The scale invariant generator technique and scaling anisotropy in geophysics /

Recently, there has been a dramatic increase in the use of scale invariance in the study of geophysical fields. However, very little attention has been paid to the anisotropy that is invariably present in these fields, in the form of stratification, differential rotation, texture and morphology. In order to account for scaling anisotropy, the formalism of Generalized Scale Invariance (GSI) was developed. Until now, only a single analysis technique has been developed which incorporates this formalism and which can be used to study the differential rotation of fields.Using a two-dimensional representation of the linear approximation to GSI, a new, greatly improved, technique for quantifying anisotropic scale invariance in geophysical fields is developed: the Scale Invariant Generator technique (SIG).The ability of the technique to yield valid estimates is tested by performing the analysis on multifractal (scale invariant) simulations. It was found that SIG yields reasonable estimates for fields with a diversity of anisotropic and statistical characteristics. The analysis is also performed on three satellite cloud radiances and three sea ice SAR reflectivities to test the applicability of the technique. SIG also produced reasonable estimates in these cases