Anisotropic Scaling Models of Rock Density and the Earth’s Surface Gravity Field

Abstract

In this paper we consider an anisotropic scaling approach to understanding rock density and surface gravity which naturally accounts for wide range variability and anomalies at all scales. This approach is empirically justified by the growing body of evidence that geophysical fields including topography and density are scaling over wide range ranges. Theoretically it is justified, since scale invariance is a (geo)dynamical symmetry principle which is expected to hold in the absence of symmetry breaking mechanisms. Unfortunately, to date most scaling approaches have been self-similar, i.e., they have assumed not only scale invariant but also isotropic dynamics. In contrast, most nonscaling approaches recognize the anisotropy (e.g., the strata), but implicitly assume that the latter is independent of scale. In this paper, we argue that the dynamics are scaling but highly anisotropic, i.e., with scale dependent differential anisotropy.