All right. The next problem I wanted to look at was if the ability of the seismic array to produce spatial spectra is somehow correlated with its NN subtraction performance. Now whatever the result is, its implications are very important. Array design is usually done to maximize its accuracy to produce spatial spectra. So the general question is what our guidelines are going to be? Information theory or good spatial spectra? I was always advertizing the information theory approach, but it is scary if you think about it, because the array is theoretically not good for anything useful to seismology, but it may still somehow provide the information that we need for our purposes.
Ok, who wins? Again, the current state of the simulation is to produce plane waves all at the same frequency, but with varying speeds. The challenge is really the mode variation (i.e. varying speeds) and not so much varying frequencies. You can always switch to fft methods as soon as you inject waves at a variety of frequencies. Also, I am simulating arrays of 20 seismometers that are randomly located (within a 30m*30m area) including one seismometer that is always at the origin. One of my next steps will be to study the importance of array design. So here is how well these arrays can do in terms of measuring spatial spectra:
The circles indicate seismic speeds of {100,250,500,1000}m/s and the white dots the injected waves (representing two modes, one at 200m/s, the other at 600m/s). The results are not good at all (as bad as the maps from the geophone array that we had at LLO). It is not really surprising that the results are bad, since seismometer locations are random, but I did not expect that they would be so pathetic. Now, what about NN subtraction performance?
The numbers indicate the count of simulation runs. The two spatial spectra above have indices 3 (left figure) and 4 (right figure). So you see that everything is fine with NN subtraction, and that spatial spectra can still be really bad. This is great news since we are now deep in information theory. We should not get to excited at this point since we still need to make the simulation more realistic, but I think that we have produced a first powerful clue that the strategy to monitor seismic sources instead of the seismic field may actually work. |