The multiple-scatter theory of wave propagation in randomly irregular media is now well developed. Moreover, work in fields such as coherent optics and radio astronomy has stimulated the development of asymptotic formulas that can be used in various scattering regimes. In this paper the power law phase screen model is used to derive the form of the intensity correlation function for strong ionospheric radio wave scattering when the Fresnel radius lies within the power law continuum. The model allows fully for the anisotropy of the scattering medium. Asymptotic formulas valid under conditions of very strong scattering are developed. It is shown that the results depend critically on the power law index such that an important transition in the structure of a strongly scattered field occurs when the three-dimensional index is greater than 4.