SONAR   - physical facts, implementation theories and notes
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To correctly simulate underwater acoustics or at least to approximate
its simulation we need to take care of some physical facts.


Noise sources
-------------

There are many sources of noise in the ocean. Beside the disturbances of
the ocean surface by the wind and sudden events like exploding depth
charges etc. the most important source are the vessels cruising around
the sea.  This means the ships and submarines of the game.

Each noise source has a (characteristic) spectrum of frequencies it
emits. We can visualize such a spectrum by a 2d graph, that has the
frequency as the horizontal scale and the corresponding amplitude as the
vertical scale.

^ Amplitude (dB)    xxx                                     
|                  x | x                                                         
|                  x | x           gaussian curve or similar
|                 x  |  x                                                        
|               xx   |   xx                                                      
|             xx     |     xx                                                    
--------------------------------------------> frequency (Hz)
                     |
          peak frequncy or typical frequency

The spectrum shape depends on type of the engine and the throttle of it
and of course of many other things. To simplify simulation we state that
the spectrum is shaped similar like a gaussion curve around a typical
frequency. This frequency is shifted by the throttle of the engine. Thus
each vessel type or engine type has one characteristic frequency. Of
course the strength of the signal is also increased with higher
throttle.

Of course each noise source emits a characteristic composition of
frequencies, that can be identified by the human ear or brain as a
specific noise. E.g. warship steam turbines sound different than a
submarine's piston engine. For the simulation of detection of the
signal's source we can simplify this fact.

The passive sonar devices or hearing devices used by german submarines
worked with underwater microphones that were sensible for a specific
frequency (GHG around 900Hz). Direction of sound sources was detected by
turning the device's internal apparatus so that the sound signal reaches
its maximum amplitude. The accuracy of this measurement depends on the
frequency of the signal: the higher the frequency, the more accurate is
the angular resolution of direction measurement.

This leads us to the conclusion that for simulating detection via GHG
and other devices we need to take care only of the typical frequency of
the source. This determines the range of the signal and the accuracy of
direction finding, combined with a correction factor that reduces
strength of the signal depending on distance and deviation against
optimal microphone listening frequency.

Another idea is to transform the typical frequency spectrum to a
discrete form. Partition the whole frequency spectrum in a fix number of
frequency bands, like low, medium and high frequencies or a few more
categories. Then compute the strength of the sound for each band for any
sound source. The distribution of the strengths over the bands give the
typical noise signature.

It can be helpful to simulate the sound strengths in a logarithmic base,
as sound strengths can vary greatly. The unit is already logarithmic (dB
= deci-Bel, tenth of a Bel, wich is the logarithm of basis 10 of the
strength). So sound strength in dB is 10 * log_10 ( Strength ). We can
name the strength also intensity (I).

A low number of frequency bands (around four or five) should be enough
for simulation. Low band would be below 500Hz or so, Medium-low around
the typical hydrophone listening frequency of 900Hz, Medium 1khz to 3kHz
and High from 3kHz and above. Sounds with higher frequencies than 7kHz
are very rare and should fall off too fast to be detected.


Physics of sound
----------------

Sound propagates as waves underwater, its speed depending on many
factors, like temperature (the most important), pressure, salination and
other values of the water (amount of algae etc.).

Computing the noise level at any point in the ocean we can use the ray
tracing model to simulate sound propagating from an arbitrary
source. Sound waves propagate in water, are reflected and refracted on
borders between layers in the water and so on. If the sound ray
intersects a the border between two layers with different speed of
sound, the ray is reflected and refracted according to Snell's law. Also
other vessels can reflect sound waves etc. This simulation can be
extended to a great complexity.

The speed change is not so important in horizontal (x/y) direction, but
in vertical (z) direction as the water forms mostly horizontally
oriented layers. Temperature is the most important factor. We need to
simulate reflection and/or refraction at border of those layers, at
least for active sonars like ASDIC.

Hiding the submarine "below" a thermal layer was and is an important
tactical aspect of submarine warfare.

Sound strength is decreased with growing distance when the sound spreads
in the water. Lower frequencies are transmitted over a longer range.

This is named propagation and absorption. Strength of the sound is
distributed over the area the sound is spread. Because the area grows
quadratically with the distance, the strength falls off with the square
of the distance. Absorption depends on frequency of the sound, higher
frequencies are absorpted with an much higher rate. Using the
logarithmic model for sound strengths the squares etc. can be written as
multiplications or divisions, which gives simple formulas.

We add the background noise strength (ambient noise) as well as all the
noise sources to the strength of one signal, subtract the
signal-to-noise-ratio level of the receiver (signals weaker than a
certain level are cut off) and do this for each frequency band. This
gives the frequency spectrum that is received at the sub's sonar.


Hearing device specials
-----------------------

The number of microphones and the number of strip lines (membranes) in
the device determine the resolution of direction finding, as well as the
frequency and strength of the signal.

To correctly detect the signal and to distinguish between left/right and
front/aft signals, groups of the microphones could be disabled.

To allow reliable detection a submarine needs to dive below 20m to avoid
the disturbing noises of the ocean surface.

The operator of a device can detect any number of signals (as long as
the resolution allows it). But to keep track of more than one signal he
needs to switch permanently between two signals and redetect them. This
is a difficult and time consuming process. Thus the simulation should
limit the number of signals he could keep track of to, say,
max. five. Of course he could mix up two signals that are to close to
each other and start tracking a wrong signal. And the update of the
actual position of each signal is delayed by the detection process for
the other signals. E.g. if the operator needs 5 seconds to localize one
signal and keeps track of three, he can update the position of each
signal only every 15 seconds. This is an important aspect of
simulation. Too many noise sources will disturb the correct localization
as well.

Sound simulation
----------------

Some more aspects need to be taken into account. There is always some
background noise in the sea, so we have to take care of the "signal to
noise ratio" of each signal.