  This article addresses a modification of local time for stochastic processes,
to be referred to as `natural local time'. It is prompted by theoretical
developments arising in mathematical treatments of recent experiments and
observations of phenomena in the geophysical and biological sciences pertaining
to dispersion in the presence of an interface of discontinuity in dispersion
coefficients. The results illustrate new ways in which to use the theory of
stochastic processes to infer macro scale parameters and behavior from micro
scale observations in particular heterogeneous environments.
