  COSINE-100 is a direct detection dark matter search experiment that uses a
106 kg array of eight NaI(Tl) crystals that are kept underground at the
Yangyang Underground Laboratory to avoid cosmogenic activation of radioisotopes
by cosmic rays. Even though the cosmogenic activity is declining with time,
there are still significant background rates from the remnant nuclides. In this
paper, we report measurements of cosmogenic isotope contaminations with less
than one year half-lives that are based on extrapolations of the time dependent
activities of their characteristic energy peaks to activity rates at the time
the crystals were deployed underground. For longer-lived $^{109}$Cd
($T_{1/2}=1.6$ y) and $^{22}$Na ($T_{1/2}=2.6$ y), we investigate time
correlations of characteristic $\gamma$/X-ray peaks. The inferred sea-level
production rates are compared with caluclations based on the ACTIVIA and
MENDL-2 model calculations and experimental data. For $^{3}$H, which has a
long, 12.3 year half-life, we evaluated the activity levels from the exposure
times and determined a cosmogenic activation rate that is consistent with other
measurements.
