Approaches to Scaling of Geo-Spatial Data

This chapter focuses on the fractal approach to the scaling phenomena of spatial data. It introduces some of the most basic concepts of fractal geometry and describes some of the commonly used algorithms for fractal analysis. Two important types of dimension are commonly used in fractal research: the topological dimension and the fractional dimension. The topological dimension is always an integer and coincides with the intuitive dimension in Euclidean geometry. Malinvemo evaluated the performance of a fractal model and an autoregressive model for describing sea floor topography. Both models appeared to describe the data fairly well. The fractal model gave a superior fit to the autocorrelation for small lags and to the general trend of the variance of the increments. The "Poisson-Brown" primary model has isotropic increments and satisfies many of the theoretical abstractions from actual observations of natural terrains.