Stable isotope data from hydrothermally altered rocks often show signi
ficant scatter. Such scatter cannot be quantitatively interpreted by m
odels in which each lithologic unit is assumed to have a uniform perme
ability. If a stochastic modeling approach is used instead, heterogene
ous permeability maps can be constructed to approximate the statistica
l distributions of natural systems, and both overall isotopic trends a
nd data scatter can be matched. Three models are presented for the Alt
a, Utah, contact aureole to show that the observed scatter in delta(18
)O values is consistent with subhorizontal down-temperature fluid infi
ltration through carbonates with heterogeneous permeabilities. Infiltr
ation through rocks with heterogeneous permeabilities creates irregula
r, lobate isotope patterns, so that the idealized isotope profiles pre
dicted by one-dimensional homogeneous permeability models do not devel
op. Localized sampling is unlikely to yield an accurate estimate of th
e overall importance of fluid-rock interaction or of dominant flow dir
ections. In heterogeneous systems, large-scale hydrothermal alteration
and how patterns can best be estimated from statistically unbiased an
d spatially distributed data sets.