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Message ID: 177     Entry time: Tue Jan 25 11:57:23 2011
Author: Jan 
Type: Computing 
Category: Seismometry 
Subject: wavelets 

Here is the hour of truth (I think). I ran simulations of wavelets. These are not anymore characterized by a specific frequency, but by a corner frequency. The spectra of these wavelets almost look like a pendulum transfer function, where the resonance frequency now has the meaning of a corner frequency. The width of the peak at the corner frequency depends on the width of the wavelets. These wavelets propagate (without dispersion) from somewhere at some time into and out of the grid. There are always 12 wavelets at four different corner frequencies (same as for the other waves in my previous posts). The NN now has the following time series:

Data_WA4f3.jpg

You can see that from time to time a stronger wavelet would pass by and lead to a pulse like excitation of the NN. Now, the first news is that the achieved subtraction factor drops significant compared to the stationary cases (plane waves and spherical waves):

Perf_rel_Spiral20_WA4f3.jpg

And the 4*pi, 10 seismometer spiral dropped below an average factor of 0.88. But I promised to introduce an absolute figure to quantify subtraction performance. What I am now doing is to subtract the filtered array NN estimation from the real NN and take its standard deviation. The standard deviation of the residual NN should not be larger than the standard deviation of the other noise that is part of the TM displacement. In addition to NN, I add a 1e-16 stddev noise to the TM motion. Here is the absolute filter performance:

Perf_abs_Spirals_WA4f3.jpg

As you can see, subtraction still works sufficiently well! I am now pretty much puzzled since I did not expect this at all. Ok, subtraction factors decreased a lot, but they are still good enough. REMINDER: I am using a SINGLE-TAP (multi input channel) Wiener filter to do the subtraction. It is amazing. Ideas to make the problem even more complex and to challenge the filter even more are welcome.

 

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