Modeling anisotropic geophysical fields using generalized scale invariance and universal multifractals.

摘要

This thesis focuses on a universal multifractal, Fractionally Integrated flux model. Although this type of model is one of the first continuous multiplicative cascade models developed, and in fact the first chapter of this thesis dates back six years, it still remains an excellent model for a wide range of systems. Using the framework of GSI, extended in this thesis, it has been shown here that sea ice, cloud radiances and topography are all fields that can be modeled by universal multifractals. The multifractal parameters of such fields are given, and classification of anisotropies using GSI parameters is made. In addition, the anisotropic universal multifractal model is used for magnetization, and the implications for magnetic anomaly field are examined. The model agrees not only with magnetization data, but with the magnetic field data, and correctly predicts what could otherwise be considered an anomalous scale break. This theory is easily generalized to gravitational potential fields and rock density, and has applications in the modeling of other physical systems.