  Radioactive decays from ^{42}Ar and its progeny ^{42}K are potential
background sources in large-scale liquid-argon-based neutrino and dark matter
experiments. In the atmosphere, ^{42}Ar is produced primarily by cosmogenic
activation on ^{40}Ar. The use of low radioactivity argon from cosmogenically
shielded underground sources can expand the reach and sensitivity of
liquid-argon-based rare event searches. We estimate ^{42}Ar production
underground by nuclear reactions induced by natural radioactivity and
cosmic-ray muon-induced interactions. At 3,000 mwe, ^{42}Ar production rate is
1.8E-3 atoms per ton of crust per year, 7 orders of magnitude smaller than the
^{39}Ar production rate at a similar depth in the crust. By comparing the
calculated production rate of ^{42}Ar to that of ^{39}Ar for which the
concentration has been measured in an underground gas sample, we estimate the
activity of ^{42}Ar in gas extracted from 3,000 mwe depth to be less than 2
decays per ton of argon per year.
