[转贴]The Sonar Equations(声纳方程)

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Sonar may be either active or passive. Active sonar provide their own sound source and listen for echoes as they are reflected from the target which they are trying to detect. Passive sonar have no such source. They are simply listening devises that rely on the target to emit their own noise source (e.g. engine noise from an enemy ship or communication noises from a whale).
The sonar equations were developed during World War II to facilitate calculations of the maximum range of sonar systems. A knowledge of sonar range is essential in military operations in order to plan appropriate strategic tactics . Since this time the sonar equations have been used to design and evaluate a whole range of underwater instrumentation. The sonar equations deal with all aspects of sound generation, propagation and attenuation underwater and for this reason provide an excellent framework for an academic study of underwater acoustics.

The sonar equations are founded on the basic equality between the desired (signal) and undesired (background) portions of the received signal. For sonar to successfully detect an acoustic signal we require that:

Signal Level > Background Level

This basic equality can be expanded in terms of the sonar parameters. These parameters can be separated into 3 groups parts including those that deal with:

1) The equipment.
     e.g. Source Level (SL), Directivity Index (DI), Detection Threshold (DT)
2) The medium.
    e.g. Transmission Loss (TL), Reverberation Level (RL), and Noise Level (NL)
3) The target.
    e.g. Target Strength (TS)

Note that all of these parameters are expressed on a logarithmic scale in dB. Here the source level (SL) is a measure of the acoustic intensity of the signal measured one metre away form the source. This parameter assumes that the acoustic energy spreads omnidirectionally outwards away from the source. However, most acoustic sources are designed to focus the acoustic energy into a narrower beam in order to improve efficiency. This effect is accounted for in the sonar equations by the directivity index (DI), a measure of focusing. The detection threshold (DT) is a parameter defined by the system. If the observed signal to noise ration exceeds the detection threshold a target is deemed to be present.

The intensity of an acoustic signal reduces with range. This observed reduction in the acoustic signal with distance from the source is due to the combined effects of spreading and attenuation and is accounted for by the transmission loss term (TL).

The target strength (TS) is a measure of how good an acoustic reflector the target. The echo level will increase with target strength.
  

There are essentially two types of background that may mask the signal that we wish to detect:
1) Noise background or Noise Level (NL). This is an essentially a steady state, isotropic (equal in all directions) sound which is generated by amongst other things wind, waves, biological activity and shipping.
2) Reverberation background or reverberation level (RL). This is the slowly decaying portion of the back-scatted sound from one's own acoustic input. Excellent reflectors in the form of the sea surface and floor bound the ocean. Additionally, sound may be scattered by particulate matter (e.g. plankton) within the water column. You will have experienced reverberation for yourself. For example if you shout loudly in a cave you are likely to here a series of echoes reverberating due to sound reflections from the hard rock surfaces. These reverberations decay rapidly with time.

Although both types of background are generally present simultaneously it is common for either one or the other to be dominant. This is illustrated in the figure below:

The graph above shows a how the intensity (dB) of the echo level (EL) is reduced with range due to both spreading and attenuation. The reverberation level (RL) also drops off with range but less rapidly than the echo level. In the example shown above there is a range Rr above which the RL > EL. At ranges greater than Rr, the signal will be undetectable. Notice that the noise level for this case (solid black line) is too low to become limiting. This case is referred to as reverberation limited.

An alternative situation is illustrated by the dotted black line (noise level 2) where there exists a certain range Rn, above which the noise level exceeds the echo level thus preventing detection. This second example is the noise limited case. Notice that the noise level is independent of range.

There are three basic forms of the sonar equations:
1) Active noise background sonar equations.
2) Active reverberation background.
3) Passive sonar equation.

Let us consider these in turn:

1) The Active Noise-background Sonar Equation.
This is probably the most commonly implemented form of the sonar equations. In an active sonar system the return signal will be increased by the source level, directivity index and target strength but reduced by the two way transmission loss and noise level. Thus, the echo to noise ratio as determined by the sonar is:

SL + DIT + TS - 2TL - (NL-DI)
Equation 1.

Remember that since these parameters are all in dB the addition and subtraction represents multiplication and division in real terms. Notice also that there has been a distinction made in the equation above between the directivity of the source (DIT) that focuses the source energy and the directivity index of the hydrophone that reduces the effective noise level. The later in analogous to an ear trumpet that used to be used by people with poor hearing. When placed to the ear this conical devise not only amplifies the acoustic signal, it also reduces isotropic ambient noise.  This is because the device only excepts sound from a limited range of directions. Thus, sonar performance can be improved by having both directional source and hydrophone, providing that they are directed towards the target. Often the acoustic source also acts as the hydrophone. In this situation, DIT and DI are equivalent.

It is customary to define a critical signal to noise ratio that defines whether a target is present or absent. This parameter is defined as the detection threshold (DT). Thus, the full expression for our active noise background sonar equations is:

SL + DIT + TS - 2TL - (NL-DI) = DT
Equation 2: The Active, Noise-background Sonar Equation

2) Active Reverberation-background Sonar Equation
In the reverberation limited case sound energy from the acoustic source is backscattered (from the sea surface / bed or particulates within the water) masking the received signal. The effect of reverberation puts an upper limit on the source level. In general, it is true that increasing the source level will increase the echo level. However, there is a definite upper limit to the increase in efficiency with source level. When SL exceeds a certain level, the amount of backscattered sound (reverberation) swamps the signal. The reverberation-limited case will be particularly important when trying to detect targets that are close to the seabed or seafloor. In the case of reverberation, the directivity of the receiving hydrophone is not appropriate, as reverberation is not isotropic. Thus, the NL-DI term in the active sonar equations is replaced by the reverberation level term, RL.

SL + DIT + TS - 2TL - RL = DT
Equation 3: The Active Reverberation-background Sonar Equation

3) The Passive Sonar Equation (listening devises)
In the passive case, the sonar itself is the source (SL), target strength becomes irrelevant, and the transmission loss term (TL) is one-way. Thus, the passive sonar equations is:

SL + DIs -TL - (NL-DI) = DT
Equation 4: The Passive Sonar Equation

Notice that DIs in this case refers to the directivity of target-source. The passive sonar equation will always be noise limited as sound will always be back-scattered towards the target and not the receiving hydrophone. You will also notice that the two-way transmission loss (2TL) has been replaced by the one way TL.

来自中科院海底声学教研室

[ 本帖最后由 upload 于 2006-11-10 07:22 编辑 ]

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中文版本见刘伯胜教授的《水声学原理》绪论