Fractal modeling techniques for spatial data

The paper presents convolutional linear data models for the processing of one-dimensional (1D) and two-dimensional (2D) spatial data. The models assume that the measured data is the superposition of a stochastic innovation process and a deterministic system function. The innovation process is described by a fractal scaling noise, which has a power spectral density proportional to some power (-β) of the frequency. The system function is assumed to be symmetric and is constructed using autoregressive (AR) filtering procedures. Iterative deconvolution procedures are developed to recover the fractal innovation from the data. For computational convenience, these procedures assume a spectrally white (β=0) innovation, but modify the data prior to inversion by prewhitening the a priori assumed fractal innovation. The filter coefficients recovered by inverting the modified data are then applied to the original data to recover the fractal innovation. The ability of the deconvolution procedures to recover the fractal innovation is demonstrated using 1D and 2D synthetic data sets. As a practical example, the 2D deconvolution technique is applied to an aeromagnetic map from northeastern Ontario, Canada, and is shown to be effective in enhancing magnetic field anomalies