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The Neil Gehrels Swift Observatory carried out prompt searches forgravitational wave (GW) events detected by the LIGO/Virgo Collaboration (LVC)during the second observing run ("O2"). Swift performed extensive tiling ofeight LVC triggers, two of which had very low false-alarm rates (GW 170814 andthe epochal GW 170817), indicating a high confidence of being astrophysical inorigin; the latter was the first GW event to have an electromagneticcounterpart detected. In this paper we describe the follow-up performed duringO2 and the results of our searches. No GW electromagnetic counterparts weredetected; this result is expected, as GW 170817 remained the only astrophysicalevent containing at least one neutron star after LVC's later retraction of someevents. A number of X-ray sources were detected, with the majority ofidentified sources being active galactic nuclei. We discuss the detection rateof transient X-ray sources and their implications in the O2 tiling searches.Finally, we describe the lessons learned during O2, and how these are beingused to improve the \swift\ follow-up of GW events. In particular, we simulatea population of GRB afterglows to evaluate our source ranking system's abilityto differentiate them from unrelated and uncatalogued X-ray sources. We findthat $\approx$60-70% of afterglows whose jets are oriented towards Earth willbe given high rank (i.e., "interesting" designation) by the completion of oursecond follow-up phase (assuming their location in the sky was observed), butthat this fraction can be increased to nearly 100% by performing a thirdfollow-up observation of sources exhibiting fading behavior.

Swift-XRT Follow-up of Gravitational Wave Triggers in the Second Advanced LIGO/Virgo Observing Run