shows the mean phase error at each frequency. The dashed black lines show linear phase error associated with one and two sample periods ($\Delta t \sim 340 \mu$s).[]{data-label="merging_calphase"}](fig9)

The argument of the cross spectra gives the phase delay between the two signals at a given frequency ${\textrm{arg}}(S_{12})=\textrm{tan}^{-1}\left(\frac{\textrm{Im}\{S_{12})\}}{\textrm{Re}\{S_{12}\}}\right)$. As each sensor observes the same time series, zero-phase difference should exist at each frequency between the sensors. Each of the 22 intervals on 11/05/2018 used in gain calibration are separated into 1024 sub-intervals. The sub-division allows for the calculation of 22528 individual cross-spectra. The distribution of phase delay as a function of frequency is then calculated between the MAG and SCM using the ensemble of cross-spectra.

Figure \[merging\_calphase\] shows the measured distributions of phase difference between the MAG and SCM obtained via cross spectra. The MAG and SCM are shown to be in good agreement in the cross over frequencies: at 4 Hz the mean time-delay between the MAG and SCM measurements is 190 $\mu$s, 84 $\mu$s, and 100 $\mu$s for the respective $x$,$y$, and $z$ axes; the standard deviations are 76 $\mu$s, 59 $\mu$s, and 89$\mu$s respectively. For each vector component, approximately two standard deviations of the measured ensemble fall within 