Fractal stochastic modeling of aeromagnetic data

Abstract

We present a convolutional linear data model for the processing of aeromagnetic data. The model assumes that the data derive from the superposition of a deterministic system function and a stochastic innovation process. The two‐dimensional system function is described by a four‐pass autoregressive (AR) filtering procedure and is radially symmetric. The innovation process represents the distribution of near‐surface magnetic sources and is modeled as a spectrally self‐scaling (i.e., fractal) noise. The appropriate fractal noise is determined by examining aeromagnetic power spectra from various areas of the Canadian Shield. The AR coefficients of the system are determined using an iterative deconvolution procedure. For computational convenience, we make the traditional assumption of a spectrally white innovation, but modify the data prior to its deconvolution by prewhitening the assumed fractal innovation. The recovered system function is then removed from the original data in order to produce the fractal stochastic surface. This deconvolution technique is applied to two aeromagnetic maps from northeastern Ontario, Canada and is shown to be effective in delineating lithologies and enhancing magnetic field anomalies. We propose a particular statistical description of near‐surface magnetic sources for modeling aeromagnetic data in “shield‐type” geologic environments.