. In 1827, Colladon and Sturm measured the speed of sound in water using a light flash coupled with the sounding of an underwater bell to obtain 4707 ft/s at 8~ Rayleigh

384 Offshore Engineering

published his famous "Theory of Sound" in 1877, and it is republished as Strutt (1945). The magnetostrictive and piezoelectric effects, discovered respectively by Joule in 1840 and Curie in 1880, are used to produce transducers that generate and receive underwater sound. Fessenden developed the first high powered underwater sound source in 1912 and later developed the first commercial application for an underwater acoustic device in which a foghorn and underwater bell were used to determine distance from shore. He also designed a moving coil transducer, called the Fessenden oscillator, for echo ranging.

During World War I (1914-18), a system of underwater echo-ranging was developed under the acronym ASDIC (Allied Submarine Devices Investigation Committee). The principle of echo-ranging was that a pulse of sound was transmitted into the water, and any reflection (echo) from a submarine was received by a hydrophone. The received signal was heard on headphones, and the time delay between transmission and reception was used as a measure of the range of the submarine. If sound transmission could be made directional, then target directions could be determined. In the United States, Hayes pioneered the field of passive sonar arrays at the New London Experiment Station, currently the New London Division of the Naval Underwater Warfare Center (NUWC), in New London, Connecticut. In the United States, the term ASDIC was replaced by SONAR, which is an acronym for Sound Navigation and Ranging. Langevin used the piezoelectric effect in underwater sound equipment to detect submarine echoes at distances as great as 1500 m.

In 1925, the Submarine Signal Company coined the word fathometer, a trade- mark of the Raytheon Company, that was an acoustic device used by ships in the US and Great Britain for depth sounding. Adequate sonar systems were developed and produced in US in 1935, and US ships were equipped with underwater listening and echo ranging equipment. In 1937, Spilhaus invented the bathythermograph that measures the temperature versus depth of water. This device was installed on all submarines to measure the temperature profile of the ocean to assist in the determination of characteristics of sound propagation and sonar detection. Surface vessels were equipped in 1938 with echo ranging equipment and operators searched in bearing with headphones and a loudspeaker. Submarines were equipped with line hydrophone arrays with headphones for listening.

After WWlI, underwater sound applications greatly expanded. Signal processing developments have been greatly advanced and target noise has been greatly reduced. Some underwater acoustic applications since then are:

�9 Fishing aids (locating commercial fish). �9 Ocean engineering/oceanography (telemetry of data, acoustic Doppler cur-

rent meter, acoustic release mechanism, vertical echo sounders, dynamic positioning systems).

�9 Geophysical research (oil exploration).


�9 Underwater communications (surface ships, submarines, divers, remotely operated vehicles).

�9 Navigation (depth sounders, beacons, transponders, acoustic speedometers, upward-looking depth sounders for navigating under ice).

�9 Underwater search and hydrographic surveying (side scan sonar, subbottom profilers, depth sounders).

�9 Coastal processes and Dredging (sediment thickness and characteristics, acoustic flow meters).

�9 Acoustic tracking ranges (surface ships, submarines, torpedoes).

Sonar systems that occur in nature are found in porpoises, whales, and bats for navigation. Porpoises and bats also use their natural sonar capability for search, detection, and localization of food sources. A valuable source of reference texts have been developed [ 1, 5, 7, 8, 13, 16, 17, 19, 24, 29, 37, 38, 40--43, 50].

Underwater Acoustic System Categories

Underwater acoustic systems can be divided into four categories such as active sonar systems, seismic systems, underwater communications and navigation systems, and passive systems. Examples of these systems are

1. Active Sonar Systems

�9 Active echo ranging sonar is used by ships, submarines, helicopter, fixed underwater installations, and sonobuoys to locate submarine targets. These sonars use a short pulse of sound that is transmitted into the water by a sound projector (transducer). For reception, the same transducer or a second transducer is used as a hydrophone to receive the returning sound signal (echo). Fixed transducer arrays such as line, conformal, cylindrical, and spherical are used as well as towed line arrays.

�9 Torpedoes use moderately high frequencies to echo range on targets and then steer on reflected signals.

�9 Depth sounders send short pulses downward and time the bottom return. �9 Side-scan sonars are used for mapping ocean terrain at fight angles to a

ship' s track. �9 Subbottom profilers are used for showing features of the ocean subbottom

directly beneath the ship's track. Frequently, the transducers for side-scan and subbottom sonars are contained together in a hydrodynamical ly designed tow body to collect seafloor and subbottom information simultaneously.

�9 Fish finding aids are forward or side looking active sonars for spotting fish schools. These sonars may also use multiple beams.

�9 Diver hand held sonars are for diver location of underwater objects.


�9 Position marking beacons transmit sound signals repeatedly. �9 Position marking transponders transmit sound only when interrogated. �9 Acoustic flow meters and wave height sensors are used to measure flow

rate and wave height, respectively. Acoustic Doppler current profilers (ADCP) measure ocean currents.

�9 Fluid levels in tanks are frequently measured using active sonar systems. �9 Sonobuoy is a floating buoy that is equipped to send and receive acoustic

signals. It is used as the link between an aircraft and underwater explosive source when used to track submarines.

2. Seismic Systems

�9 Seismic profilers are used to explore the ocean subbottom, or sub-floor. The acoustic pulses used are basically unidirectional pressure pulses that are generated by explosive charges, underwater arcs (sparkers), com- pressed air release (air guns), and electromagnetic devices (thumpers). These seismic devices produce results that show the geological features of the ocean floor.

3. Underwater Communications and Telemetry Systems and Navigation

�9 Underwater telephone is a device used to communicate between a surface ship and a submarine or between two submarines.

�9 Diver communications use a full face mask that allows the diver to speak normally underwater and a throat microphone to acquire speech signals. A transducer is used to transmit the signal. The same transducer is used to receive, and the signal is passed to the diver via an ear piece.

�9 Telemetry systems transmit data from a submerged instrument to the surface. �9 Doppler navigation uses a pair of transducers pointing obliquely down-

ward to obtain speed over the bottom from the Doppler shift of the bottom returns. A pulsed Doppler system uses only a single transducer.

�9 Acoustic tracking ranges are used for tracking submarines, surface ships, and torpedoes.

4. Passive Systems

�9 Passive sonars use a hydrophone array that detects acoustic radiation from another vessel or object (e.g., line, conformal, cylindrical, and spherical hydrophone arrays and towed arrays used by submarines).

�9 Acoustic mines explode when the received acoustic radiation reaches a certain value.

�9 Torpedoes home on acoustic radiation of a submarine or ship.


Underwater Sound Fundamentals

Sound is the small amplitude periodic variation in pressure, particle displacement, and particle velocity in an elastic medium. Sound is produced by mechanical vibration and the energy from the vibrating source is normally transmitted as a longitudinal wave (to and fro motion). Sound waves are longitudinal waves, because the molecules transmitting the wave move back and forth in the direction of propagation of the wave, producing alternate regions of compression and rarefaction. The main reason acoustic waves are used in underwater detection and communications is that electromagnetic waves do not propagate for long distances in water except at very long wavelengths. At these long wavelengths, the waves are not useful for most underwater search purposes, but long wavelength electromagnetic waves are used in communication systems.

Transmission of sound waves is very complicated, so plane waves of sound are studied, and these are the simplest type of wave motion propagated through a fluid medium. For a plane wave, the acoustic pressures, particle displacement, and density changes have common phases and amplitudes at all points on any given plane perpendicular to the direction of wave propagation. Plane waves are easily produced in a rigid pipe with a vibrating piston. In a homogeneous medium, plane wave characteristics are attained at large distances from their source.

The term particle of the medium is understood to mean a volume element large enough to contain millions of molecules so that it may be considered a continuous fluid, yet small enough so that the acoustic variables of pressure, density, and velocity can be considered as constant throughout the volume element. For the case of a plane wave of sound, the acoustic pressure (p) is related to the particle velocity (u) by

p=pcu (1)

where p - pressure p = density c = propagation velocity of the plane wave

pc = called the specific acoustic resistance u = particle velocity

The specific acoustic resistance for seawater is 1.5 x 105 g/cm2s and for air is 42 g/cm2s. This equation is also known as Ohm's Law for acoustics.

The energy involved in propagating acoustic waves through a fluid medium is kinetic energy due to the particle motion and potential energy resulting from the stresses in the elastic medium. For a plane wave, the acoustic intensity (I) of a sound wave is the average rate of flow of energy through a unit area normal to the direction of wave propagation. The average intensity is


~2 I = ~ ( 2 )

pc where P2 = time average of the instantaneous acoustic pressure squared

If the units of pressure (p) are gtPa (1 BPa = 10 -5 dynes/cm2), density (p) are gm/cm 3, wave propagation velocity (c) are cm/s, then the units of intensity are ergs/cmZ-s. Intensity is commonly expressed in units of W/cm 2, which is also power per unit area, where one watt is equal to 107 ergs/s, and then the expression for intensity is

p2 I = ~ x 1 0 -7 ( 3 )

pc

For transient signals, the energy flux density (E) in W-s/cm 2 is a useful term, and it is the integral of the instantaneous intensity.

f ~ ~o p--~-2 E = dt = pc dt (4)

Spectrum level refers to the level of a sound wave in a frequency band 1 Hz wide, and the band level refers to a level in a frequency band greater than 1 Hz wide. The units of frequency are hertz (Hz), which is defined as 1 cycle per second (Hz = s-l).

D e c i b e l S c a l e s

In practice it is common to describe sound intensities and pressures using logarithmic scales known as sound levels. Two reasons for using logarithmic scales are the very wide range of sound pressures and intensities encountered in the ocean and the fact that the human ear subjectively judges the relative loudness of two sounds by the ratio of their intensities. The most generally used logarithmic scale for describing sound levels is the decibel scale. The intensity level (N) of a sound of intensity I 1 is defined by

N = 10 log ~I 1 (5) I2

where 12 is the reference intensity. Also used is the sound pressure level that is defined as

N = 20 log Pl (6) P2


where P2 is the reference pressure. The reference level must be known to ensure proper interpretation of the decibel (dB) value. Previous reference pressures are 1 dyne/cm 2 and 0.0002 dyne/cm 2, and the latter reference pressure (0.0002 dyne/cm 2) is the threshold of hearing for humans. The current reference pressure is (1 ktPa) where 1 ktPa is equal to 10 -5 dyne/cm 2. Also, 1 Pascal is equal to 1 psi multiplied by 6895. It is often necessary to convert from one reference (P2) to another (P3)- An expression for converting a sound pressure level referenced to an acoustic reference pressure (P2) to a level with a new reference pressure (P3) is

Np3 = Np2 + 20 log P___L2 (7) P3

For example, it is desired to express 125 dB relative to 0.0002 dyne/cm 2 (P2) in dB relative to 1 dyne/cm 2 (P3)" Using Equation 7, the new sound level is determined as

= 1 2 5 + 20 log ~0"0002 =125 - 74 = 51 dB rel dyne/cm e (8) Np3 1

If the 125 dB is expressed relative to the current reference pressure of 1 ktPa, the result is 151 dB re 1 ~tPa.

The level of a sound wave is the number of decibels by which its intensity, or energy flux density, differs from the intensity of the reference sound wave. For clarity the level should be written as "N dB re 1 ktPa" that means the sound level in decibels relative to the intensity of a plane wave of acoustic pressure equal to 1 micropascal.

Sonar Equations

The sonar equations are a means for determining the effects of the medium (ocean), the target, and the sonar equipment. These equations are one of the design and prediction tools available to the engineer for underwater sound applications. The practical uses of the sonar equations are (1) prediction of sonar equipment performance and (2) sonar design.

The total acoustic field at a receiver is defined as a desired portion (signal) and undesired portion (background). The background is the noise or reverberation (back scattering of output signal). The objective of the design engineer is to find a means for increasing the overall response of the sonar system to the signal and decreasing the response to the background. A sonar system is just accom- plishing its purpose when the signal level exceeds the background level by an amount sufficient enough for the observer to distinguish the signal from the noise. The sonar parameters are defined in relation to the equipment, medium, and target as tabulated in Table 1.


Table 1 Classification of Sonar Parameters

Equipment related parameters

Medium related parameters

Target related parameters

Projector source level Noise level Receiving directivity index Detection threshold Transmission loss Reverberation level Ambient noise level Target strength Target source level

(SL) (NL) (DI) (DT) (TL) (RL) (NL) (TS) (SL)

Active Sonar Equation (Noise Limited)

To describe the meaning of the sonar parameters, consider the example of an active sonar (Figure 1). The sound source produces a level of SL dB at a reference distance (e.g. 1 yd or 1 m), and it acts as the receiver as well. The radiated sound signal is reduced by the transmission loss when it reaches the target. The level at the target is then SL - TL. As a result of reflection and scattering by the target whose target strength is TS, the reflected or backscattered level is SL - TL + TS at a distance of 1 yd from the acoustic center of the target in the direction back toward the source. In traveling back, the level is again attenuated due to transmission loss and consequently, the level on return to the receiver is SL - 2TL + TS. If the ambient background noise (NL) is isotropic, then the background noise level is reduced by the directivity index (DI), and the relative noise level is NL - DI. When the noise level is not isotropic, the directivity index is replaced by the array gain (AG), which is discussed later. Therefore, the signal to noise ratio is SL - 2TL + TS - (NL - DI). Generally, detection is the purpose of the sonar, so some means of determining when the target is present is needed. A detection threshold (DT) is established such that when the signal to noise ratio is above the DT then a decision is made either by a person or the electronics that a target has been detected. The active sonar equation, Equation 9, is now written as an equality in terms of the detection threshold as

SL - 2TL + TS = NL - DI + DT (9)

This equation applies to a monostatic sonar that means the source and receiver are coincident and the target return is back toward the source. A bistatic sonar has the source and receiver separated or in different locations, and therefore the transmission loss (TL) values from source to target and target to receiver are not always the same.

Detection Threshold (DT)

Directivity Index (DI) or

Array Gain (AG)

Noise Level (NL)

Electronics

Headphones

Source Level (SL) at 1 yd

(TS)

One-way Transmission Loss (TL)


Figure 1. Definition of sonar parameters for active sonar equation.

Active Sonar Equation (Reverberation Limited)

A modification of the active sonar equation is necessary when the background is reverberation instead of noise. In this case DI is not correct as defined for noise. For reverberation background, the term in Equation 9 (NL - DI) is replaced by an equivalent reverberation level RL. An increase in system performance can not be achieved by raising the source level further once the system reaches its reverberation limit. This is in contrast to the noise limited case where increases in source level produce corresponding increases in performance. The reverberation limited active sonar equation then is

SL - 2TL + TS = RL + DT (10)

Passive Sonar Equation

In the case of a passive system, the target itself produces the signal by which it is detected. Therefore, the source level parameter refers to the level of the radiated signal of the target at the distance of 1 yd, or 1 m. Also, the target strength (TS) parameter is no longer meaningful. Again, the directivity index is replaced by the array gain (AG) when the noise level is not isotropic and if AG is known. The transmission loss only occurs from the target to the receiver. Thus, the passive sonar equation is


SL - TL = N L - DI + DT (11)

Table 2 contains definitions of sonar parameters. The performance figure (SL - ( N L - DI) is the difference between the source level and the noise level measured at the receiver. The Figure of Merit (SL - (NL - DI + DT)) is the maximum allowable transmission loss in passive sonars, or the maximum allowable two-way loss for active sonars when TS is 0 dB. When the detection threshold (DT) is zero, then the sonar equations are a statement of the equality between the desired part of the acoustic field (signal---echo or noise from target) and the undesired part (background of noise or reverberation). This equality holds at only one range in most cases. Echo and reverberation decrease with range, and noise is usually a constant.

Transient Form of the Sonar Equations

Previous sonar equations were written in terms of the average acoustic power per unit area of the sound emitted by the source or received from the target. Average implies a time interval. The time interval causes uncertain results whenever short transient signals are used or whenever severe distortion is present due to scattering from the target. A more general approach is to write equa-

Table 2 Summary of Sonar Parameter Definitions [43]

Parameter Name Symbol Reference Definition

source intensity Source Level SL 1 yd from source 10 log on acoustic axis reference intensity *

Transmission Loss TL 1 yd from source and at target

signal intensity at lyd

10 log signal intensity at target or receiver

echo intensity at 1 yd from target Target Strength TS 1 yd from acoustic 10 log center of target incident intensity

noise intensity Noise Level NL At transducer 10 log location reference intensity *

Receiving DI At transducer t0 log Directivity Index terminals

noise power generated by equivalent

nondirectional transducer

noise power generated by actual transducer

Reverberation At transducer 10 log

Level RL terminals reverberation power at transducer terminals

power generated by signal of reference intensity

At transducer Detection Threshold DT terminals 10 log

signal power to just make decision

noise power at transducer terminals

*Reference intensity is that of a plane wave with rms pressure of 1 ~tPa.


tions in terms of energy flux density (E) that is the acoustic energy per unit area of wave front.

o o if E = pc p2(t)dt (12)

o

The intensity (I) is the mean square pressure of the wave divided by the specific acoustic resistance and averaged over a time interval (T).

I = 1 i p2(t____~) dt (13) T .I pc

0

For long-pulse sonars, T is the duration of the emitted pulse and is nearly equal to echo duration. For short-pulse sonars, the duration of the echo is vastly different from the emitted pulse, and it can be shown that the intensity form of the sonar equations can be used if the source level is defined as

SL = 10 log E - 10 log x e (14)

where x e is the duration of echo of source at 1 yd and measured in energy flux density units of a 1 l.tPa plane wave over an interval of 1 s. For pulsed sonars emitting a flat topped pulse of constant source level (SL') over a time interval x o, and because energy density is the product of average intensity times duration, then the energy flux density (E) may be expressed as

10 log E = SL' + 101ogx e (15)

By combining Equations 14 and 15, an equation for the source level of pulsed sonars is

SL = SL' + 10 log a:o/a: e (16)

For long-pulsed sonars, x o is equal to x e and SL and SL' are identical. For short- pulsed sonars, x e is greater than x o. For active short-pulse sonars (Figure 2), echo duration x e is a parameter in its own fight. The echo duration (Xe) consists of three components that include duration of emitted pulse at source (x0), additional duration caused by two way propagation (Xm), additional duration caused by the target (xt). Thus, the echo duration is

"1; e = I; 0 -t- "gm + "l;t (17)

Typical examples of the three components of an echo duration are tabulated in Table 3.

The sonar equations have several limitations. These include the requirement to correct the source level for short pulse sonars. Correlation sonars must account


short pulse near source

1 . , . .

_ ~ ~ m ~ ~ l ~ Bear target

~o + 1; m

i , ~ _ , J ,, , ,

, . . ,

echo

Figure 2. Characteristics of echo duration for short pulse sonars.

Table 3 Examples of the Components of Echo Duration [43]

Duration of the emitted pulse at short ranges (xo)

Duration produced by multipaths ('lim)

Duration produced by submarine target (xt)

Explosives: 0.1 ms SONAR: 100 ms Deep Water: 1 ms Shallow Water: 100 ms Beam Aspect: 10 ms Bow-stern : 100 ms

for correlation loss. Additional limitations are related to the medium being inhomogeneous, having irregular boundaries, and the fact that one boundary is in motion. In addition, some of the sonar parameters fluctuate randomly with time. There are also unknown changes in equipment and platform conditions. There- fore, the sonar equations yield a time averaged result of a stochastic problem.

Properties of Transducer Arrays

Underwater sound equipment provides the means to detect the existence of an underwater sound wave. This equipment consists of a hydrophone array that converts acoustic energy into electrical energy and this energy is then fed into a signal processing unit to display it. Transducers are devices that convert sound and electrical energy into each other. Hydrophones are transducers that convert sound into electrical energy. A projector is a transducer that converts electrical


energy into sound energy. The conversion of sound into electrical energy and vice versa is accomplished with the use of materials that have certain properties.

Piezoelectric materials such as quartz, ammonium dihydrogen phosphate (ADP), and Rochelle salt acquire a charge between the crystal surfaces when placed under pressure, and conversely they acquire a stress when a voltage is placed across the surfaces. For example, the electrical potential across a piezoelectric material may be varied periodically at the frequency of a desired sound signal, and as a result, the material vibrates at the desired frequency. Elec- trostrictive materials have the same effect as piezoelectric materials. However, these materials are ceramics that have been properly polarized. Examples are barium titanate and lead zirconate. Magnetostrictive material changes dimensions when it is subjected to a magnetic field, and conversely its magnetic field is changed when it is stressed.

The design of transducers is an art and is a special technology in its own right. Some research and measurement activities use single elements of piezoelectric or magnetostrictive material as hydrophones. In most other cases, hydrophone arrays are used that consist of a number of elements spaced in a particular way. Arrays have the advantages of being more sensitive, possessing directional properties, and having a greater signal to noise ratio than "small" single elements or elements the size of those used in the array. A large single element the size of the array has the same beamwidth characteristics as the array, but it must be mechanically steered.

Array Gain

One of the important advantages of using a hydrophone array is the improvement of signal to noise ratio. The improvement of signal to noise ratio is measured by the array gain (AG)

(S / N)array (18) AG = 10 log (S / N)element

One approach to evaluating AG is to consider the directional patterns of the signal [S(0,~)] andjnoise [N(0,~)] fields along with the beam pattern of the array as expressed in the following equation

f S(O, r b (0, r dn / J" N(O, r b (0, r

AG = 10 log 4g t' /'4~ (19) df~

4x 4n

Each integral in the numerator is the directional pattern of signal or noise weighted or multiplied by the beam pattern and integrated over all solid angle (t2).


The second approach considers the coherence of signal and noise across the dimensions of the array. Coherence is the degree of similarity of either the signal waveform or the noise wave form between any two elements of the array. The coherence is measured by the cross correlation coefficient (p) of the outputs of the different elements of the array.

Z Z ( P s ) i j

i j (20) AG = 10 l~ Z Z ( P n ) i j

i j

For amplitude shading

ZZaiaj (Ps) i j i j

A G = 1 0 l o g Z Z a i a j ( P n ) i j

i j

(21)

where Ps and Pn are the cross correlation coefficients of signal and noise respectively. The term a i is the root mean square (rms) voltage produced by the ith element due to signal or noise. Expressions for Ps and Pn are tabulated in Table 4.

When both the signal and noise are completely coherent across an array, there is no array gain (AG = 0). If the signal and noise are completely incoherent across an array, then the array is unable to distinguish between signal and noise. For a perfectly coherent signal in incoherent noise, then

(Pn)ij = 0 where i ~ j and (Pn)ij = 1 when i = j

and

(22)

AG = 10 log n (23)

where n is the number of elements. For a perfectly coherent signal in only par- tially coherent noise, then

(Pn)ij = p i ~ j and (Pn)ij =1 i = j (24)

and

n AG = 10 log (25)

l + ( n - 1 ) p

The gain of an array depends on the statistics of the desired and undesired por- tions of the sound field in which the array operates.


Table 4 Expressions for Cross Correlation Coefficients [43]

Signal, Ps Isotropic Noise, Pn

Single frequency, cos (tyt w sin(cod) no time delay \ c )

cod c

Single frequency, cos t.0(x w + x e) time delay sin( )

cod c

COS CO "C e

Note: co = 2x (frequency) x w = signal travel time between array

elements = (d/c)cos 0

d = array element separation

x e = electrical (steering delay) 0 = the angle to the line joining the

two elements c = sound velocity

Receiving Directivity Index

When a signal is a unidirectional plane wave (perfectly coherent) and when the noise is isotropic (same in all directions, N(0,t~) = 1) then the array gain reduces to the quantity called directivity index.

5 df2 47c

AG = DI = 4/ t - 10 log 2n n/2 (26)

I b ( O ' * ) d " f ~ b (O,t~)cosOdO df~ 4 x

0 - ~ / 2

If the beam pattern has rotational symmetry and is nondirectional in the plane in which t~ is determined, then

4 ~ DI = 10 log x / 2 (27)

2r~ ~ b(O) cos 0 dO

- x / 2

For simple arrays (line and circular plane) the directivity index can be computed using expressions tabulated in Table 5.

The directivity index (DI) is restricted to the special case of a perfectly coherent signal in isotropic noise, but these conditions seldom occur in the real ocean.


Table 5 Mathematical Expressions for Directivity Index of Simple Transducers [43]

Transducer Type Beam Pattern

Function [b(O)] Directivity Index (DI)

Continuous line with length L, where L >>

Piston with diameter D in infinite baffle where D >> ~,.

sin ( - ~ ) sin012 10 log ( ~ )

( -~1 sin0

sinO

Line array with "n" elements equally spaced a distance "d" apart.

Two element line array spaced "d" apart sin sin 0]

2 sin ( -~) sinO

10 log

10 log

l+- - n

p=l

,n ~ / 2p~d

1+ sin( /

2~d

Signals transmitted in the ocean are perfectly coherent only at short ranges, and at long ranges signals are received from various directions and along different paths. Noise is anisotropic in the real ocean. Thus, the directivity index is only useful for approximate calculations and array gain (AG) should replace DI in sonar calculations when the characteristics of signal and noise are known.

Transducer Responses

Normally a hydrophone linearly transforms sound energy into electricity and the proportionality factor for this transformation is called the response. It relates the generated voltage to the acoustic pressure of the sound field. The receiving


response is the number of decibels relative to 1 volt produced by an acoustic pressure of 1 l.tPa and is expressed as N dB re 1V/ll.tPa. For a response o f -80 dB re 1V/ll.tPa, the voltage generated is determined by

V - 8 0 = 20 l o g -

1

logv = - 4 . 0

v = 0.0001 or 10 -4 volts (28)

Thus, the hydrophone generates an rms voltage of 10 -4 volts when placed in a plane wave sound field having an rms pressure of 1 l.tPa. Transmitting current response is the number of decibels relative to 1 micropascal measured at 1 meter (1 yard), produced by 1 amp into the terminals of the projector and is expressed as N dB re 1 ~Pa/A.

For a transmitting response of 100 dB re 1 ktPa/A at 1 m (add 0.78 dB for 1 yd), the acoustic pressure generated at 1 m is determined as follows

20 log p = 100 1

log p = 5

p = 105 kt Pa at lm (29)

Beam Pattern

The response of a transducer array varies with direction relative to the array. This very desirable property of array directionality permits the determination of the direction of arrival of a signal and also facilitates resolution of closely adjacent signals. In addition, directionality reduces noise relative to the signal arriv- ing from other directions. The response of an array varies with direction in a manner specified by the beam pattern of the array. Expressions for simple arrays are tabulated in the previous Table 5.

The beam pattern is

b(O, (~)- V 2 (0, ~) (30)

and response V(0,t~) is normalized such that V(0,0) is equal to one. For hydrophones, b(0,~) is the mean square voltage produced by an array of unit response when sound of unit pressure is incident on it in the direction (0,~). For projectors, b(0,~) is the mean square pressure produced at unit distance when unit current is fed into the projector. The direction of (0 = 0, ~ = 0) is arbitrary, but is usually taken as the direction of maximum response (acoustic axis). Direc- tion for which b(0 = 0, t~ = 0) is called the acoustic axis of the array. Decibels are normally used in describing responses and beam patterns. Arrays can be


steered mechanical ly and electrically. Electrical steering is accomplished by inserting appropriate phasing or time delay networks in each element 's circuitry. Examples of beam patterns are illustrated in Figure 3, and an example calculation is illustrated in Table 6. The significance of the -3 and - 6 dB beamwidths (Figure 4) is that they are the �89 and �88 power points for the system, respectively.

Acoustic Axis

Line Transducer

_ Acoustic Axis

Circular Plane Array

Figure 3. Three dimensional beam patterns for line and circular plane arrays [43].

Table 6 I l lus trat ive Ca lcu la t ion of the B e a m P a t t e r n for a Line A r r a y

Given:

Find:

n = 5, equally spaced line array d = 0.5 ft, c = 5000 ft/s, f = 5 kHz b(O)

Solution" X c 5000 f 5000

lft

b(O) = sin I ( - ~ 3 sin 01 2

n sin [(_~d_) sin ~ =

2 sin/' ~ 1 . _{ sin !7.854 sin ~ l 2

5 sin [(~ 10_~.5) sin 01 5sin (1.571 sin 0)J

For 0 = 0, the value of b(0) in the limit is equal to 1, and therefore 10 log b(0) is 0 dB. A tabular listing of 0 and 10 log b(0) is shown below. The angle 0 must be converted to radians (multiply by re/180) to use in above equation to get results below.

0 (deg)

0 1 5

10

10log b(0) 0 10log b(0) 0 10log b(0) (dB) (deg) (dB) (deg) (dB)

0 15 -6.883 35 -12.05 -0.02613 20 15.30 40 -13.03 -0.6621 25 -24.83 45 -16.55 -2.775 30 13.98 50 -24.96

0 (deg)

60 70 80 90

10 log b(O) (dB)

-19.88 -14.95 -14.04 -13.98

dB


width at -3 dB

acoustic axis

"~--"--elements , , , , _ , . . . .

Figure 4. Definition of the beam width at -3 dB for a line array.

Special Arrays

When an array consists of individual elements that are directional, then the product theorem is used to determine the array beam pattern. This theorem states that the beam pattern of an array of identical equally spaced direct ional hydrophones is the product of the pattern of each hydrophone alone, and the beam pattern of an identical array of nondirectional hydrophones as described in Equation 31.

b n (0, (I)) = V 2 (0, r = b (0, (I)) bnond (0) (31)

Mills Cross is an array of two line transducers in which the outputs are multiplied, or correlated together. When the two line arrays have "n" elements the beam pattern of a Mills Cross array with 2n elements is the same as a rectangular array with n 2 elements. The Mills Cross beam pattern is the same as for a rectangular array on the major axes only, and the beams are much wider than that for a rectangular array everywhere else. Its advantages are that it is light in weight and economic to build. The disadvantages are lower array gain and lower sensitivity.


Shaded Area

m m

3 dIB do~ total l ~ v

o degre

s ~ 7 e 9 =~ zo 30 40 5o 6o7oeo ,oo

I J ~ A m y ke= l~ in w a v e ~

Figure 5. Beam width for a line array with elements spaced L/2 apart for various steering angles to broadside [12].

When the beam pattern of an array of particular geometry is controlled or changed, it is called shading (Figure 6). For amplitude shading, the responses of individual array elements are adjusted to provide the most desirable pattern. The arrays are usually adjusted so that the maximum response is at the center and least response at the ends. Superdirectivity results in very narrow beams and the elements are spaced less than �88 wavelength apart with signs, or polarities, of adjacent elements reversed. Phase shading varies the spacing of array elements, but has not been commonly used. In adaptive beam forming, a null can be placed in the beam pattern to cancel out an undesired signal (noise) in a certain direction.

Previous arrays have been linear and additive. The output is linearly proportional to acoustic pressure, and the outputs are simply added together. In the case of multiplicative or correlative arrays, the outputs are multiplied together. These types of arrays find applications in conditions of high signal-to-noise ratio and when narrow beams or high resolution are needed and when a reduction in size or number of elements over a linear array is necessary.


N a m e Unshaded Two element, end weighted Two element, center weighted Binomial Dolph-Chebyshev

Shad ingFo~ula 1,1,1,1,1,1 1,0,0,0,0,1 0,0,1,1,0,0 0.1,0.5,1,1,0.5,0.1 0.3,0.69,1,1,0.69,0.3

Line Tvoe

. , .

%<.:..~.:

-I0

Ii lira;! ,,-' ',,_ ii,,. !f II l t i , , \ \\1

-4Oo m lO 3O 4O SO r~l ro lio

0 (degrees)

Figure 6. Beam pattems for different shading [43].

gO

Underwater Sound Projector

Active sonars use a projector to generate acoustic energy. The projector normally consists of an array of individual elements that produce a directional beam in a desired direction. Source level (SL) designates the amount of sound radiated by a projector. Transmitting directivity index is the difference between the level of the sound generated by the projector and the level that would be produced by a nondirectional projector radiating the same total amount of acoustic power (Figure 7). Transmitting directivity index is defined as

DI T = 10 log ld (32) Inond

The relation between source level and radiated acoustic power is determined by assuming a nondirectional projector is in a homogeneous, absorption-free medium. At a large distance r, the intensity of the sound emitted by the projector will be I r. For r very large, the plane wave assumption is valid and

f . . . . . . . - . / nondirectional projector

\ \

\ \

/ / /

/ /

/ I

I t !

. . . . . . . . . . J.. I I

\ \ /

/


' Inond N / / , . _

F directional projector

acoustic axis

I d

Figure 7. Comparison of directional and nondirectional sound sources.

2 ir = P_._r_r • 10-7 ( W / c m 2 )

pc

where Pr = rms pressure in dynes/cm 2 9 = density in gm/cm 3 c = velocity of sound in cm/s

(33)

For p = 1 gm/cm 3, c = 1.5 • 105 cm/s, and converting to yards

I r -- 5 . 5 8 X 10 -9 p2 (W/yd z) ( 3 4 )

In the case of a nondirectional projector, this intensity corresponds to a radiated power output of

Pr = 4rt r2Ir = 70 • 10 -9 p2 r 2 (W) (35)

At a distance of 1 yd, the power is

p = 70 • 10 -9 p2 (36)

where Pl = rms pressure at 1 yd in dynes/cm 2 Converting to decibels and recalling that SL is 10 log p~ referenced to 1 ~Pa, then

10 log P = - 171.5 + SL (37)

If the projector is directional, then

SL = 171.5 + 10 log P + DI T (38)

Underwater Acoust ics 4 0 5

which is illustrated in Figure 8. The quantity P is the total acoustic power radiated. In the case of an electroacoustic projector, P is less than the electric power (Pe) input to the projector, and the difference is related to the projector efficiency (1] = Pe/P). The source level is then expressed as

SL = 171.5 + 10 log Pe + 10 log r I + DI T (39)

Typical ranges of shipboard sonar parameters are an acoustic radiated power (P) of 300-50,000 W, a transmitting directivity index (DIT) of 10-30 dB, a source level (SL) of 210-240 dB, and an efficiency (1"1) 20-70%. Limitations of sonar power are due to cavitation and interaction of elements. Cavitation bubbles form on the face of the projector when the power is increased to a certain value. It is also possible to have cavitation several feet, or about one meter, away from the face of the transducer where the beam starts to form. The cavitation threshold may be raised by increasing frequency, decreasing pulse length, or increasing depth. Interaction between sonar elements can also reduce the sonar's power when one element absorbs power from the other.

Explosives as Sound Projectors

Explosive charges of material ranging from a few grains to a few pounds in weight are commonly used as underwater sound sources. When explosive material

230

220

210

- - 1 9 0

180

r,~ 170

J /

f

J J / / j

I / / j

/ I . , i /

=P

/ �9 " j

f /

/ J J

1 1 I I I 1 ] l I I I I I I I 1111

2 5 t0 2O 5O1O0 Acoustic Power Output (W)

/ j r

�9

1 6 0 ' ' ** ' * j =*'* 0.t 0.2 Q5 I t,(XX) t 0 ,000

Figure 8. Source level as a function of acoustic power for different transmitt ing directivity index [43].

4 0 6 Offshore Engineering

is detonated, a pressure wave initiated inside the material propagates into the surrounding medium (Figure 9). The pressure signature of a detonating explosion consists of shock wave and small bubble pulses at short ranges. For long range, the signature is complicated by refraction and multipath-propagation effects in the sea.

The shock wave has a pressure time relationship

t

P = P0 e to (40)

where p = instantaneous pressure at t Po = peak pressure occurring at time t = 0 t o = time constant of the exponential pulse (time to decay to 0.368 Po)"

P0 2.16 • 104 / wl/3 / 1"13 = psi r

(41)

t o 58wl/3( wl/31 --0.22 r

(42)

where w = charge weight (lb) r = range (ft)

pressure

sea surface �9 i ! i i i ii

d e p t h !

, ,f....~.. ,.

gas bubble 6 ( ! \~. .~

h o c k w a v e

[ I 1st 2nd ] r d ~ , p u ~ pulse pulse ~.

, t . . . . . . t . . . . . . . . . J J i ~ ; 0

i

' i / ""~, 0 ". /

" / bubble migrat ion as it , . . . . . . . . . . . .

e x p a n d s and col lapses

�9 ~'= t i m e

F i g u r e 9. Shock wave and bubble migration for explosive source.


Values for Po and t o are plotted in Figure 10 and for a 1 lb TNT charge. Bubble pulses are the series of positive pressure pulses emitted by the pulsat-

ing gas globe at the instant of minimum volume. The amplitude of the pulse decreases progressively as the energy is dissipated. The time interval T(s) between the shock wave and the first bubble pulse is

Kw 1/3 T = (43)

(d + 33) 5/6

where K is a proportionality constant, w is the charge weight (lb), and d is the depth of detonation below sea level (ft). The constant (K) depends on type of explosive (e.g. K is 4.36 for TNT). Advantages of explosive sound sources include being very mobile, easily launched, detonated at any depth, nondirectional, and a short high power broad band pulse. The disadvantages are that explosive sound sources are not very repeatable, the processing of the received signal is difficult because of its short duration, and reverberation can occur. Explosive sources are used for research, antisubmarine warfare (ASW), and seismic profiling.

10 e

e | :

t 0 6 _

] -

�9 1 0 ~

=')

1 I I J I I I I I , I I l = = = = = = I ==~=

2 3456e,0 20 5o ,00 200 soo

i t t~e, r (yd)

Z 4 0

e !

1 22o

! 200

Figure 10. Peak pressure and for I Ib charge of TNT [3].


' ~ 1,000

1 I00

1

74

l 1 1 I I l l 1 | I 1 l I 1 1 I I I I 1 1 1 1 I

~0 tO0 ~,000

Range, r (yd)

Figure 11. Time constant for I Ib explosive charge of TNT [3].

Underwater Sound Propagation

The flow of acoustic energy from a source to a receiver is described in terms of its intensity at a reference distance such as 1 yd, or 1 m, from the source and the reduction in intensity between this point and the receiver. The transmission (propagation) loss is the reduction in intensity between the reference point and receiver. Transmission (propagation) loss is affected by spreading and attenuation. S.preading is the result of acoustic energy becoming diluted as it spreads over a larger area, and thus intensity is reduced. Near the source, spreading is spherical and the intensity reduction is proportional to the inverse square of the distance. At larger distances the spreading is affected by refraction (bending of rays along paths that the waves travel). Attenuation is the loss of energy from the sound wave as a result of absorption and scattering. Absorption is caused by the conversion of acoustic energy into heat (frictional effects). Scattering is the process whereby objects in the medium cause some of the energy to be deflected in various directions.

Absorption is dependent on the acoustic frequency and is very severe at high frequencies. Included in the scattering losses is the loss of energy resulting from reflection at the bottom and surface of the ocean. This loss is due in part to the scattering of sound in other directions and to transmission of energy to the adjoining medium. Scattering is a function of sea state, but surface losses are usually small (1 dB). Bottom losses can be severe (20 dB) and are strongly


affected by the nature of the bottom. Hard bottoms are good reflectors and soft bottoms are poor reflectors.

Spreading Laws

Spherical Spreading. For spherical spreading, consider a source located in a homogeneous, unbounded, and lossless medium as shown in Figure 12. Then, the power (P) generated by the source is radiated equally in all directions so as to be distributed over the entire surface of a sphere surrounding the source.

Because power equals intensity times area, then

P = 4~;q 2 11 = 4~;r~ 12 = .... (44)

If r 2 is expressed in yards and r 1 is taken as 1 yd, then Equation 44 reduces to the inverse square law

I 2 = 1 (45)

or the transmission loss is expressed as

TL = 10 log I-L1 = 10 log r 2 (46) 12

which is called the spherical spreading law. This law shows that the intensity decreases as the square of the range, and the transmission loss (TL) increases as the square of the range.

Cylindrical Spreading. Spreading that occurs in a medium between two parallel planes and at a certain range from a source is called cylindrical spreading. In this case, the power (P) is radiated over a cylindrical surface and is expressed as

P = 2r~qHI 1 = 27~r2HI 2 = ... (47)

r

[ ~ r . ) . -~ ~ "-I~ power (p)

~ ~ - - 4 g q2

unbounded medium

Figure 12. Schematic of spherical spreading.


[ ~ ~ ' ~ : ~ medium between IH ~ 2xrlH twO parallel planes

Figure 13. Schematic of cylindrical spreading.

If r 2 is set to 1 yd, then

P

2r~qH TL = 10 log I-L = 10 log = 10 log r 2 (48)

12 P

2r~reH

which is called the cylindrical spreading law. Cylindrical spreading occurs at moderate and long ranges whenever sound is trapped by a sound channel.

No spreading occurs for propagation in a lossless tube or pipe of constant cross section. The area over which the power is radiated is constant, and therefore the intensity and TL are independent of range. For time stretching (hyperspherical spreading), the signal from a pulsed source is spread out in time due to multipath propagation as the pulse propagates through the ocean, especially in areas such as the deep ocean sound channel. A summary of these spreading laws is tabulated in Table 7.

Absorption of Sound in the Sea

The loss of sound intensity in the sea due to absorption is the result of the conversion of acoustic energy into heat (frictional) as sound propagates through the medium. The loss of intensity for a plane wave propagating in the horizontal (x) direction may be written as

Table 7 Summary of Spreading Laws [43]

Intensity Varies Transmission Type as Range (r) Loss (dB) Propagation

No spreading r ~ 0 Cylindrical r -1 10 log r Spherical r -2 20 log r Hyperspherical r -3 30 log r

Tube Between parallel planes Unbounded Unbounded with time stretching


dI = - nIdx (49)

where n is a proportionality constant and the negative sign indicates dI is a decrease in intensity. Solving the differential equation by separation of variables yields

dI = - ndx (50)

I

Integrating yields

l n ( ~ 2 ) = - n(r2 - r l) (51)

which can be reduced to

10 log 12 = 10 log I 1 - 10n(r 2 - r 1) l og e (52)

Now, let ~ be (10 n log e), and then

10log/i ): rl) where o~ is the logarithmic absorption coefficient expressed in dB/kiloyard

The absorption of sound is due to viscosity of pure water and the presence of dissolved salts in the water whose effect is dominant in seawater when the frequency is below 100 kHz. Francois and Garrison [15] presented a relationship for evaluating absorption that considers the sum of the effects of boric acid, magnesium sulfate and pure water. The expression for sound absorption (a) is

B1Dlfl f2 B2D2f2 f2 0~ = f2 +f2 + f2 + f2 + B3D3 f2 (54)

where f is frequency in kHz, fl and f2 are relaxation frequencies in kHz, and ct is the absorption coefficient in dB/km (multiply by 1.0936 to get dB/kyd). The first term of Equation 54 represents the effect of boric acid in seawater, and the equations for evaluating the coefficients B 1, D1, and fl are

8.86 x 10 (0"78pH- 5) B 1 = C D 1 =1

(S ~0.5 (4 1245 / fl = 2 . 8 \ - ~ j 10 - ~ J

c = 1412 + 3.21T + 1.19S + 0 .0167d (55)


where c is sound speed in m/s, T is temperature in ~ S is salinity in parts per thousand (0/00), and d is depth in m. The second term in Equation 54 accounts for the effects of magnesium sulfate, MgSO 4, in seawater and the coefficients B 2, D 2, and f2 are determined from

21.44S B 2 = ~ ( 1 + 0.025T)

c D 2 = 1-1.37 x 10-4 d + 6.2 x 10 -9 d 2

(8-1990 / 8.17x10 273~-TJ

f2 = 1 + 0.0018(S- 35)

(56)

The third term represents the contribution of pure water to absorption, and the coefficients B 3 and D 3 are evaluated using

D 3 = 1 - 3.83 • 10 -5 d + 4.9 x 10 -1~ d 2

forT < 20~

B 3 = 4.937 x 10 -4 - 2 . 5 9 x 10 -5 T+9.11 x 10 -7 T 2 -1 .50 x 10 -8 T 3

for T > 20~

B 3 = 3.964 • 10 -4 - 1.146 x 10 -5 T + 1.45 x 10 -7 T 2 - 6.5 x 10 -l~ T 3 (57)

Figure 14 developed by Francois and Garrison [15] shows the variation of the absorption coefficient (ix) as a function of frequency from 0.1 to 1000 kHz at zero depth (surface) for a salinity of 35 o/oo and pH of 8.0. The accuracy of the predicted absorption coefficients is estimated by the developers as _+5% for the ranges of 0.4 to 1000 kHz, -1.8 to 30~ and 30 to 35 o/oo.

Spherical Spreading and Absorption

Propagation measurements made in the ocean indicate that spherical spreading together with absorption yields a reasonable approximation to measured data for a wide variety of conditions. Therefore, transmission loss may be expressed by

TL = 20 logr + t~(r x 10 -3) (58)

where r is the range in yards and ct is the absorption coefficient in dB/kyd. The procedures and results for evaluating the absorption coefficient and transmission loss using Equation 58 are tabulated in Table 8 using the following example. Consider an active sound source operating at a frequency of 50 kHz and located at a depth of 4,000 ft where the temperature is 8~ pH is 8, and salinity is 30 o/oo. It is desired to detect a target at a range of at least 4,000 yd. If the major causes of transmission loss are spherical spreading and absorption, predict the magnitude of the two way transmission loss.


I 0 0 0

I00

I0

Temperature ('C)

Seawater / / / ////// s=ss oIoo/ / II/Pure w ~ r

o.o,~ o / ~ / , o / / / e q ~ = o ,, , (mrr=~)

oDo( 0.1 I I 0 I 0 0 I O 0 0

Freqae~y (kHz)

Figure 14. Absorption coefficient and correction for depth over useful sonar frequency range for salinity of 35 o/oo and pH of 8 [15].

Speed of S o u n d in the Sea

The speed of sound in water has been determined both theoretically and experimentally. One equation is that developed by Leroy [23]:

c = 1492.9 + 3 ( T - 1 0 ) - 6 x 10 -3 (T-10)2 - 4 x 10 -2 ( T - 18) 2

+ 1 . 2 ( S - 3 5 ) - 10 -2 (T - 1 8 ) ( S - 35) + d /61 (59)

Another more recent sound speed equation is that developed by Mackensie [26]:

c=1448.96 + 4 .591T- 5.304 • 10 -2 T 2 + 2.374 x 10-4T 3 + 1.340 (S - 3 5 )

+ 1.630 • 10-2d + 1.675 x 10 -7 d 2

- 1.025 x 10-2T ( S - 3 5 ) - 7.39 • 10-13Td 3 (60)

(continued on page 415)


Table 8 Illustrative Example for Evaluating Transmission Loss in the Ocean

Given: f = 50 ld-Iz r = 4, 000 yd pH = 8

d = 4 , 0 0 0 f i T = 8 ~ S = 3 0 o / o o

Find: Two way transmission loss (2 x TL)

Soln: TL = 20 log r + tx r x 10 -3

Use Equation 12 to evaluate coefficients for first term of Equation 11

c = 1412 + 3.21 (8~ + 1.19 (300 / oo) + 0.0167 (4000 ft / 3.28 ft / m) = 1493.7 m / s

8.86 x 10 (~ (pH)- 5) 8.86 x 10 (0.78(8)-5) B 1 = = = 0.1031 dB / (km - kHz)

c 1493.7

D 1 =1

1245 ) ( 30 /0 . 5 1245 ) 014- 1014 fl = 2.8 k , - ~ j 1 =2.8k,-~) = 0.962 kHz

Using Equation 13 to obtain coefficients in term 2 of Equation 11

B 2 = 2 1 . 4 4 S ( 1 + 0 . 0 2 5 T ) 21.44 3 0 o / o o c 1493.7 m ! s

(1 + 0.025 (8~ = 0.517 dB / ( k m - kHz)

02 :l_l.37x,0 d+6.2x,0_9d2_1_1.37x10 / ( )2 + 6.2 x 10 -9 = 0.5512 3.28 ft / m 3.28 ft / m

1990 ] 8.17 x 10 8- 27---3-~+T)

f2 = 1 + 0.0018 (S - 35)

8 - 1990 ) 8 . 1 7 x 1 0 273+8~

= = 68.28 kHz 1 + 0.0018 (30 - 35)

Using Equation 14 to obtain coefficients for term 3 of Equation 11

03 1 383x,05d+49x,oo 2:l 383x,05(4 ft) ,olo(40 ft/2 + 4.9 x = 0.8546 3.28 ft / m 3.28 ft / m

Because temperature (T) is less than 20~

B 3 = 4.937 x 10 -4 - 2.59 x 10-ST + 9.11 x 10-7T 2 - 1.50 x 10-8T 3

B 3 = 4.937 x 1 0 - 4 - 2.59 x 10-5 (8~ + 9.11 x 10-7 (8~ 2 - 1.50 x 10-8 (8~ 3 = 0.000337dB / (km - kHz 2)

B1Dlfl f2 B2D2f2 f2 o ~ = ~ + ~ + B 3 D 3 f2

f2 + f2 f2 + f2

(0 .1031)(1) (0 .962)(50) 2 (0 .517) (0 .551) (68 .28) (50) 2 tx = + + (0.000337) (0.8546) (50) 2

(50) 2 + (0.962) 2 (50) 2 + (68.28) 2

tx = 7.61dB / km, or ct = 7.61dB / km (1.0936 km / kyd) = 8.3dB / kyd

Evaluate transmission loss (TL) using spherical spreading and absorption (Equation 15)

TL = 20 log r + a (rx 10 -3 ) = 20 log (4, 000 yd) + 8.3 dB / kyd (4 kyd) = 72.0 + 33.2 = 105 dB

Therefore the two way transmission loss = 2(105) = 210 dB


where c = sound speed (m/s) T = temperature (~ at the depth S = salinity (ppt) d = depth (m)

The range of validity for the Mackensie [26] equation is �9 0~ < T _< 30~ 30 o/oo < S < 40 o/oo, and 0 m < d < 8,000 m. The expressions are good for practical work and shows that sound speed increases with temperature, salinity, and depth.

Sound Speed Structure in the Ocean

The sound speed profile, variation of sound speed with depth, is illustrated in Figure 15. The surface layer is where the sound speed is subject to daily and local changes in heating, cooling, and wind action. Seasonal thermocline is the negative thermal or velocity gradient that varies with season. In the summer and fall, the near surface waters are warm and seasonal thermocline is well defined, but in the winter and spring, it tends to merge and be indistinguishable from the surface layer. The main thermocline is affected only slightly by seasonal changes, and it is here that the major decrease in temperature occurs. The deep isothermal layers of the deep Atlantic, Pacific, and Indian ocean waters the temperatures are about 32.5 to 35~ and the sound velocity increases are due most- ly to the effect of depth only. Characteristic sound speed profiles for deep ocean locations are shown in Figure 16. Temperature is an important factor affecting sound speed and example monthly and daily temperature variations are illustrated in Figure 17.

Instruments Used to Measure Sound Speed. A bathythermograph measures temperature as a function of depth as it is lowered into the water. A velocimeter measures sound speed in terms of sound travel time over a fixed path. The principle of the velocimeter is that a projector sends an initial pulse and a receiver accepts the signal and triggers a second pulse by the projector. This results in continuous repetition, and the repetition frequency of the pulses is a measure of the sound speed. Such a sound velocimeter is also called a "sing around velocimeter."

A third instrument (Figure 18) is the expendable bathythermograph (XBT) that measures temperature versus depth without having to retrieve the sensing unit. The operational principle is that a thermistor probe sinks at a known constant rate. The probe is connected to electronic equipment on ship by a fine wire that is paid out from spools on the launch vessel and probe. The thermistor bead changes its resistance with temperature, and the trace obtained is resistance (temperature) versus time (depth). The bathythermograph trace is converted to sound speed without considering the effects of salinity, and its trace is compara- ble with that of the velocimeter that does account for changes in salinity.


147g 4850 m ft

915 3000

DEPTH

1829 6000

2744 9000

SOUND SPEED 1494 1509 1524 m/= 4900 4950 5000 ft/s ..=

Surfo~e - ~ ~ ~ ~ _ _ Loyer ~ ~ S| Thermocllne

_

Figure 15. Typical sound speed profile in the deep ocean.

1 2 4 3

012 i 1 ] 4 i '" i" i i

! l

4,850 4,890 4,930 4,970 5,010 5,050

Speed (rUs)

Figure 16. Example sound speed profiles for various deep ocean locations. 1. Antarct ic Ocean (60~ 2. North Pacific (45 to 55~ 3. Southern oceans (45 to 55~ 4. Pacific and South Atlantic (40~ and Indian Ocean under influence of Red Sea outf low, and North Atlantic under influence of Mediterranean Sea outf low (US Navy 1970).


0.9 ~ 1.2 ~ 1.3 ~ 3.0 ~ 53" 4.5" 4.0" 2.8 ~

0615 0800 t000 1200 1407 t600 1800 0610 ( = ) L o r ~ - e ( h r )

o

. . . , ~ ~ ~ �9 ~ ~h ~. ~-8 I,,- U) h . r-. h- (I) 0D r h.. I~-. . ,

�9 0 �9 0 �9 �9 0 0 0 0 �9 �9 �9 0 �9

~~'~176 I I F I Ir I I r I I r r IF" r i W l i l I1 2~176 I ! I I I I I ! Ir r w i t P ' l l I1 ~ r I f i ! a r l [ f l !1 4 0 0

t3 t7 26 9 t3 26 11 28 18 31 17 12 3 30 t7 27 25 t9 ' - . v - ' ~ ' ' v "-----e ~ ~

M o t / ~ ' i l M o y J u n e J u l y A u g S e p t O c t N o v D e c J o n Feb

s Momh

Figure 17. Time (a) and monthly (b) variability of temperature in ocean waters near Bermuda [43].

ship d isp lay of ! t t e m p e r a t u r e

vs t ime ( d e p t h ) ~ 1 [ ~ ~ wire

thermis tor

wire spool

Figure 18. Schematic of expendable bathythermograph.


Snell's Law

Figure 19 shows a plane wave that is traveling downward in the first medium at a ray angle 01 with the boundary. The wave front at the instant when the ray AB reaches the boundary is shown by BB' which is perpendicular to AB and A'B'. As the wave crosses the boundary, the speed of propagation is suddenly changed from c 1 to c 2. Therefore, while ray A'B'C'D' is traversing the distance B'C', the ray ABCD traverses a different distance BC. When ray A 'B 'C 'D ' reaches the point C', the wave front lies along the line CC'. To locate the point C, swing an arc of radius BC about the point B and then draw a tangent line from C' to the arc. The time to travel from B'C' and BC is a constant, and the magnitude of BC is C2At. The tangent line determines the direction 0 2 in which the ray BCD travels.

BC B'C'

C 2 C 1

BC = BC' c o s 0 2

B ' C ' = BC' cos02 (61)

Therefore

BC' cos 0 2 BC' COS 01

C 2 C 1

COSO 2 COSO 1

C 2 C 1 (62)

A A'

c = c 1

B' @1

~ . . . . . . . . . . . . , , O'

" D ~ D '

C - - C

c 2 > c 1

Figure 19. Schematic illustrating Snell's Law.


For many layers

C 1 C 2 C 3 = ~ = ~ = . . . = const = c v (63)

COSO 1 COSO 2 COSO 3

Approximating the ocean with layers in which the sound speed is constant and let- ting the number of layers approach infinity and the thickness of the layer go to zero, then limitations of Snell's Law are that it is valid only when the speed of sound is a one dimensional space function. The constant c v applies only to a particular ray and is the speed of propagation at the depth at which the ray is horizontal.

The critical angle (0c) is defined in Figure 20 and Equation 64.

cos 0 c = c---L (c 1 < c 2) (64) C2

When a ray in the slower medium is incident upon the boundary at an angle 01 > 0 c with the horizontal, the ray enters the faster medium and is bent toward the horizontal. At the critical angel 0 c the refracted ray travels along the interface (02 = 0). When the incident ray is more nearly horizontal than the critical ray (01 < 0 c) the ray does not enter the faster medium but is totally reflected. When a ray is incident from the faster medium, there is no critical angle. Refraction occurs for all angles of incidence, and the angle between the refracted ray and the horizontal will never be less than 0 c.

The Ray Solution of the Wave Equation

In the real ocean, the speed of sound varies spatially and the solution of the basic differential equation (wave equation) is generally not possible. Therefore, approximate methods are necessary and one of these is the method of rays. In three dimensions, the wave equation is

~)2p-F ~)2p ~)2p 1 ~)2p (65) C)X 2 ~ ' ~ + /)Z'--T = C-- T at--g-

incident ray slow medium (el) incident ray x ~ ~

.. ~ , reflected ray ncldent ray. . ,., "~ \ ,_,.

. . . . . . . . . ~ ......... "':-->_.~_~..-,-',-"'" _ ~ layer interface

refracted ray

Figure 20. Critical angle for sound rays. fast medium (c2)


Families of rays are obtained as a solution to the simpler equation called the Eikonal Equation (Equation 66), which is a solution to the wave equation in special cases and under certain conditions is a good approximate solution.

( ow fow (ow (66)

where W (called the Eikonal)=

W (x, y , z ) = c--s176 (o~x + 13y + yz) (67) C

The direction cosines of the ray are defined as o~, 13, and 7 with respect to the x, y, and z coordinate axes, respectively. The speed of sound in water is c, and c o is an arbitrary reference sound speed. The criterion for the validity of Equation 66 is that the change in the velocity gradient over a wavelength is small compared to c/;k o. Mathematically

XoAg ~ < < 1 (68)

where Ag = the change in velocity gradient over the distance of one wavelength. The Eikonal equation is applied to typical ocean conditions where c is mainly

a function of depth (y), and the problem is two dimensional. In this case, x is the horizontal distance from the source, y is vertical distance from the source, s is distance from the source along the ray path, t is the time along the ray path, 0 is the angle of the ray relative to the horizontal and measured positively upward (Figure 21), and g is the velocity gradient (dc/dy). The objective is to determine

water surface x (horizontal distance) , . ,

Y

(depth)

wave front

/

Y

Figure 21. Schematic of coordinate system for ray.


the characteristics of the ray path by finding relationships between the variables x, y, s, t, and 0. The resulting solution to the Eikonal equation is four differential equations that are expressed as

dx Cv Cv = ~ cos 0 dO; dy = - - - sin 0 dO g g

d s = c--2-v dO; d t = dO g g cos 0

(69)

The slope of the ray is dy/dx = -tan 0. If g is assumed constant, then Equation(s) 69 can be integrated and the results are

C v C v x = ~ sin 0 + const ; y = ~ cos 0 + const

g g

c v 1 s = ~ 0 + const (0 is in radians) ; t = l n ~

g 2g

1 + sin 0

1 - sin 0 + const (70)

where c v is called the vertex velocity of the ray and is defined as c v = Co/COS 0 o. Sound rays are arcs of very large circles. For a positive velocity gradient the

origin of the ray arc is in the sky and in the case of a negative velocity gradient the origin is well below the bot tom of the ocean. The speed of sound at the source depth is Co, and the angle of inclination of a ray at the source is called the initial angle, 0 o. Considering a family of rays leaving the source in any one vertical plane, then each individual ray of the family is identified by its own particular value of 0 o. If the source is at depth Yo and the sound speed at Yo is c o, then the constants in Equation(s) 70 are evaluated from the initial conditions of (0 =

0o; x = 0; y = Yo; s = 0; and t = 0). The result is

C O Co x = ~ ( s i n 0 - s i n 0 0 ) ; Y-Yo = ~ ( c ~

g cos 00 g cos 00

c o 1 F l + s i n 0 l + s i n 0 0 s = ~ ( 0 - 0 0 ) " t = L l n ~ - l n ~

g cos 00 ' ~ 1 - sin 0 1 - sin 00 J (71)

Practical computations of ray paths in a constant-gradient medium are usually made by treating y as the independent variable and then (1) selecting a value for y, (2) solving the y equation for cos 0, (3) determining 0 and sin 0, and finally (4) computing x, s, and t. There is an ambiguity in algebraic sign in the determination of 0 and sin 0 because both plus and minus values of 0 give the same value for cos 0 (Figure 22). The physical significance of this ambiguity is demonstrated by the fact that a horizontal line (y = constant) intersects the ray circle at two points.

422. Offshore Engineering

y = const

F boundary between layers

~ •

Figure 22. Ambiguity of sign in ray equations.

Multiple Constant Sound Speed Gradient Layers

Constant-gradient layers have rays that are arcs of circles and curve upward when the gradient is positive and downward when it is negative. Consider the simple case (Figure 23) of two constant-gradient layers having different gradients. Any ray such as SA that leaves the source with a positive, upward angle continues to rise upward. A ray whose initial angle is slightly negative (i.e., below the horizontal) descends to a vertex and then rises again due to the upward curvature of the ray path. A ray such as SD has a large negative initial angle and crosses the boundary between layers with a slope greater than zero at E and penetrates into the second layer where it curves downward. Somewhere in between SD and SB there is a special ray whose vertex occurs at a point of tangency T on the boundary. This ray is the limiting case between SB and SD and is called the limiting ray. Beyond the vertex T, it splits into two branches, the upper branch TC and the lower branch TC'. Between TC and TC' is a region, according to ray theory, where no sound rays enter, and this region is called the shadow zone. Shad- ow zones occur in the vicinity of a region of maximum sound speed. Shadow zones do not truly exist in the strict sense of the real ocean because sharp dis- continuous changes in velocity gradients do not occur in nature and ray theory breaks down whenever the velocity gradient changes rapidly with depth. How- ever, very pronounced shadow zones where the sound intensity is very small are

~.~ th

sound velocity (c) A B

source (S) shadow e

v

Figure 23. Example of ray paths for two constant-gradient layers.


actually observed in the ocean. The effects described above result in a continuous transition into the shadow zone rather than a mathematically abrupt one, but the spreading loss inside the zone is so high that detection is not likely. A similar pattern exists when the source is located in the lower layer and the limiting ray leaves the source with an upward angle.

The ray SPQR (Figure 24) leaves S horizontally, crosses the boundary at P, and is refracted upward in the lower layer. It vertexes at Q and T and the vertex at T is the same depth as the source. The ray oscillates up and down but remains within the boundaries of the two layers, and the area between these boundaries is called a sound channel. The ray SP'Q'R' is the limiting ray at boundary A, and it crosses the sound channel axis at Q' and vertexes at R' at depth C. Since the ray is horizontal at both A and C, it is evident from Snell's law that the speed of sound is the same at both depths. Thus, the limiting ray from S is confined to the channel A to C, and this is true for a source located at any depth within the channel. The ray that leaves at a steeper angle than SP'Q'R' will leave the boundary. Any ray such as SP"Q"R that leaves at a correspondingly steep downward angle vertexes at a depth Q" below C and upon returning upward leaves the channel at T". If the ray is sufficiently steep it may cross the lower boundary and leave the channel.

A region in which the sound speed passes through a minimum gives rise to a sound channel. The depth of this minimum is the axis of the sound channel. To determine the thickness of the sound channel, locate the smaller maximum sound speed above or below the channel axis. Draw a vertical line to where it intersects other gradient. The intersections are the limits of the sound channel.

Vertex. A sound ray vertexes when the ray angle 0 is zero. The location of a ray vertex is determined by setting 0 to zero and solving for values of x, y, s, and

sound velocity (c)

A v P' T"

. . . . . . "T

(s) depth (y)

Figure 24. Illustration of sound rays in a three constant gradient layer ocean medium. Point B is sound speed minimum and points A and D are sound speed maximums. Rays leaving S all curve downward.


t using Equations 71. As an example, the x location (x v) is determined for 0 = 0 and a constant gradient (g l) as

x v = - c o sin 00 / (gl cos 0 o) (72)

Limiting Ray. The limiting ray from a source in layer 1 vertexes at Y12 and the vertex speed c v is C12. TO locate the limiting ray, its initial angle (0 L) must be determined. This is found from Snell 's Law (Equation 63) using (c = c12, 0 - 0,

0 o = 0 L) as follows

C _ C O . C12 - C O ; t h e n C O S 0 L -- c o (73) cos0 cos0 o 1 C O S 0 L C12

The values of x, s, and t are determined by setting 00 = 0 L and 0 = 0 in Equation 71.

Ray Path in Othe r Layers . If the initial angle is large enough, the ray crosses into the layer below. The value of x at the boundary between layers 1 and 2 is

C 0 X12 = ~ (sin 012 -- sin 00) (74)

gl cos 00

To determine x at any depth in the second layer we return to the original equation. The vertex velocity (c v) is constant in all layers. The initial conditions in the second layer are x = x12 when 0 = 012. Therefore the increment of x in second layer is

CO X- X12 -" ~ (sin 0 - sin 012) (75)

g2 cos 0 0

At the boundary between layers 2 and 3, the above equation becomes

C0 X23 -- X12 = ~ ( s i n 023 - sin 012) (76)

g3 cos 0 o

The increment in the third layer is

X - X23 = CO (sin 0 - s i n 023 ) (77) g3 cos 0 o

and so on. The cumulative value is the sum of all the increments. For example, the total horizontal distance (xt) for the three layers is

X 1 = X 1 2 + ( X 1 2 - - X12 ) + ( X - X 2 3 ) (78)

The corresponding values of s and t are obtained in a similar manner. An example of a ray tracing problem is illustrated in Table 9.


Table 9 Example Ray Tracing for Constant Gradient Ocean M e d i u m

A sound source is located at 1500 m and the sound speed profile for that location is shown below. Determine the x and y coordinates for the vertex point of a ray which leaves the source with an initial angle of zero degrees.

o

1 ooo

2o0o depth

C%~o 4OO0

50012

sou.d ~ (m/s) 14.80 1490 1500 1510 horizontal distance (x) --r ' l ' t = i ~ "

C o C v - -

cos 0 o

gl = 0 ; g 2 =

1 ,490 m / s

cos(O) = 1 ,490 m / s;

1 ,480 - 1, 500 m / s

2 , 0 0 0 - 1 , 0 0 0 m = - 0 . 0 2 s - l " g 3 =

1,510 - 1 ,480 m / s

5 , ~ - 2 , ~ m = 0.01 s -z

Angle of ray crossing interface 23

C o Y23 -- Yo = ' ( C O S 0 2 3 - c O S O o )

g 2 c O S O o

1490 2 , 0 0 0 - 1 , 5 0 0 = ( C O S 0 2 3 -- 1)

( - 0 . 0 2 )

500 (--0.02)

1, 490 + 1 = COS 023

0 2 3 ---- 6.64 ~ = - 6 .64 ~ (nega t ive s ign is inse r ted b e c a u s e a n g l e is m e a s u r e d d o w n w a r d )

Co (cOSOv -- C0S023) Yv --Y23 = g3 COSOo

1 ,490 m / s Yv - 2 , 0 0 0 = ~ (cos(O) - c o s ( - 6 . 6 4 ) )

0.01 S -1

yv = 3 , 0 0 0 m

Horizontal distance

c o x 2 3 =

Y2 cOSOo ( s i n 0 2 3 - s in 0 o ) =

1 ,490 m / s _ 0 . 0 2 s _ 1 ( s i n ( - - 6 . 6 4 ) - s i n ( O ) ) = 8 , 6 1 4 m

X v -- X23 ---- C o

g3 c ~ (s inO v - s in 0 2 3 ) ; x v - 8 , 6 1 4 m =

x v = 8 , 6 1 4 + 17 ,229 = 25 ,843 m

1, 4 9 0 m / s

0.01 s -1 (sin(O) - s i n ( - 6 . 6 4 ) ) ;

(table continued on next page)


Table 9 (Continued) Example Ray Tracing for Constant Gradient Ocean Medium

Distance along path

S23 = ~ c o

g2 cos 0 o

1,490m/s ( 6.64 ) (023 - 0 o ) = ~0-~-s- i- - 1--~--0 =8,634m

co '490m's( / s v -s23 c o s 0 - ~ ( 0 v - 0 2 3 ) ; s v - 8 6 3 4 m = ~ 0 - -

0.01 s -1

Time to travel along path

1 I l+sin023 l+s in0o] 1 ( 1 + s i n ( - 6 . 6 4 ) 1 + 0 t23 = ~ In - In = In - In = 5.8 s 2g 2 1- sin023 1- sinO o 2(-0.02 s -1 ) 1 - sin(-6.64) 1 - 0

[ 1 1 [ 1+0 1 + sin(-6.64) ] 1 lnl+sinOv Inl+sin023 ;t v 5.8s+ -l In - In tv -t23 = 2g 3 l - s i n e v 1-sin023 2(O.Ols ) 1 - 0 l-sin(-6.64)

=5.8+11.6= 17.4s

T r a n s m i s s i o n L o s s M o d e l s

Transmission Loss from Ray Diagrams

The intensity (I1) at 1 yd from a source located at O l and the intensity (12) at

location 0 2 are

AP AP I 1 = ~ ; 12 = ~ (79)

A m I A m 2

The transmission loss is then expressed as

TL = 10 l o g - - I1 = AA2 (80) I 2 Am 1

Figure 25. Schematic for transmission loss model using ray separation [43].


Because AA 1 = 2rt cos01A0 and A A 2 = 2r~rpAL = 2~rAh c o s 02, then

TL = 10 log rAh c~ (81) A0cos01

By Snell's Law, c~ = c-L and then (81a) cos01 c 1

TL = 10 log rAhc2 (82) A0c I

where r is the range (yd), Ah is the vertical separation (yd) of rays at P, A0 (radians) is the vertical angle of separation of rays at location 01, c~ is the speed of sound at 01, and c 2 is the speed of sound at 0 2. The assumptions are: (1) no crossing of acoustic energy between rays, (2) no scattering, and (3) no diffraction.

Sea Surface and Bottom Loss

The sea surface is both a reflector and a scatterer of sound. When the sea surface is rough, the reflection loss is not zero. For example, the surface loss is approximately 3 dB for 1-ft waves at a frequency of 25 kHz. At 30 kHz, the surface loss is 3 dB for 0.2 to 0.8 ft wave heights and at lower wave heights, the loss is less. The Rayleigh parameter (R)

R = kH sin 0 (83)

is used as a criteria for evaluating the roughness of sea surface where k is 2n/~,, H is the rms wave height, and 0 is the grazing angle. When R << l, the surface is primarily a reflector and when R >> 1, the surface is rough and acts as a scatterer.

The sea bottom is also a reflector and scatterer of sound. Its effects are more complicated because of its diverse and multilayered composition. The reasons are that the bottom is more variable in its acoustic properties (hard rock to soft mud) and the bottom is often layered so that sediment density and sound speed change with depth. Therefore, reflection loss of the seabed is not as easily predicted as for the surface. Complete or total reflection occurs at grazing angles less than the critical angle. For angles greater than the angle of intromission, all sound rays are totally transmitted into the bottom. Measured bottom losses for a 10 ~ grazing angle at 24 kHz are 16 dB for a mud bottom, 10 dB with mud-sand bottom, 6 dB for sand-mud, 4 dB for sand and stony bottom. All bottom materials tend to absorb sound. Sound attenuation (tx) in sediments is a function of frequency (~ = k f n) dB/m, where f(kHz), n = 1, k = 0.5 for porosity 35 to 60% (additional values for k can be located in Hampton [16]).


Transmission Loss Model for Mixed Layer Sound Channel

In many ocean areas of the world, the temperature profile regularly shows the presence of an isothermal layer just beneath the sea surface. The layer is main- tained by turbulent wind mixing of the near surface water and is called the mixed layer sound channel or surface duct. In this layer of depth (H), the sound speed increases with increasing depth. A model for evaluating transmission loss (TL) in this layer is

TL = 10 log r 0 + 101ogr + (~ + ~L)r • 10 -3 (84)

where r = the range in yards = absorption coefficient in dB/kyd

r o and ff"L are defined below. If the layer sound speed gradient is constant, the radius of curvature (R = Co/g) is much greater than the layer depth (R >> H), and 0 o is small (sin 0 o << 1), then the skip distance of the limiting ray (x), the maximum angle of limiting ray (0o), the angle (0) of limiting ray at the source depth, and the range (ro) are determined from the following equations

x = ~/8RH = skip distance of limiting ray

00 = ~/2H / R = maximum angle of limiting ray, rad

0 = -~[ 2 ( H - ci) -- angle of limiting ray at source depth R

r~ = H - d 8 H - d

where H = thickness (ft) of the mixed layer d = depth (ft) of the source

Leakage of sound from layer is caused by scattering of sound out of the layer and transverse diffusion, and the leakage coefficient o~ is

~L = 2S~ f (86)

where H is the layer depth, S is the sea state, and f is frequency (kHz).

Deep Sound Channel Transmission Loss Model

The deep sound channel (sometimes called SOFAR channel). The axis of this channel (minimum velocity) varies from 1220 m (4000 ft) in mid-latitudes to


Baa~ (=1) 20 30 40 5O 60 70 80

I:

!

| v o v v v

Figure 26. Ray diagram for deep ocean sound channel for source near axis [43].

near the surface in polar regions. Long ranges can be obtained from a source of moderate acoustic power output located near the axis of this channel. The transmission loss model for a deep sound channel is

TL = 10 logr 0 + 10 logr + txr x 10 -3 (87)

where r o and r are ranges in yd and o~ is the absorption coefficient in dB/kyd.

Arctic Propagation Loss

Sound transmission reaches long ranges due to repeated reflection from under ice surface. Low propagation loss in the Arctic is caused by the positive gradient of the sound speed profile that results in continuous upward refraction of all sound rays. The rays then interact with ice-ocean interface and essentially results in a surface duct. The propagation loss is low because there is no interaction with the ocean bottom.

Transmission Loss Models for Shallow Water

Range of sound transmission in shallow water is effected by repeated reflections from surface and bottom. Marsh and Schulkin [27] developed semi-empiri- cal expressions for evaluating the transmission loss that are based on measurements in the frequency range of 0.1 to 10 kHz. A parameter (F) is defined as

F = (d + H) (88)

where F = kyd d = depth of water, ft H = layer depth, ft


The equation used depends on the relationship between the range and the parameter F as follows For r < F

TL = 20 log (r x 10 -3) + cz(r x 10 -3) + 60 - k L (89)

For F < r < 8F

(r x 10 -3) _ 1/ TL = 15 log (r x 10 -3) + cz(r x 10 -3) + ~t F

+ 5 log F + 6 0 - k L (90)

For r > 8F

(r x 10 -3) _ 1/ TL = 10 log (r x 10 -3 ) -4- ct(r x 10 -3 ) 4- t3~ t F

+ 10 log F + 64.5 - k L (91)

where r is the range in yd, F is in kyd, and ot is the absorption coefficient in dB/kyd. Table 10 provides data for the shallow water attenuation coefficient (cz t) and the near-field anomaly k L.

Ambient Noise

Ambient noise is the composite noise from all sources at any specific point in the ocean except for desired signals and the noise inherent in the measuring equipment and platform. The ambient noise level (NL) is expressed as

NL = intensity of ambient background (92)

intensity of plane wave having rms pressure of 1 l-tPa

Common sources of ambient noise in deep water (Figure 27) are tides, seismic, turbulence, ship traffic, wind waves, and thermal noise. Pressure fluctuations resulting from tides and hydrostatic effects of waves cause very low frequency noise, but it is not too important at frequencies of interest in underwater sound. Tidal currents can cause flow induced noise. The intensity levels of ambient noise in the deep ocean vary with frequency and this variation with frequency is called the spectrum level of ambient noise that is expressed in dB re 1/.tPa as illustrated in Figure 27.

Constant seismic activity results in low frequency noise (<1 Hz). Turbulence in the ocean induces motion of the transducer, causing self noise, and pressure

I'-,

..1

0 lm

E~ I=

~J

l,,t

iJl

r~

ee~ I r~

rf~

r~

o

c,,,I ~

v'~ ~

o ~t-

oo ("~1 t-.-- ~c:)

~ c~

~

o~

~

~ ~

~ ~

.

ce~ t,,..

c,~1 o t---. t'--.

oo cr~

ir~

,.~ c,~

~t- oo

o ~

~ ~

~.

4 3 2 Offshore Engineering

Q.

QQ

Q,) a,

E

Qa Q.

1 2 0

llO. -

90-

e0-

70

60-

5O

40-

30-

~l T i d e T u r b u l e n c e

I !

Wind Thermal I

!-/"' ' " ! 1 I I S h i p p i n g i I I I

~ t I I I - a I I

i \-8 to -101 i I \dS/octave I I I \ J I I

I I I ! \ i t

i ', I I I ~ - s ,o -6 I I I I ~,~s/~t,~ I , 20 soo ~ sozx~ , 6 /

1 I l 1 t l

1 tO tOO 1.000 10,0OO SOO~X~

Frequency (Hz)

Figure 27. Ambient noise spectrum level in the ocean [43].

changes associated with turbulence may be radiated. Ship traffic is the principal source of noise in the frequency range of 10-500 Hz. Surface waves create ambient noise between 500 Hz-25 kHz that correlates well with sea state or wind force. Causes include breaking white caps, flow noise (wind blowing over rough sea surface) and cavitation (collapse of air bubbles). Rough sea surface is a dominant noise source at 1-30 kHz. Thermal noise is the result of molecular agitation in the sea and is important typically at frequencies greater than 75 kHz, but it can be a limit when frequencies are above 40 kHz in calm seas. A summary of deep water ambient noise is shown in Figure 28. Data indicate the deep water noise is not isotropic, but is directional in the 10 to 500 Hz range where shipping noise dominates.

Intermittent sources of ambient noise do not persist over periods of hours or days. Any biological sounds from whales, porpoises, dolphins, shellfish cause noise in the 10-500 Hz frequency range. Noise from snapping shrimp occurs in the 500 Hz--20 kHz range. Heavy rain can result in 30 dB increase between 5-10 kHz. Steady rain can cause a 10 dB increase around 20 kHz. Seismic explosions from seismic surveys are another noise source. If shipping and biological noise are absent and wind is the primary contributor, then shallow and deep water noise levels are nearly the same. In general, shallow water is a noisy and highly variable environment for most underwater acoustic operations. Aver- age ambient noise level is higher in winter than in summer due to better sound transmission conditions. Shallow water ambient noise levels undergo wide vari-


I • I zo JL - I Z o =L

I 1 0 1 1 0

,oo \ ~L---, . . . . ,oo " ".""PP.'mJ

r 70 . ~ 70

~" - - ' . .L -~e . , , I s o

E , o ,

4 0

I 1 J i l l I 1 1111 I 1 J i l l I I f i l l I I 1111 I i

1 2 S tO ~ SO tO0 ~ X ) SO01.000 ~0.000 tOO~XX) 5 0 0 . 0 0 0

wRq~mcy (Hz)

Figure 28. Average deep water ambient noise spectra.

ations with respect to time and place and are a mixture of shipping and industrial, wind noise, and biological noise.

Examples of noise spectra for New York harbor in the daytime (AA), upper Long Island Sound (BB), and an average of many WWII measurements (CC) are shown in Figure 3a. Also shown are average subsonic measurements. Data are for the range of 1-20 kHz. Additional sources beyond those mentioned in deep water are: industrial activity, marine life, tidal currents. In coastal waters, wind speed appears to be the main cause of noise. Studies show the noise level is dependent on wind speed at frequencies between 10-3,000 Hz as shown in Figure 29.

For an infinite layer of uniform water with a plane surface along which the sources of noise are uniformly distributed, the ambient noise level (NL) should be independent of depth for frequencies <10 kHz. At frequencies >10 kHz absorption should cause NL to decrease with increasing depth. More realistic results must consider refraction and multipath propagation. At a location north of St Croix, Virgin Islands and offshore San Diego, California, the noise level in the 50 to 3,000 Hz range was found to generally decrease slowly with depth (1 dB/1,000 ft) for depths to 14,000 ft [42-46]. For a non-continuous ice formation, ambient NL of 5 to 10 dB higher than those measured at the same sea state in ice-free waters. With continuous ice coverage, very low noise levels occur for rising temperatures. Impulsive popping noises increase the levels for falling temperatures. The conclusion is that NL is highly variable and depends on ice conditions, wind speed, and snow cover.


I I I I I I i l i | I 111111 I 1 I l l l l l I I I I i i i i

~ . . ,,,

2.0 ~ .,,

,,o ~'/~ ,oo " r >~ ,o " < ~ ~ ~ . . . .

.~ ,o ~~..~ �9 o ~

4 0 l~l �9 I llllll I I IIIIII I II IIIIII I I IIIIII I I IIIIII

g~ ~ sO sO0 I.s tOs t ~ r~

Frequency 01~)

t lO

, , ~ 8 0

I 1 i ' 1 1 1 1 1 i i 1 I i 1 I i I I I i i i i i i ! i i ! l l l l l

- - Knudsen et at (1948)

-- Were (1962)

Wi.d Sp~.d Omot,)_

~ - - - 22 - 2 r -

, , ~'-- 7- I0-

~11 l 1 1 1 1 1 1 1 1 i i i 1 1 1 1 1 I I I l l l l J 1 1 1 1 1 1 1 1

t 0 t 0 0 ~ . 0 0 0 ~0.000 ~O(XO00

Frequency (Hz)

Figure 29. Typical noise levels in bays and harbors (a) and coastal waters (b) [43].

Scattering and Reverberation Level

Reverberation is the sum of the acoustic energy scattered back to the receiving array by inhomogeneities in the ocean medium, such as dust particles, schools of fish, sea mounts, and marine organisms. Reverberation can severely limit sonar system performance. Types of reverberation include volume, surface, and bottom reverberation. Volume reverberation occurs in the volume of the sea and is caused by marine life, inanimate matter, and the inhomogeneous structure of the sea itself. Surface reverberation is caused by scattering from waves and bubbles while bottom backscattering from the boundary and inhomogeneities in and on the sea bottom produces bottom reverberation.

A scattering strength parameter (Ss,v) is defined as

Ss, v = 10 log Isca----~t (93) Iinc

where Iscat is the intensity of sound scattered by an area of 1 yd 2 or volume of 1 yd 3 and Iinc is the intensity of the incident plane wave (Figure 30).

U n d e r w a t e r A c o u s t i c s 4 3 5

Equivalent plane wave reverberation level (RL) in sonar equations is the level of an ax ia l ly inc iden t p lane wave that wou ld p roduce the same hydrophone output level as the reverberation does. The propagation loss is assumed to be due to spherical spreading only. Other assumptions include: ran- dom, homogeneous distribution of scatterers, density of scatterers is large, pulse duration is short, and there is an absence of multiple scattering. The volume reverberation is evaluated by

RL v = S L - 40 log r + Sv + 10 logV

V = c 1 7 _ r 2 2 I1/ (94)

where c is velocity of sound, x is pulse duration, r is range, and ~ is the composite-transmit receive pattern beam width or equivalent two-way beam width. SL is source level, and S v is scattering strength.

Surface reverberation is reverberation produced by scatterers distributed over a nearly plane surface. The expression for equivalent plane wave level of surface reverberation is

RL s = SL - 40 log r + S s + 10 log A C'17

A = - - @ r (95) 2

where A is the area of the surface of scattering strength (Ss) lying within the ideal beam width (~) which produces the same reverberation as that actually observed. The ideal beam width (~) is tabulated in Table 11.

! inc

~1 , . . ~ _ / ' . , 4- . . . . . . . . ~.~

/ ..... , ,.t"," a l p \ / -.>1..- / ........ �9 . . . . . . .~ ",...

/ / / / " ~'x../. P . - / " " "~" . 1 " ' , r / / " ,A/ \ . , o ~ ",, / / / m , ~ . "'. \ / , ; , ~ ; ,,, ,, \

', ~ _ "I" 3 / .." \ \Unit Volume = I yd ..... /

! inc

/

~ : " , ......... �9 ........ "~.

" / yd \ \

Unit Area = 1 yd 2

Volume

I lscat Surface S = 10 log scat

S v = 10 log s I inc I lnc

F i g u r e 30. S c h e m a t i c o f v o l u m e and b o t t o m reverberation.


Table 11 Values of Equivalent Two-Way Beam Widths W and ~ in Log Units

Array 1O log ~ dB re I steradian 10 log �9 dB re I radian

Integral expression j,2n i,~/2

10 log | | b(O, tp) b'(O, tp) x cosO dO d~0 dO t/-lt/2 ~0 TM

10 log b(O, O)b'(O, (p)d( p

Circular plane array, ( ~ _ ~ / in an infinite baffle 20 log + 7.7 or 10 log ~" 2ha

of radius a > 2~, 20 log y - 31.6 10 log y - 12.8

+ 6.9 or

Rectangular array in an X2 10 log ~' infinite baffle, side a 10 log 4~ab + 7.4 or 2ha + 9.2 or

horizontal, b vertical, 10 log ya Y b - 31.6 10 log y a - 12.6 with a, b >> ~,

X X Horizontal line of 10 log + 9.2 or 10 log + 9.2 or

2nL 2nL length L > ~,

10 log y - 12.8 10 log y - 12.8

Nondirectional 10 log 4n = 11.0 10 log 2n = 8.0

(point) transducer

Note: y is the half angle, in degrees, between the two directions of the two-way beam pattern in which the response is 6 dB down from the axial response. That is, y is the angle from the axis of the two-way beam pattern such that b(y)b'(y) = 0.25. For the rectangular array, Ya and Yb are the corresponding angles in the planes parallel to the sides a and b.

2 0 0

600

1,000

1,400

1,800

2 , 2 0 0

Z,600 3,000

I ! u !

10 kH~

_ ~ / Night

" / / / ~ Day

t I , ,I I ,

- ~ - s o - ~ -7o

S, (~B)

. . . . . If I �9

60 25 kBz

../.- - 180

- 4 2 0 ~

~ o ~

78O

A l = l I

-.~o -so -eo -to

S, (d]B)

Figure 31. Mean profiles of S v at two frequencies for six locations between Hawaii and California [2].


The scatterers that cause the volume reverberation are commonly biological in nature (marine life in the sea). The deep scattering layer (DSL) is a complex aggregate of different biological organisms and its scattering strength varies with frequency, location, season, and time of day. The DSL has a diurnal migration in depth, and it is at a greater depth by day than at night. A rapid depth change occurs at sunrise and sunset. The depth migration is over several hun- dreds of feet, and the DSL appears to adjust its depth to maintain a constant intensity of light illumination. Typical characteristics of DSL are that it rises at sunset and descends at sunrise, is expected at depths between 600-3,000 ft by day at mid-latitudes and shallower at night, has a volume scattering strength -70 to -80 dB near 24 kHz, and S v is frequency dependent between 1.6 and 12 kHz. Layers of scatterers occur in shallow water as well, and they are located directly under the ice in the Arctic.

The sea surface is frequently rough and has entrapped air bubbles just beneath surface which makes it a good scatterer. The sea surface scattering strength as a function of angle, frequency, and roughness (measured by wind speed) are illustrated in Figure 32. The sea floor is an effective reflector and scatterer of sound, and the variations of selected scattering strengths are shown in Figure 33, and the under ice reverberation data are shown in Figure 34. An example reverberation problem is tabulated in Table 12.

,~II:Xtl

~~176 ~ ~ 3 ; L - ~ s . l s

e; x64.15

�9 ...:> ' , ~ , m~ ,z ~s x2.1'3 Z.t6 f ='__

-ZO x , . , 2 ~ ~ ' ~/-=-t'-t6 "5

-, ,__~,o~- ~ _ / ' 7 ~,o - - " "~U5 o,~,~ o4 Io

oZ.~O ~ Z Z " / , , ~ 4 . , K ~ / . ,,~.,~t5 x 1'/13/~)

A 7119155

:3,10 ^ T/21/~t -,o ~.~,~, ~, -~,," ~.~ / j

z.s ~ ^~o., ~ No. of pings averaged II II J" I | I t , I ,, | I ~ _ J

-500 SO 20 30 40 50 SO ~ 80 gO

Grazing Angle ((leg)

Figure 32. Variation of sea-surface scattering strength at 60 kHz with angle at different wind speeds off Key West, Florida [44].

E 0 0 L_

o o

~ ~

~ .

T ,

T

Ill

lap) q~C~m

s 8

"r-

! i

! �9

o

u_

r~

-

o ~

,~ ~

T ,

T ,

(llP) q

~u~ts

~u.ua~:)S~l:)~8 a:).uapu~l

IR ;' 0

.0

f,,}

- IR .~

-N

~L

438


Table 12 Example of Reverberat ion Predict ion

Given: Echo ranging sonar, f = 50 kHz, SL = 220 dB, pulse duration 1 ms. Line transducer, 1 ft long, 100 ft above mud bottom, k - 0.1 at 50 kHz, Grazing angle 0=9 .5 ~

Find: RL for diagonal range to bottom of 200 yd.

Soln: c = k f = 0.1 (50000) = 5000 ft/s From Table 1

0.1 10 log �9 = 10 log "~n + 9.2 = 10 log 2n(1) ~ + 9 . 2

10 log �9 = -8 .8 = 0.13 rad or 7.5 degrees

A = nc'l: ~ = 5000 ft / s (0.001 s)

2 2(3 f t /yd) (0.13) (200 yd) = 22 yd 2

From Figure 33, Ss = -41 dB RL = SL - 40 log r + Ss + 10 log A = 220 - 40 log 200 - 41 + 10

log 22 = 2 2 0 - 9 2 - 41 + 13 RL = 100 dB re 1 ~tPa

Target Strength

The target strength (TS) refers to the echo returned by an underwater or sur-

face target, and is defined as

intensity of sound returned by the target

TS = 10 log at a distance 1 yd from its acoustic center _ I r

incident intensity from the source I i (96)

Assume the sphere in Figure 35 has a radius "a" and is an isotropic lossless

reflector (echo distributed equally in all directions). The sphere is insonified by

a plane wave of sound intensity I i. The power intercepted by the sphere is

P = ~:a2Ii (97)

Using the isotropic assumption, the intensity of the reflected wave at a distance r

in yards from the acoustic center (center of sphere) is


: /

/

/ i

\

\ \

/ f "~'~,

lit' .,

\

/ f - ............. --.,, \ \ \

" 1 i

..... --- J / / x,\ /

. . /

Figure 35. Incident and reflected waves for a sphere.

na2Ii a 2 I = - I ~

r 4 71; r 2 - i 4r 2 (98)

For r = 1 yd

a 2

I r = Ii 4

a 2 TS = 10 log =

4 (99)

Thus, the arbitrary reference often causes the target strength (TS) to be positive for targets. This should not be interpreted as meaning more sound is coming back from target than is incident upon it. It is a consequence of the reference distance. Theoretical target strengths of a number of geometric shapes and forms are presented in Table 13. These expressions are reasonable approximations for complex targets and are found to provide useful results when no measured data are available. Complex targets may be broken into elemental parts and by replacing each part by one of the various simple forms. The variation of target strength for a submarine at various aspect angles is illustrated in Figure 36 and nominal target strength values for different targets are tabulated in Table 14.

Radiated Noise Levels

Ships, submarines, and torpedoes are all sources of radiated noise. The machinery in these vessels generate vibrations that appear as underwater sound at a distant hydrophone after transmission through the hull and through the sea.

F o r m

Finite P l a t e u

any shape

Table 13 Target Strength for Simple Forms [43]

Target strength = 10 log t

Rectangular

Plate

Circular Plate

Ellipsoid

Average over-

all aspects--

Circular disk

Conical tip

Any convex

surface

Sphere- - la rge .

Spheremsmal l

Cy l inde r - -

Infinitely long

Thick

Cy l inde r - -

Infinitely long

Thin

Cy l inde r - -

Finite

Plate--Inf ini te

(plane surface)

2 a )

a 2

8

( 8 - ~ ] 2 t a n 4

qo 1 - cos2 qs

al a2

a 2

4

V 2 61.7 m ~4

a r

2

911;4 a 4 ~ r ~2

aL2/2~,

aL2/2~,(sin~/~) 2 COS20

Symbols

A = area of plate

L 1 = greatest linear

dimension of plate

L 2 = smallest linear

dimension of plate

a,b = side of rectangle

13 = ka sin0

a = radius of plate

13 = 2ka sin 0

a,b,c = semimajor axes

of ellipsoid

a = radius of disk

tp = half angle of cone

ala 2 = principal radii

of curvature

r = range

k = 2/7t X

a = radius of sphere

V = volume of sphere

X = wavelength

a = radius of cylinder


L = length of cylinder



13 = kL sin 0

Incidence Direction

Normal to plate

At angle 0 to normal

in plane containing

side a

At angle to 0 normal

Parallel to axis of a

Average over all

directions

At angle 0 with axis

of cone

Normal to surface

Any

Any

Normal to axis of

cylinder

Normal to axis of

cylinder

Normal to axis of

cylinder at angle 0

with normal

Normal to plane

Conditions

r > I-'~

k L 2 >> 1

a 2

r > m

k b > > l

a > b

a 2

r > ~

ka >> 1

ka, kb, kc

1

r >> a, b, c,

ka >> 1

(2a) 2 r > ~

0 < t p

kal ,ka 2 :,, 1 r > a

k a : , , 1

r > a

ka << 1

k r > > l

k a ~ 1 r > a

k a , , : 1

k a : ~ 1 r > LE/X

Note: All dimensions are in yards.


0 !

2 7 0 ~

1 8 0 ~

>

I

\

9 0 ~

Figure 36. Target strength variation for a submarine at different aspects [43].

Table 14 Nominal Values of Target Strength [43]

Target Aspect TS (dB)

Submarines Beam +25 Bow-stem + 10 Intermediate + 15

Surface ships Beam +25 (highly uncertain) Off-beam +15 (highly uncertain)

Mines Beam +10 Off-beam +10 to -25

Torpedoes Bow -20 Fish of length L (inches) Dorsal view 19 log L -54 (approx.) Unsuited swimmers Any -15 Seamounts Any +30 to +60

Passive sonar systems distinguish between radiated noise and a background of self and ambient noise. Noise spectra are of two basic types that are called broadband (continuous spectrum) and tonal noise (line component).

The radiated noise from vessels is usually measured by having the vessel move by a stationary distant hydrophone array system. The Atlantic Undersea Test and Evaluation Center (AUTEC) is instrumented for the measurement of


radiated noise from submarines. The measured noise levels are normally reduced to the 1 yd reference distance, and spherical spreading is normally used for this reduction.

Sources of radiated noise are machinery, propeller, and hydrodynamic. Machinery noise is vibration that is coupled to the sea by the hull. Noise origi- nates inside the vessel from rotating parts, reciprocating parts, cavitation and turbulence, and mechanical friction. Propeller noise is the result of cavitation at the propeller tip and on the blade surface, and it has a continuous spectrum. There is a critical speed at which the cavitation noise suddenly begins. For WWII subs, the critical speed was 3-5 kts at 60 ft (periscope depth), and the critical speed increased with increasing depth.

Damaged propellers make more noise than undamaged propellers. Turns and accelerations result in more noise. Singing propellers result when the propeller blades are excited by the flow into vibrational resonance. Propeller noise is amplitude modulated or has a beat that increases with rotation speed and can be used to estimate speed. Hydrodynamic noise is caused by irregular and fluctuat- ing flow of fluid past the moving vessel. Flow noise is the result of flow of a vis- cous fluid over immersed bodies. Flow noise is a normal characteristic.

Tabular and graphical radiated noise level data for surface ships and submarines are contained in Table 15 and Figure 37 and Figure 38. These data are from the World War II era and in many cases are not representative of today's vessels.

Self Noise Levels

Sources of Self Noise

Self noise differs from radiated noise since the receiving hydrophone is located on the platform making the noise. Sources of self noise are the vessel's machinery (reduce by sound isolation), propellers (cavitation), and hydrodynam-

Table 15 Average Spectrum Levels for a 1 Hz Band for Several

Types of Surface Ships (dB re 1 ~tPa at 1 yd)

Frequency, Freighter, Passenger, Battleship, Cruiser, Destroyer, Hz 10 kt 15 kt 20 kt 20 kt 20 kt

100 152 162 176 169 163 300 142 152 166 159 153

1000 131 141 155 148 142 3000 121 131 145 138 132 5000 117 127 141 134 128

10000 111 121 135 128 122 25000 103 113 127 120 114

4 4 4 Of fshore Engineer ing

~ ' " ~ I ' ' ' ' " ' ' " " ' " " ' " ' " " ' ' ' " ' " " " " ~ s N l ~ I ~ " ~ ~ , ! '

l" Bottlesl~ps / A I E~.o,.,, I " t4 I_ ,=r=4.9 / /m . =r=52 " !

0 I y

I (orrie~ I / / / / , I i . ~ ~ . / I Freighte, i / ' s ~ ~ ~ ~ ' ~ I I - - ( N o ooo~ ~.o,),,,/--,~--~

,,~1 i ~"~Escortl I .'~.'~.~' 1 / / ~ ~ ; , I ,oo,, /

| Potrol croft ~ ~ ( x ~ , ~ ,,oI / ',~ _ __ c~'~r, 3 m ~ . ~ _ ~ , ~ ~ _ o ~ , , ~ ] . / / '

/ I / / / / [ , 7 ~ ~m~,e"8"1 i

tOO I / / / potrot boot I "1:~ ,,,--,,, _ l ~ ~ ~ ' ~ Y ' l ..2.~ j --/--,.~~

Tug (oceon- going-] . . . . ~.:' 4.:3 -.. 9o' I I / ,/'#' I so~>ge) , I

I / 7 - , , - .~.s I I | i I i l l i l t i t I l I | [ / ' [ I i I i I l | I l l l l m i l i l i l i l i l l | I I I | l i l l I l l i l

6 7 8 SO t5 20 30 3 4 5 6 7 8 t0 t5 20 30 5 6 7 8 10 15 20

F igure 37. Average rad ia ted spec t rum levels (s tandard dev ia t ion of o) for sur face sh ips [11].

160 r " - i f II w i l l ] 1 ! 1 I I I 1 - I " I I

"~ tso ,

1 4 0 -~ ~ ~ ~.....~Periscope Depth 'Speed r 130 . . . .

~ - - - - ~ ~ , ~ 110,, ~ ~ _ ~ ' - 6

r162 10o . . . . . . - ~

~ ,4o ~ . ~ . ~ . ~ Surface . . . .

I . , I 0 CJI

IOO[---:-l [_],llll l__ ~ 6 1 , mOO t . O 0 0 JO.O00

Frequency (1~)

Figure 38. Radiated noise level of several d i f ferent submar ines [22].


ics (water flow past hydrophone and vessel support structures). Figure 39 indicates that machinery is the predominant cause of self noise at low frequency and that the propeller and hydrodynamic noise are the main cause of self noise at high frequency. The self noise associated with machinery is relatively independent of the vessel speed, but the propeller and hydrodynamic noise are strongly affected by speed. Example data for self-noise on a destroyer and submarine are illustrated in Figure 40.

Speed

i

Propeller" Mac j Hydrodynamic

Ambient i

Low " High Frequency

k v

Figure 39. S p e e d a n d frequency relationship for self noise.

5O

| , , |

1 #

/ /

/ , r

/ / ~ / I J

/ / ' Propeller and h y d r ~ l ) ~ i c n ~i~

. . . . . . . i 0 S IO IS 20 2S

Speed (knm) (a)

(

\\

- . . . ,

i i l l l l ] I i l l l i six) r soo t~oo z.ooos~o

--i i

(b)

/

Figure 40. Self noise level for a destroyer (a) and submarine (b) [43].

/ /

/

. / . 2 �9 6


Flow Noise

Flow noise is a form of hydrodynamic noise and is the result of turbulent pressure fluctuations over the face of the hydrophone. Pressure fluctuations are the result of the turbulent boundary layer about the hydrophone. Surfaces should be free of roughness which extends through the laminar boundary layer and affects the turbulent flow. Otherwise, the surface is considered smooth. The coherence of turbulent pressures is determined by experimental correlation coefficients (p) have been evaluated as

PL (S) = e-~ longitudinal separation

PT (S) = e -Sisl transverse separation (100)

where S = Strouhal number (S = fd/u c) f = frequency d = separation distance

u e = convection velocity

The convection velocity represents the velocity at which turbulent eddies trans- late past the hydrophone.

A pressure transducer of finite size discriminates against flow noise to an extent determined by PL and PT" A discrimination factor 13 is defined as

R p

13 = - - (101) R

where R' is the mean squared voltage output of the array in the flow noise and R is the mean squared voltage output of a very small transducer in the same flow noise and having the same sensitivity as the array. Thus, the discrimination factor is a measure of the reduction of flow noise experienced by an array, and it is expressed in Equation 102 and illustrated in Figure 41 for rectangular and circular arrays for elements having a uniform response function. The parameter T should be much greater than one. Variable response functions were investigated by Randall [36] and were found to reduce the response of the array to flow noise in some cases.

0.659 RectangularArray: 13 = ~r where ), =

0.207 CircularArray: I] = T2 where T =

2 n f L

uc (102) 2 n f r

U c


I 0

.| o-, i

ODOI

Underwater Acoustics I 1 1 " 1 1 1 1 1 ' 1 1 �9 I I 1 1 1 ' ' " 1 I l l l l ~

I ' J O

\ kX .... o

- i i 1110

I I 1 1 1 1 1 1 l l I l I I I I I l

t.O ~O tOO

2 x f ~ 2 x f r Strouhal Number

Uc U c

Figure 41. Discrimination of rectangular and circular arrays against flow noise [10, 49].

Flow noise reduction is accomplished by making the hydrophone larger, moving the hydrophone forward, removing hydrophone from turbulent boundary layer, and ejecting polymer fluids. Domes reduce self noise by minimizing turbulent flow, delaying onset of cavitation, and transferring the flow noise source away from the transducer. The domes must be acoustically transparent, produce no large side lobes, be streamlined, and kept free of marine fouling.

Detection Threshold

Detection threshold (DT) is the ratio of the signal power (S) in the receiver bandwidth to the noise power (N) in a 1 Hz bandwidth measured at receiver terminals required for detection with some assigned confidence.

S DT = 10 l o g - (103)

N

Detection probability is for a correct decision that a signal is present, and false- alarm probability is for incorrect decisions when a signal is present. The threshold concept sets a threshold so that the decision "target present" means the threshold was exceeded.


I

C~

O.C

OCO01 0 .~ 0.2 ! 5 20 40 GO 80 ~ ~ ~ . 9 ~J.~Jg

Probability of False Alarm p(FA) %

Figure 42. Detection index (d) as a function of the probabilities of detection p(D) and false alarm p(FA) [43].

For a known signal in Gaussian noise, the detection index is

2E d = ~ (104)

No

where E = total input signal energy in the receiver band N O = noise power in a 1 Hz band

The detection threshold for a known signal power (S) and over a duration time (t) is

S d = = 10 log (105) DT 10 log ~-

No A t

For an unknown signal in Gaussian noise and band width (w), the signal to noise ratio is

s sw

N O N (106)


and the detection threshold is

S dw DT = 10 log . . . . 5 log ~ (107)

N o t

As a rule of thumb, the detection threshold for reverberation

dw DT R=51og , (108)

t

However, reverberation bandwidth w' is generally larger than w (receiver bandwidth). Therefore

dw DT R = - 10 log w' + 5 log ~ (109)

t

Underwater Acoustic Applications

Seismic Exploration

The purpose of seismic exploration is to search for ocean subbottom structural features that might have oil and mineral deposits. One of the necessary conditions for the formation of oil and gas fields are that the rock below the seabed has supported simple life. The adjacent rock stratum must be permeable to allow migration of hydrocarbon molecules in an upward direction. There must be an impermeable barrier to capture the upward migrating hydrocarbons, and the bar- tier must be strong enough to remain impermeable for millions of years. There must be a suitable structure or space below the impermeable barrier consisting of permeable rock to allow hydrocarbon accumulation. The combination of an impermeable barrier and permeable rock must have occurred before or during the migration of hydrocarbons. Therefore, the age of the structure is as important as the size and isolation of that structure.

The various types of subbottom structure where oil and gas are likely to be trapped include anticlines, salt domes, faults, pinchouts, and limestone reefs. An anticline is a common type of trap that occurs below the seabed, and if the anticline has an impermeable layer overlaying a permeable layer, then it may also serve as a hydrocarbon reservoir. Salt domes are formed when a mass of salt flows upward and results in a mushroom type structure beneath the sea bed. The salt structure is impermeable to hydrocarbons, and consequently, petroleum reservoirs may form around the sides of the dome when permeable layers inter- sect the salt dome. A fault that occurs in the seabed may result in an impermeable layer overlaying a permeable layer, and it is called a fault trap. Pinchouts occur when a reservoir bed gradually thins and eventually pinches out. Lime-


stone reefs are often covered by deposition of impermeable material and the reef material is usually porous and acts as a trap for petroleum.

The seismic survey principle uses an acoustic source that is activated at or near the water surface at a known time. Selected acoustic and energy sources for conducting marine seismic profiling are tabulated in Table 16. Acoustic waves radiate downward through the ocean waters and bottom sediments. When there is a major discontinuity between one type of rock and another, part of the signal is reflected back to the surface. Then, by measuring the time taken for this signal to reach and return from each stratum, an estimate of the depth of the stratum below the surface can be determined by assuming a sound speed in the layers. Hydrophones are placed in a straight line (i.e. streamer) at specific distances to record characteristics of the signals and times of their arrivals. Seismic records are stored and played back for interpretation, and grid lines are followed by the vessels conducting the seismic survey.

Analysis of Seismic Reflection Data. Seismic reflection data are recorded on a reflection record that is a record of the voltage output from each hydrophone as a function of time. Each line on the record represents a hydrophone in the array of hydrophones being towed behind the seismic vessel. The distance from the seismic source near the vessel to the individual hydrophones is known and constant. Also the time of initiation of the source signal (e.g., air gun, sparker, boomer) is known and recorded on the record. The reflection record has a series of timing lines or marks across the record at selected time intervals (e.g., 0.01 to 0.005 s). The seismic signal travels through the water and into the seafloor where a portion of the signal is reflected off the first subfloor interface and is received by the hydrophones in the seismic array. The reflected signal is received at different times for each hydrophone and recorded on the seismic

Table 16 Marine Seismic Reflection Profiling Methods and Equipment

Acoustic System Energy Source

Explosive Sources

Air Gun Aquapulse Sparkers

Boomer Vaporchoc

Dynamite Nitrocarbonitrate High pressure air escapes from chamber and oscillates like a bubble. Detonation of propane and oxygen Sound waves are generated by sudden discharge of current in the water between electrodes Disk moves against water High pressure stream injected into the water.


record. Reflections from all the layers detected are identified and marked on the reflection record. The seismic record is analyzed to determine the time that the reflected signal from each layer is received by each hydrophone. These data are then used to determine the depth to the layer. Using similar information for each initiation of seismic signal and the exact geographic location of the seismic vessel, the structure of the ocean subfloor is mapped. These results are subsequently analyzed to locate subfloor structure that is likely to have oil and gas. Explorato- ry drilling and coring is then used to confirm the presence of gas and oil.

Consider the simple case of a level reflecting bottom surface and uniform layer velocity as illustrated in Figure 43. The location (S) represents the seismic source and the location D represents a receiving hydrophone. The horizontal distance between the source and the hydrophone is denoted by "X" and the distance to the reflecting interface or layer depth is denoted by "Z." The straight line distance the signal travels from the source to the reflecting surface is determined by the product of the average sound speed (velocity) of the layer material and one half of the time it takes the signal to reach the hydrophone as determined from the seismic record.

Using the results of the well known Pythagorean theorem, an expression for the relationship between X, T , V and Z is obtained as

= + Z 2 (110)

and after rearranging, the expression is

S D L x J

reflecting surface i R

Figure 43. Simple seismic reflection where S is location of seismic source, D is location of receiving hydrophone, V is average sound velocity in the layer, and T is travel time of reflected ray.


T 2 X 2 4Z 2 = -~T + ~ V2 ( I I I )

This equation is a l inear express ion with a slope (1/V 2) and an in tercept (4Zz/V2). The seismic record analysis provides data for the time it takes the reflected signal to reach each hydrophone whose distance from the source is known and constant. Linear curve fits to the seismic record data of T 2 versus X 2

for example data are tabulated in Table 17.

Table 17 Linear Curve Fits to Example Seismic Record Data

Layer T 2 = f(X 2) Slope Intercept

1 T 2 = 6.7 x 10 -9 X 2 + 0.27054 6.7 X 10 -9 0.27054 2 T 2 = 5.74 x 10 -9 X 2 + 0.53445 5.74 • 10 -9 0.53445 3 T 2 = 4.98 x 10 -9 X 2 + 0.72866 4.98 X 10 -9 0.72866 4 T2= 5.12 x 10 -9 X 2 + 3.12385 5.12 • 10 -9 3.12385

The slope and intercept values are used to evaluate the average sound speed (velocity) (V) in the layer and the depth (Z) to the layer reflecting surface. Example results are tabulated in Table 18 showing the depth to the layer and the average sound speed in the layer. This method of analysis is very simplified, and the analysis of actual seismic records are much more compl ica ted . More advanced texts such as Coffeen [9] should be consulted for more details and

explanations.

Acoustic Position Reference System for Offshore Dynamic Positioning

An offshore dynamic positioning system is used on offshore drilling vessels to maintain position of the vessel over wellheads located on the sea bottom. This system is composed of several basic elements as illustrated in Figure 44.

The purpose of the sensors is to gather information with sufficient speed and accuracy for the controller to calculate the thruster commands so that the vessel performs the desired task. Information required is vessel position, vessel heading, wind speed, and direction. The offshore position reference must include not only navigation but also an accurate and repeatable local position reference. The navigation position is the location on earth 's surface, and the local position needed for thruster control is the location relative to a point of interest on the


Table 18 Example Problem for Data from Seismic Record

Example Calculations for Slope and Average Sound Speed (Velocity) in Layer I

slope = T 2 / X 2 1 S 2 = ~ - = 6.7 • 10 -9 ~ f t 2

V2 _. 1 = 1.4925 x 108 ft 2 / sec 2 6.7 X 10 -9

V - 12,217 f t / s

4 Z 2 ft 2 intercept = - - ~ = 0.27054 - - - " T

0.27054 V 2 Z 2 =

4 Z = 3,177 ft

0.27054 ~ - 12,217

= 10.095 x 106 ft 2

Summary of Example Results

Layer Average Velocity Depth

1 12,217 3,177 2 13,200 4,825 3 14,175 6,050 4 13,975 12,350

ENvIRONME~rT Wind

Waves Position & Current Heading '

C ~ Thrust dThrus'ter' d--Vessel . . . . ~- -~ ,,. C~176 ] Comm=~l.l~ System - I~ Dynamics I

" ] HeadingSemors ~q . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 44. Schematic of an offshore dynamic positioning system.


seafloor. One of the commonly used local position sensors is an acoustic position reference system (Figure 45). The local acoustic systems are restricted to a relatively small coverage area. Types of acoustic position reference systems are the short and long baseline systems that use time of arrival, phase comparison, pinger, and transponder acoustic systems. Typically, the short baseline system uses phase comparisons and the long baseline system uses time of arrival. All systems depend on propagation of an acoustic signal from one point to another through the ocean medium. Therefore, the propagation characteristics of acoustic energy in water affect the performance of the system.

Acoustic systems operate by projecting acoustic energy into the ocean medium. In simple systems the acoustic energy travels only from the subsea beacon to receivers on the vessel. In more complicated acoustic systems the acoustic energy is transmitted from the vessel to a subsea transponder, then the transponder transmits an acoustic pulse back to the vessel. As previously mentioned, the transmitted acoustic signal is affected by the medium through which it must travel. The acoustic signal experiences transmission loss that can be estimated using the spherical spreading plus absorption equation,

TL = 20 log r + o~ r (112)

Ambient and self-noise are also problems that affect the system performance and range of operation.

Supporting Equipment

Vessel Mounted Acoustic Transducers

Propagation Path

. . . . . . . . . . . . . . . . . . . . . . . .

Subsea Acoustic Transducer

L. . . . . . . . . . . . . . . . . . . . . . . J

/ . . . . . . . . . . . . . " - ' - , ' - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

,~I Signal Position FllP' Interface to Processor ~ Computer

. . . .

DP System

: Position |

', Display i

L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J

Figure 45. Schematic of basic acoustic position reference system.


Short B a s e l i n e S y s t e m . A geometrical pattern of transmitters or receivers is located either on the vessel or on the sea bottom. The short baseline system has the array located on vessel, and the long baseline system has the array on sea bottom. The basic surface mounted array geometry (short baseline system) is illustrated in Figure 46. The geometrical arrangement of the array elements and the subsea transducer are shown in Figure 46a. The geometry resultant range (Ro) and its projection on the XA-Z A and Y A-ZA planes is illustrated in Figure 46b, which also shows the angles 0vx and 0vy. These angles are used to determine the horizontal distances between the subsea transducer and the center of the plane containing the vessel mounted array. The vessel uses this information to maintain position relative to the subsea transducer using its dynamic positioning system. If the subsea transducer is located on a subsea wellhead, then the

YA

2d, 3 r - ~ - - - - - ~ 2 Horizoatai Phme of Elemems (1, 2, ;3 & 4) 2 ~ ~ ~ ~ Attacl~d to Botlom of Vemd

g

ZA T ~ r (X~. YA, ZA)

(a) Geometry for E ~ Array meat Sudace (Short Budime)

Y.

"7 ZA

, t X.

Tr~mlucer (XA, YA, ZA)

Co) Geometry for X u d Y Coordimates of Sulmea Tr, mdm~r Relative to Center of Eiemeut Array

Figure 46. Surface mounted array geometry [31].


dynamic positioning system can be used to keep the drilling vessel within tolera- ble limits of the wellhead.

The array elements are assumed to be in the same plane and arranged in a rectangular pattern with sides parallel to the acoustic system coordinate frame (X A, Y A, ZA)" The ranges (R l, R 2, R 3, and R 4) can be measured by the acoustic system. The resultant range R o represents the distance from the center of the vessel mounted array to the subsea transducer. The coordinates of the subsea transducer (reference point) are computed, as derived in Morgan [31 ], using

xA ER3-R2J . E J ' I R3 R2 ] - R4 - R 1 R1

YA =I R22dy-RllIR1 +R2]=[ R 3 2 2dy-N41IR3 +R412

- Oxen] (113)

The ranges for a short baseline system are required to compute the coordinates of the subsea transducer, and they can be de termined by knowing the t ime required for the acoustical signal to travel from the subsea transducer (time of departure) to the vessel mounted array elements. A technique for determining position without knowing the time of departure involves forming differences in the ranges such as

2XA dx R 3 -R 2 = ~ Z A X A R3 -R 2

tan0vx . . . . ZA 2dx

-- sin0vx (114)

Similarly, in the direction Y, the equations are

2Y A dy R 2 - R 1 = ~

ZA YA R2 - R 1

tan0vy = ~ _- Z A 2dy --- sin0vy (115)

To measure the difference in the two ranges (R2-R~), time of departure is not

necessary

R 3 - R E = c 3 (t3 - to) - c2(tg - to)

R 3 - R 2 = c(t 3 - t2) if c 2 = c 3 (116)


This is valid even if the speed of sound in the medium is not constant along the ray path. It is necessary for the sound speed (c) for the two paths to be known and equal. The position of the vessel can then be computed from 0vx and 0vy

Ovx = sin -1 c(t3 - t 1) 2dx

Ovy ---- sin -1 c(t2 - t 1) 2dy

(117)

For small angles and angular ship motions, corrections for vessel motions are important and the reader is referred to Morgan [31 ] for these procedures.

Acoustic Depth Sounders

A typical echo sounder is shown in Figure 47, and it has an electric motor that drives a rotating stylus. At the point where the stylus passes over the zero of the range-scale, a device causes the closing of the transmission contacts, allowing a current to pass through the stylus and recording chart to the earthing plate (plat- en). A mark is made on the recording chart. The stylus travels across the chart range-scale until the echo pulse generates a current that is applied to the stylus, and another mark is made. The stylus next reaches the transmission point once more and the cycle is repeated. At the same time, the motor/gearbox drive moves the chart paper in a plane at fight-angles to that of the stylus movement, and the resulting succession of marks made by the stylus constitutes a time- depth graph.

The stylus speed is adjusted in calibration to be the same speed as that of the acoustic pulse traveling to and from the seafloor. The chart speed is simply a geared-down proportion of the motor speed and is not the same as the vessel's speed. The "time-depth" graph thus does not represent a vertical-horizontal distance profile and the resulting record is not a true profile of the seabed. The chart continues to move as long as the instrument is operating, regardless of whether the vessel is moving or stopped.

Figure 47 shows that one transmission mark and one depth mark provide but little information. The depth mark could be confused with other spots that inevitably appear on the chart due to pitting of electrical contacts and small mid- water targets. Also, the attenuation of the transmitted acoustic power is such that, after the traveling to and from the sea bottom, the echo pulse may not be strong enough for the receiver circuitry to discriminate its arrival from the background noise. However, the succession of stylus marks usually produces a rec- ognizable profile of the bottom. The recorded depth measurements can be related to the position of the vessel using the event marker. Other marks may be made using mechanical cam or slip ring devices, such as time marks, depth scale graduations, and motor speed calibration lines.


Motor and Gearbox Transmission Switch

j ~ Psper Trace Movement I ! ' ' _ ~ : - - ~ _r--~. ~ i ~j

P;',I!, Depth Scale ~ ,J 11I i~ e : | : '. s ! , �9 Stylus Travel " ' ~i =' -J 1 F ~ rS~u' Belt Dflve

I~:" i' / t l + S , ~ - Trolley Bar

I | . i+. . /k ~ J ~ .:1 L. f

IlI~'~RDEll ,

Hull Plate Tram=Bit Receive Trmtsducer Tnmsducer

"t T Transmit Pulse Echo Pulse

Figure 47. Typical acoustic depth sounder [18].

The width of the recording paper is usually designed to represent a number of meters, or feet, of depth (e.g., 30, 50, or 100 m). With a width representing 0-100 m, an echo from a depth of over 100 m is usually not recorded. Also, a depth sounder operating at 30 kHz typically penetrates silty sediments and shows the seafloor and the consolidated matter beneath for several meters. How- ever, a 200 kHz system typically records reflections from the silt alone and often indicates a depth difference of a meter or more than that determined with the 30 kHz system. For this reason, depth sounders are commonly designed to operate at two frequencies simultaneously, especially when siltation and fluid mud are serious navigational problems such as found in the approaches to Europort and US ports along the Gulf of Mexico.


Side Scan Sonar

A side scan sonar is a line array that looks sideways or perpendicular to the survey vessel trace. It operates on two channels with one for each side of the vessel's track. It uses a very narrow beam in the horizontal plane to get high resolution along a strip of seafloor and a broad beam in the vertical plane. The sonar is usually housed in a towed body and images are constructed from successive scans to form a composite picture on a moving strip chart. A sketch of a typical side scan sonar is shown in Figure 48.

Surface Tow Vessel

Submerged Tow Bodl

Port Transducer

Tow Cable

.z-- Starboard Transducer

Swath Width \

Recorder Output of Bethymetry

Figure 48. Top view of a typical side scan sonar system.

A side scan sonar measures and displays ranges to targets from the tow body. The transducer produces the sound pulse and receives the echo. A graphic display shows the echoes and transmitted pulse, but in some cases the transmitted pulse is suppressed. The typical sequence of marks on the graphic display are the transmitted pulse, surface echo, bottom echo, and successive echoes from the seafloor at greater distances from the sonar (slant ranges). The horizontal distance can be calculated based on geometry. Acoustic shadows occur behind objects, and they are shown as white areas on the graphic display. The side scan sonar geometry is illustrated in the Figure 49. The depth of the side scan towbody below the water surface is designated by the numeral 1, and the height of the towbody above the seafloor is defined as numeral 2. Numeral 3 is the slant range to the target and numeral 4 represents the length of the acoustic shadow.


surface vessel . . . . . . . . . . . . .

ide scan Lowbody

3

sea floor I ' ' ' " ' " " ' ' . . . . . . . . . . . . . ' . . . . . . . - I

I L s h a d o w zone

Figure 49. Typical side scan sonar geometry.

Across-track range resolution is the ability to distinguish between two distant objects, and the theoretical minimum separation is one half the pulse thickness (spatial pulse length). Examples of minimum separation are 0.75 cm for 500 kHz sonar and 7.5 cm for 50 kHz. Across track range resolution improves with distance from the tow fish, and a side scan sonar can image targets as small as 1 cm in diameter. The along-track transverse resolution distinguishes between two distinct targets on the seafloor separated in the direction of tow. If the two objects are spread less than the spread of the beam, then the objects are merged on the graphic display. At closer ranges the beam is narrower and the two objects can be resolved. Resolution is also dependent on tow speed and the interval between pulses, but the beamwidth is the most critical factor. Higher frequency sonars have shorter pulse lengths. The narrower beams give better resolution, but the range will be decreased. Lower frequency side scan sonars have greater range but less resolution. Beamwidth can be narrow, horizontal plane (approximately 1 o), or broad, vertical plane (approximately 40~ Example beam patterns for a side scan sonar are shown in the Figure 50.

Absorption, spreading, and scattering tend to weaken a signal returning to the sonar. It is desirable for the sonar data of a given bottom type to look the same at 150-m range as it does at the 50-m range. Therefore, amplification of the returning signal is needed to overcome losses in particular operating areas, and this amplification is called time varied gain (TVG). Self noise and ambient noise can also reach the side scan sonar and interfere with the desired signals. Some detec- tive work is often necessary to determine what the noise source is and how to


~easity (dB)

Ltin Lobe

Back Front

tO"

Typical Vertical Beam Pattern

Typical Horizontal Beam Pattern

Figure 50. Beam pattems for common side scan sonar [20].

eliminate or deal with it. Sometimes you can just turn off a piece of equipment and the noise source is eliminated. Noise can enter the system acoustically or electrically. Acoustical noise enters the system from the water through the transducer as does the signal. Electrical noise is the result of the power supply, cable faults, grounding problems, and components failures.

Examples of interpretation of side scan sonar records are best illustrated in some selected records such as those shown in the following figures. Surface return echoes are illustrated in Figure 51. Multiple reflection echoes from a single target do not occur very often but do occur under certain circumstances. Examples of multiple reflections are shown in the Figure 52. Targets that pro- trude above the bottom block sound rays from reaching the bottom depending on the height of the target and sonar above the bottom. As a consequence a light area (shadow) appears on the sonar record as illustrated in Figure 53. A target projecting above the seafloor typically produces a dark mark followed by a light mark on the sonar record. A depression typically produces a light mark or area preceding the dark return. Examples of depressions are drag marks, trenches for pipelines or cables, and scours.

A target on the seafloor typically shows a shadow immediately following the dark mark of the target. A target above the bottom but below the sonar transducer shows the dark mark of the target followed by the seafloor and then a delayed shadow. A target in the water column that is above the sonar transducer typically shows the dark mark but no shadow follows. An example of a sonar record of the target in the water column is shown in Figure 54.

As a result of the side scan sonar geometry the ranges to the target are actually slant ranges. Thus, the distances on the sonar record to the target are not horizontal. Also, the differences in slant ranges to the leading and trailing edges of the target are always less than the real extent of the target. The closer the sonar

(text continued on page 464)


water surface . . . . . . . . . . . . . . . . . L

towbody(sonar)

water surface

towbody(sonar)

SONAR RECORD

surface surface return -] ~-return

SONAR RECORD

surface surface return -1 [ " r e t u r n

bottom output bottom bottom ---J Lrl L_ bottom pulse output

pulse

Figure 51. Schematic of surface retums for different depths of towbody.

su r face

soaar

pa ths

1-1

1-3-2 2-3-1 2-3-3-2

pipe

Actual Record

. . . ,~ '~. .~.~ . ..

� 9 �9 . ' ~ & �9 " .

Figure 52. Examples of multiple reflections and possible multipaths for side scan sonar.


water surface

S O W

~ONAR RECORD

output pulse depression

Figure 53. Example of depressions and projections in side scan records.

water surface

SONAR RECORD Ae~d Reem'd

output

I! m Figure 54. Example side scan record of targets.


(text continued from page 461)

is to the target, the more the distortion. Corrections can be made using horizontal offset calculations and target height calculation can also be made as shown in the Figure 55 and Equations 118 and 119. The horizontal offset (r t) to the base of the target is determined by

1

r t : ( s ~ - h s 2 ) ~ (118)

where h s = height of the tow body above the bottom s t = slant range to the target as measured from the side scan record.

The target height is evaluated by

ss(hs) h t = ~ (119)

S t + S s

where s s = length of the acoustic shadow as measured from the side scan sonar record

As an example, a survey vessel has conducted a side scan sonar survey at a speed of 3 m/s. The recorder line density was 50 lines/cm and the 40 m range was selected. Assuming the sound velocity was 1,500 m/s, determine the hori-

S \

surface vessel . . . . . . . . . . .

sea surface

~ _ _ _ ~ e scan towbody

, S t

h s

' , . . . . . . _ . . . . . . . . . . . . . , [

EL rt -1_1 t - L_ shadow zone . . w I

Figure 55. Horizontal offset and target height calculations for side scan sonar record.

0.25 cm


Across-track 2 4 6 8 10 12 14 16 18 20 cm

i I - I , I ! , t i' " i i.lil

i ~ [ . . . . 1 ! J t j ! surface bottom

Figure 56. Side scan sonar record example.

zontal d is tance (rt) to the center of buoy, its he ight (ht) above the b o t t o m and

d iame te r f r o m the part ial record shown in F igure 56.

The resul ts for the d iameter , r t and h t are tabula ted in Tab le 19. The d i ame te r

o f the buoy is 2 m and the hor izonta l d is tance to the cen te r o f the b u o y is 15.9 m

normal to t rack o f the survey vessel . The he igh t o f the cen te r of the b u o y above

the bo t tom is 2.1 m.

Table 19 Calculations from Example Side Scan Sonar Record

Across-track scale = range/paper width = 40m/20 cm = 2 m/cm Along-track scale = vessel speed • line density • range/750 = (3 m)(50 m)(40 m)/750

crn/s = 8 rn/cm

Towbody depth = number of divisions (1 division = 1 cm) across track • across-track scale = 1 cm (2 m/cm) = 2 m

Depth of water = 4 cm (2 m/cm) = 8 m Height of towbody above the bottom (hs) = 8 m - 2 m = 6 m Horizontal distance to center of buoy (rt)

Equation 118 yields: r t = afst 2 - hs 2 = ~ [(8.5 cm)(2 m/cm)] 2 - [ 6 m] 2 = 15.9 m

Height to center of the buoy

hs(s s) 6m(4.5 cm • 2m/cm) 54 Equation 119 yields: h t . . . . . 2.1 m

s t + s s 8.5 cm • 2m/cm + 4.5 cm • 2 m/cm 26

Diameter of Buoy

Diameter = number of divisions along track (1 division = 0.25 cm) • along track scale (8 rn/cm)

Diameter = 0.25 cm • 8 m/cm = 2 m

Subbottom Profiler

The opera t ion o f subbo t tom prof i lers is typ ica l ly in the low k H z range (e.g.

10 -50 kHz) . The use o f these l ower acoust ic f r equenc ies r educes the potent ia l


resolution but allows penetration into marine sediments, permitting geotechnical inspection of the seafloor, as well as the possible location of buried objects such as wreck artifacts, cables, or pipelines. Figure 57 shows a subbottom profiler output and demonstrates that brine jets with a salinity of approximately 230 o/oo (parts per thousand) are detected as the jet rises above the seafloor from nozzles in a buffed brine pipeline [51 ].

45

50

55

60

65

70

75

Depth (ft)

1~ ~ =1,~ ~.~ 11- ' . . . . . . . ~ . _~ , . , ~ . . . . . . ~1,._-.,:. . . . . . . . , , . , - t ..- ,-- I - ,, - - t . �9 ~ ".

I il ,~:

"'i: '-" ,,:c-a..:'.,:-,'~-':.U .... ~-I ,=..:-..:: ,-~::::. z,,:..:..:~.~.-: t i : : : , .~ i , :p i : ..... 1.11 .,;. : : t : ' . " " 1 ~ . . . . . . . " . . . . . . ' , t ~ ; . - ' : - ' - ~.'..~: . . . . . . ~ . ' 1 " . ' . ' - " ~ : : . . . . . . . ] l l ~ ,~ - " ,~11C~ I . ~ ' . ' - . ' : . . . . . . .

- : - ' : . . . . : = . . . . . . . . . . . . . ~' . . . . . . ~ .... : . . . . . . . . . . . . . . . . . �9 . . . . 10 | ~: . ' -~ . . . . . . . . . . �9 ~: .... " �9 '1i.~" I ~'-',: ....... :::~, ':::- . .: , ." :'-'-":~"-" ~:',:::":":i'" "," :':1 I ~ :-.-..-~::::.-,'. : : , : : .~~I.,:;-.

!i t

�9 " - , . ; ~ - . . . - . . . . . . . . . . . . ..: . . . . . ~ : ~ ' . . , i - . - : . - . ~ : : . . . . ~ ~ - - : - . ; . . . . : - : - . : r , - �9 . . . . . . :.. . . . . . ; ..... ..... - - , , - , , ..... . .

22

Depth (m)

Figure 57. Output from a subbottom profiler measuring brine jets issuing from bottom diffuser buried in seafloor.

Acoustic Positioning and Navigation

Transponders are deployed in pairs or in larger networks and can interact with each other to allow determination of their separation by acoustic pulse time-of- flight measurement. The simplest transponders are acoustic beacons that remain in a passive, listen-only mode until awakened by an interrogation pulse, usually transmitted by a searching recovery vessel. They then respond to further interrogation pulses allowing, to some degree, the surface vessel to position itself verti- cally above the beacon, at which time the transponding round-trip delay is at a minimum.

The method is extended in underwater navigation systems, by installing at least three slave transponder units at particular geographic locations. The master transponder is able to activate coded responses from each of the bottom mounted beacons (slaves) so that, as Figure 58 illustrates, slant ranges between the master and each of the slaves can be measured and, by a process of triangulation, location within the survey area is determined. There are long-baseline and short- baseline systems similar to that described for dynamic positioning systems. The


Figure 58. The circular acoustic navigation principle [8].

former terminology is for seafloor slaves and the latter is from ship- or platform- mounted equipment. The method illustrated in Figure 58 is spherical navigation. The mobile transponder is considered to be at the unique point of intersection of three hemispheres entered on each of the three slaves and of radii equal to each of the respective slant ranges. The intersection of only two such hemispheres produces a vertical semicircular locus of possible positions, rather than a unique- ly determined location. Circular, or transponding navigation has the disadvan- tage that the mobile transponder must have an active transmitter.

Acoustic Doppler Measurements

The Doppler effect is the frequency shift that occurs when either an observer moves with respect to the transport medium, or the medium itself moves. The effect is used in several types of sonar measurement equipment among which is the Doppler current meter. This device, illustrated in Figure 59, is used to measure water velocity at a point, or movement of an object through the water. The operating principle is that of a high-frequency continuous wave sonar with spatially separated transmit and receive transducers. The horizontal flow component along the sound axis between heads A and B and heads C and D of the meter generates Doppler shifts of magnitude

AfAB = fo(V/C)COS0 and mfcd = fo(V/c)sin0 (120)

From these equations, speed v and the direction angle 0 are easily obtained. A similar principle is used in Doppler logs that allow the forward speed and

sideways drift of a submersible to be determined. The calculations involved are similar, except that an additional angular dependence is introduced by a downward depression angle of the beams. The Doppler shift information is contained


C

A

Figure 59. Doppler measurement of water velocity or vehicle velocity using underwater acoustics [8].

in backscattered, rather than reflected, sound. A range-gated Doppler log has been successfully operated for ocean remote current sensing. For this application, the concept is to inspect the Doppler shift on signals backscattered in the consec- utive range cells of a pulsed high-frequency sonar. The instrument takes advan- tage of the signal processing power available using modern microelectronics.

The Doppler principle has also been used with considerable success in moni- toring seafloor geotechnical properties. In this case, a constant frequency 12- kHz transmitter is placed in the tail of a free-fall, torpedo-shaped penetrator. As the penetrator descends, it accelerates, with a corresponding Doppler shift, until it reaches a terminal velocity which, for a two-ton penetrator, can exceed 100 miles per hour (50 ms-~). At this speed the received signal at the surface is approximately 11.6 kHz. On impact the penetrator decelerates, and the Doppler shift decreases to zero. This allows the deceleration profile to be measured and the depth of penetration to be calculated. As a result, the sediment strength can be estimated remotely, without coring.

Water currents in the ocean and in the laboratory are now commonly measured using acoustic Doppler techniques. An example of an acoustic Doppler current meter is shown in Figure 60. A Doppler current meter has the capability of measuring currents at different depths. Its principle is based on the concept that the acoustic signal is reflected off particles in the water, and the speed of the particle causes a Doppler shift in the return signal. The resulting frequency shift is directly related to the water current in which the particle is traveling. This principle is also used in the laboratory to obtain three components of velocity, and an example of such an instrument is illustrated in Figure 61.


Figure 60. Typical acoustic Doppler current meter (courtesy of RD Instruments).

Transmit Receive Transducer Transducer

�9 d

b 30 ~ t d 4V

�9 �9

S~n~pling ~" VOlume

Figure 61. Acoustic Doppler velocimeter for laboratory (courtesy of Sontek).

References

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2. Anderson, V. C., 1967. "Frequency Dependence of Reverberation in the Ocean," J. Acoustical Society of America, 41:1467.

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Sound No. 2: Sounds from Submarines," National Defense Res. Comm., Div. 6, Sec. 6.1-NDRC- 1306.

23. Leroy, C. C., 1969. "Development of Simple Equations for Accurate and More Realistic Calculation of the Speed of Sound in Seawater," J. Acoustical Society of America, 46:216.

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29. Milne, A. R., 1964. "Underwater Backscattering Strengths of Arctic Pack Ice," J. Acoustical Society of America, 36:1551.

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