A spiral shape is a very good choice for array configurations to measure spatial spectra. It produces small aliasing. How important is array configuration for NN subtraction? Again: plane waves, wave speeds {100,200,600}m/s, 2D, SNR~10. The array response looks like Stonehenge:
A spiral array is doing a fairly good job to measure spatial spectra:
The injected waves are now represented by dots with radii proportional to the wave amplitudes (there is always a total of 12 waves, so some dots are not large enough to be seen). The spatial spectra are calculated from covariance matrices, so theory goes that spatial spectra get better using matched-filtering methods (another thing to look at next week...).
Now the comparison between NN subtraction using 20 seismometers, 19 of which randomly placed, one at the origin, and NN subtraction using 20 seismometers in a spiral:
A little surprising to me is that the NN subtraction performance is not substantially better using a spiral configuration of seismometers. The subtraction results show less variation, but this could simply be because the random configuration is changing between simulation runs. So the result is that we don't need to worry much about array configuration. At least when all waves have the same frequency. We need to look at this again when we start injecting wavelets with more complicated spectra. Then it is more challenging to ensure that we obtain information at all wavelengths. The next question is how much NN subtracion depends on the number of seismometers. |