The simulation is not a good representation of a real detector. The first step to make it a little more realistic is to simulate variables that are actually measured. So for example, instead of using TM acceleration in my simulation, I need to simulate TM displacement. This is not a big change in terms of simulating the problem, but it forces me to program filters that correct the seismometer data for any transfer functions between seismometers and GWD data before the linear estimation is calculated. This has been programmed now. Just to mention, the last more important step to make the simulation more realistic is to simulate seismic and thermal noise as additional TM displacement. Currently, I am only adding white noise to the TM displacement. If the TM displacement noise is not white, then you would have to modify the optimal linear estimator in the usual way (correlations substituted by integrals in frequency domain using freqeuncy-dependent noise weights).
I am now also applying 5Hz high-pass filters here and there to reduce numerical errors accumulating in time-series integrations. The next three plots are just a check that the results still make sense after all these changes. The first plot is shows the subtraction residuals without correcting for any frequency dependence in the transfer functions between TM displacement and seismometer data:
The dashed line indicates the expected minimum of NN subtraction residuals, which is determined by the TM-displacement noise (which in reality would be seismic noise, thermal noise and GW). The next plot is shows the residuals if one applies filters to take the conversion from TM acceleration into displacement into account:
This is already sufficient for the spiral array to perform more or less optimally. In all simulations, I am injecting a merry mix of wavelets and spherical waves at different frequencies. So the displacement field is as complex as it can get. Last but not least, I modified the filters such that they also take the frequency-dependent exponential suppression of NN into account (because of TM being suspended some distance above ground):
The spiral array was already close to optimal, but the performance of the circular array did improve quite a bit (although 10 simulation runs may not be enough to compare this convincingly with the previous case). |