Anisotropic Analysis of SomeGaussian Models

Although the classical Fractional Brownian Motion is often used to describe porosity,it is not adapted to anisotropic situations. In the present work, we study a class of Gaussianfields with stationary increments and spectral density. They present asymptotic self-similarityproperties and are good candidates to model a homogeneous anisotropic material, or its radiographicimages. Unfortunately, the paths of all Gaussian fields with stationary increments have thesame apparent regularity in all directions (except at most one). Hence we propose here a procedureto recover anisotropy from one realization: computing averages over all the hyperplanes whichare orthogonal to a fixed direction, we get a process whose Hölder regularity depends explicitly onthe asymptotic behavior of the spectral density in this direction.