The Fermi Gamma-ray Burst Monitor (GBM) is currently the most prolific detector of Gamma-Ray Bursts (GRBs). Recently the detection rate of short GRBs (SGRBs) has been dramatically increased through the use of ground-based searches that analyze GBM continuous time tagged event (CTTE) data. Here we examine the efficiency of a method developed to search CTTE data for sub-threshold transient events in temporal coincidence with LIGO/Virgo compact binary coalescence triggers. This targeted search operates by coherently combining data from all 14 GBM detectors by taking into account the complex spatial and energy dependent response of each detector. We use the method to examine a sample of SGRBs that were independently detected by the Burst Alert Telescope on board the Neil Gehrels Swift Observatory, but which were too intrinsically weak or viewed with unfavorable instrument geometry to initiate an on-board trigger of GBM. We find that the search can successfully recover a majority of the BAT detected sample in the CTTE data. We show that the targeted search of CTTE data will be crucial in increasing the GBM sensitivity, and hence the gamma-ray horizon, to weak events such as GRB 170817A. We also examine the properties of the GBM signal possibly associated with the LIGO detection of GW150914 and show that it is consistent with the observed properties of other sub-threshold SGRBs in our sample. We find that the targeted search is capable of recovering true astrophysical signals as weak as the signal associated with GW150914 in the untriggered data.
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