A geostatistical analysis of multiscale metallicity variations in
  galaxies [I]: Introduction and comparison of high-resolution metallicity maps
  to an analytic metal transport model
  Thanks to recent advances in integral field spectroscopy (IFS), modern
surveys of nearby galaxies are capable of resolving metallicity maps of Hii
regions down to scales of ~50pc. However, statistical analysis of these
metallicity maps has seldom gone beyond fitting basic linear regressions and
comparing parameters to global galaxy properties. In this paper (the first of a
series), we introduce techniques from spatial statistics that are well suited
for detailed analysis of both small- and large-scale metallicity variations
within the interstellar media (ISMs) of local galaxies. As a first application,
we compare the observed structure of small-scale metallicity fluctuations
within 7 local galaxies observed by the PHANGS collaboration to predictions
from a stochastic, physically motivated, analytical model developed by Krumholz
& Ting. We show that while the theoretical model underestimates the amount of
correlated scatter in the galactic metallicity distributions by 3-4 orders of
magnitude, it provides good estimates of the physical scale of metallicity
correlations. We conclude that the ISM of local spiral galaxies is far from
homogeneous, with regions of size ~1 kpc showing significant departures from
the mean metallicity at each galactocentric radius.
