Magnetotellurics (MT) is a method of determining the electrical resistivity of the
earth’s subsurface as a function of position by analyzing the electromagnetic (EM) field on the
earth’s surface. It is a passive method, in that ambient EM radiation is used as a source. In this
paper we consider model subsurfaces for MT that contain small scale random stratification; that
is, we introduce random microlayers and allow the earth’s electrical properties to vary rapidly and
randomly in space as the layer boundaries are crossed. The layers are not assumed to be plane, but
are allowed to vary laterally in space in a direction that changes smoothly on the scale of an EM
wavelength. By asymptotic analysis of the resulting stochastic differential equations with a small
parameter we generalize previous results of White, Kohler and Srnka for plane layered media; we
show that the resulting EM field may be approximated using a non-random effective medium theory,
but with random corrections. These corrections are a gaussian random process which represents
multiple scattering from the random microlayers. We show how the effective medium theory differs
from the plane layered case, and derive a spatially varying correction for the EM field on the surface
of the earth, which accounts for stratifications that are not planar.