| Anisotropic scale invariance is being widely recognized and utilized in geo-scientific studies since it is a common characteristic of most geophysical and geochemical data and it explains the texture and morphology of the related fields. In order to understand various anisotropic scale invariant systems, the Generalized Scale Invariance concept (GSI) was brought forward, which presents a formalism stating the most general conditions under which large and small scales can be related. Based on 2D linear GSI, two different anisotropic scale invariance quantification techniques were developed: the Scale Invariant Generator technique (SIG) quantifies anisotropies by estimating the GSI generator in frequency domain, a form of scale transformation defined in GSI representing how the scaling field is stratified and how it rotates, and the family of balls that best describe the scaling field; the Spectrum-Area technique (S-A) quantifies anisotropies by estimating the anisotropic scaling exponent defined in GSI through a power-law function representing the relationship between area of the set with spectral energy density above P on the 2D frequency domain and P. (Abstract shortened by UMI.)... |
