  Building on the foundation work of Brown, Milton and Torquato, we present a
tractable approach to analyse the effective permittivity of anisotropic
two-phase structures. This methodology accounts for successive dipolar
interactions, providing a recurrent series expansion of the effective
permittivity to arbitrary order. Within this framework, we also demonstrate a
progressive method to determine tight bounds that converge towards the exact
solution. We illustrate the utility of these methods by using ensemble
averaging to determine the micro-structural parameters of anisotropic level-cut
Gaussian fields. We find that the depolarization factor of these structures is
equivalent to that of an isolated ellipse with the same stretchingratio, and
discuss the contribution of the fourth order term to the exact anisotropy.
