Philippe N, Anamaria E, Robert S

PEM coupling functions are conservatively assumed to have an uncertainty of a factor of two. Much of this uncertainty comes from the fact that we have a finite array of PEM sensors which cannot be precisely placed at each and every coupling site. Varying the location of an injection source will vary its distance to both the coupling site as well as the sensor, resulting in variations in the measured coupling. The uncertainty can thus be estimated by choosing a sensor near a known coupling site, analyzing multiple nearby injections, and finding the spread between the different single-injection coupling functions. Since variations in injection location result in a multiplicative scaling of the coupling function, the spread is best quantified by computing the geometric standard deviation (GSD) of coupling factors in each bin. Figure 1 shows single-injection coupling functions for H1:PEM-CS_ACC_HAM5_SRM_Y_DQ measured from three shaker injections in the HAM5/6 area, as well as the GSD of each frequency bin. Averaged across all bins, the GSD between injection locations is 1.4, i.e. coupling functions measured from vibrational injections, as well as vibrational noise projections to DARM, vary by a factor of 1.4, noticeably less than the conservative estimate of a factor of two.

The same approach can be applied to magnetic coupling functions, but magnetic injections during O3 were done mostly through 7.1-Hz comb injections, which give relatively few data points per channel, so the method has to be expanded to several channels to extract useful statistics. Figure 2 shows the GSD frequency distribution of six magnetometers, each of which was chosen based on having multiple injections close enough to be used for the study (three electronics room injections for H1 LSCRACK, three LVEA injections for L1 VERTEX, and two VEA injections for each of the end station VEA magnetometers). The average GSD for these magnetometers is 1.7, again below the conservative estimate.

The single-injection coupling functions used here were taken from the O3a injection data set: https://ldas-jobs.ligo-wa.caltech.edu/~philippe.nguyen/pem_injections/19aMarPEMinjections/