The reader of this paper should first imagine a plate, as large as a continent. We can place on the borders of this plate instruments, that are sensitive to vibrations (earth- or platequakes), that can occure somewhere on the plate. And now we will try to imagine, that such earthquake happens on our plate (for example in the middle of it).
On a drawing it can be shown in following way:
Arrows are showing the places, where our instruments are situated. How we can obtain the information, where was the source of earthquake (epicenter). It is probably very popular knowledge, that this can be calculated, if the time of flight of the signal form the epicenter to our instrument is known and readings from at least two instruments are available. Because we normaly do not known the time of flight, but only the moment, when the signal from earthquake was measured, three instruments and three measurements are necessary.
In the case of the earthquake it is naturally more complicated, because it is necessary to know the speed of the wave on the way to the receiver and this can change on the way. But it is true, that for a not very exact calculation of the loaction of the earthquake source a relativ simple calculation can be enough.
Now we can imagine a more realistic situation: If we take a thic metal (or glass) plate and place on their side microphones, that can receive sounds, propagating in the plate, we can make following experiments:
If we generate a sound somewhere in the medium of the plate for example knocking on it, our microphones will receive - after some time, necessary for its propagation - this sound, and we can calculate, at which place this sound was generated.
If we generate a sound wave in the middle of plate, that is going from their bottom to the upper wall, our microphones will not hear anything, because the sound wave will be reflected back and for the between both walls. But the experiments shows, that in the case, if in the region, where this sound wave will be reflected, something is lying (in contact with the surface of the plate) part of the sound wave will be scattered in different directions, and along the plate too. Our microphones will receive the sound and we can calculate where our object is lying on the plate.
This effect can be called as a contact scattering and is probably easy to imagine, what causes it: If nothing is disturbing the surface of the plate, the wave will be reflected and propagates toward the source on the opposite wall. But if the surface is disturbed by something lying on it, the reflection is not normal and part of the wave energy is taking another way. We are now not able to tell exactly and describe theoretically, what happens in this case (especially depending on materials in contact, pressure, etc.), butthis can be easily shown.
We can assume, that the point of contact becomes a kind of secondary sound sorce, that our microphones can "hear". And it is easy to imagine, that the situation is about the same as in the case of investigating of earthquakes, but may be simpler, because we have here a homogenous plate.
It is easy to imagine, that the detection of small amount of sources can be made with a simple mathematics (signals are easy to separate). Especiall easy is to imagine, what happens, when we have one source and many detectors. This situation can be shown on the following picture, and was detected with the setup, where the plate was round and the source of pulse not central. Timeof flight (coming of pulse) detected by each detector (y-axis) is different (x-axis), but the differences are smooth and shows a sinus line on the picture:
After calculation (reconstruction), the location of the sound source can be shown:
It is more complicated to explaine, how to calculate the signals in the situation, where many sources are existing. But even this is not as complicated as it seems to be. And it could be interesting for the reader, that procedures, that can be used here was first proposed more than two hundred years ago for earthquakes localisation and earth structureresearch with sound waves, that was artificially generated.
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