So I was curious about comparing the performance of the array-based NN Wiener filter versus the single seismometer filter (the seismometer that sits at the test mass). I considered two different instrumental scenarios (seismometers have SNR 10 or SNR 1), and two different seismic scenarios (seismic field does or does not contain high-wavenumber waves, i.e. speed = 100m/s). Remember that this is a 2D simulation, so you can only distinguish between the various modes by their speeds. The simulated field always contains Rayleigh waves (i.e. waves with c=200m/s), and body waves (c=600m/s and higher).
There are 4 combinations of instrumental and seismic scenarios. I already found yesterday that the array Wiener filter is better when seismometers are bad. Here are two plots, left figure without high-k waves, right figure with high-k waves, for the SNR 1 case:
'gamma' is the coherence between the NN and either the Wiener-filtered data or data from seismometer 0. There is not much of a difference between the two figures, so mode content does not play a very important role here. Now the same figures for seismometers with SNR 10:
Here, the single seismometer filter is much better. A value of 10 in the plots mean that the filter gets about 95% of NN power correctly. A value of 100 means that it gets about 99.5% correctly. For the high SNR case, the single seismometer filter is not so much better as the Wiener filter when the seismic field contains high-k waves. I am not sure why this is the case.
The next steps are
A) Simulate spherical waves
B) Simulate wavelets with plane wavefronts (requires implementation of FFT and multi-component FIR filter)
C) Simulate wavelets with spherical wavefronts
Other goals of this simulation are
A) Test PCA
B) Compare filter performance with quality of spatial spectra (i.e. we want to know if the array needs to be able to measure good spatial spectra in order to do good NN filtering) |