In this paper we present an analysis of scattering from an ensemble of locally homogeneous patches as described by Kolmogorov (1941). The analysis allows power law spectral density functions of the form &kgr;-p, where 2<p<4. Neither an outer scale nor an inner scale need be specified explicitly. We show that there is a Fresnel radius dependence of the scattering cross section that acts to increase the quadratic wavelength dependence that characterizes the usual strictly homogeneous scattering. For spectral p indices between the Kolmogorov value p=11/3 and the limiting value p=4 we find good agreement between the theory and the ionospheric scintillation data described in a companion paper. In a locally homogeneous medium a large-scale trend term is specified separately from an integral structure term. We show that the intensity ratio of these two components is highly variable. By noting a correlation between scintillation rate and the relative intensity measure for the two components we are able to attribute the changes at least partially to the structured component. We also show that under an additional Gaussian statistical hypothesis the wavelength dependence of the scintillation index is such that the simple &lgr;(p+2)/4 asymptote is not achieved until the scattering is very weak. The effect is an overestimate of the p index when the wavelength dependence of S4 is used.