KAGRA Logbook

# Summary
(only violin modes within 160-200Hz)
I show the figures that the shift in the peak frequency (Fig1) and the change in the fitted width(Fig2) with respect to Oct15. Peak frequency is systematically shifted toward higher frequency. Width seems not be systematically changed.

Fig3 shows the estimated width. Some points indicate exact zero. These correspond to the peaks that are not identified by the monitoring tool (see below) but can be identified by the human eye.

# identification and ASD fitting

- Peaks in ASD are found by line monitor tool that is being implemented by Takahiro S Yamamoto and Hirotaka Yuzurihara.
- The tool generate ASD by using 86400sec data, tsft=1800sec, toverlap=900sec, window=hann. Also, the normalized periodograms are generated and used to identify the artificial lines.
- Line monitor tool can give a curve fit by the violin function and a Gaussian function. The violin function is defined by

$$ G_\mathrm{violin}(f; f_\mathrm{loc}, w, A) = \frac{A f_\mathrm{loc}^2 w^2}{(f^2 - f_\mathrm{loc}^2)^2 + w^2 f^2} $$

where $f_\mathrm{loc}$ is the peak frequency, $A$ is the amplitude and $w$ is the full-width-half-maximum (FWHM). The tool fit ASD by using `scipy.optimize.curve_fit`. The peak frequency is fixed, and $A$ and $w$ are optimized. The fitting range is crucial for the fitting. We start from the range of $[f_\mathrm{loc} - 2/1800(=0.0011\cdots)\mathrm{Hz}, f_\mathrm{loc} + 2/1800 \mathrm{Hz}]$. If the optimized $w$ is wider than the fitting range, we extend the fitting range by twice. We repeat this process and stop the loop when the optimized $w$ is narrower than the fitting range or the fitting range reaches 0.1Hz.

# not done
- The fitting range is not optimized by the statistics.
- The global fitting, which is carried out in the O3GK noise budget paper, is not done.
- Error bar is missing.