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Message ID: 176     Entry time: Mon Jan 24 15:50:38 2011
Author: Jan 
Type: Computing 
Category: Seismometry 
Subject: Multi-frequency and spherical 

I had to rebuild some of the guts of my simulation to prepare it for the big changes that are to come later this week. So I only have two results to report today. The code can now take arbitrary waveforms. I tested it with spherical waves. I injected 12 spherical waves into the field, all originating 50m away from the test mass with arbitrary azimuths. The 12 waves are distributed over 4 frequencies, {10,14,18,22}Hz with equal spectral density (so 3 waves per frequency). The displacement field is far more complex than the plane-wave fields and looks more like a rough endoplasmic reticulum:

Field_SW4f3.jpg

The spatial spectra are not so much different from the plane-wave spectra:

Map_10Hz_SW4f3.jpg

The white dots now indicate the back-azimuth of the injected waves, not their propagation direction. And we can finally compare subtraction performance for plane-wave and spherical-wave fields:

Performance_Spiral20_PW4f3.jpgPerformance_Spiral20_SW4f3.jpg

Here the plane-wave simulation is done with 12 plane waves at the same 4 frequencies as the spherical waves, and in both cases I chose a 20 seismometer 4*pi spiral array. Note that the subtraction performance is pretty much identical since the NN was generally stronger in the spherical-wave simulation (dots 5 and 20 in the right figure lie somewhere in between the upper right group of dots in the left figure). This makes me wonder if I shouldn't switch to some absolute measure for the subtraction performance, so that the absolute value of NN does not matter anymore. In the end, we don't want to achieve a subtraction factor, but a subtraction level (i.e. the target sensitivity of the GW detectors).

Anyway, the result is very interesting. I always thought that spherical waves (i.e. local sources) would make everything far more complicated. In fact, it does not. And also the fact that the field consists of waves at 4 different frequencies does not do much harm. (subtration performance decreased a little). Remember that I am currently using a single-tap FIR filter if you want. I thought that you need more taps once you have more frequencies. I was wrong. The next step is the wavelet simulation. This will eventually lead to a final verdict about single-tap v. mutli-tap filtering.

 

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