A method to analyze self-affinities is introduced, andapplied to the large scale fold geometries of the Quaternary andTertiary in the inner belt of the Northeast Honshu Arc. Based onthis analysis, their geometries are found to be self-affine and canbe differently scaled in different directions. We recognize the selfaffinitiesfor the amplitude and the wavelength of folds, anddiscover a crossover from local to global altitude (vertical)variation of the geometries of folds in the Northeast Honshu Arc.Buckingham's Pi-theorem has been applied to similar systems ofinhomogeneous viscous Newtonian fluid under similar boundarycondition. However, Buckingham's Pi-theorem cannot give us theself-affinities of folds. A general renormalization-group argumentis proposed to the applicability of the similarity theory. By thisargument, we derive the self-affinities for the amplitude and thewavelength of folds as a parameter for the anisotropic stress field
