Airborne magnetic field data exhibit downward continued power spectra of the form $1/f sp beta$ (where f is the spatial frequency and $ beta$ is a non-negative real number). This form of spectrum is observed for magnetic data recorded over a range of sampling scales from various areas of the Canadian Shield. Two scaling regimes have been discovered. The first has a $ beta$ value near 3 for wavelengths $ sbsp{ sim}{$25 km. These results suggest a "variable fractal" description of the distribution of near-surface magnetic sources. / From a data modelling viewpoint, the magnetic measurements are derived from a linear superposition of a deterministic system function and a stochastic excitation process. A symmetric operator corresponds to the system function, and the near-surface magnetic source distribution represents the excitation process. The deconvolution procedure assumes an autoregressive (AR) system function and proceeds iteratively using bi-directional AR (BDAR) filtering in one dimension, which is extended to four-pass AR filtering in two dimensions. The traditional assumption of a spectrally white innovation is used in the deconvolution procedure. The data are modified prior to deconvolution by a Fourier domain prewhitening technique, to account for the long wavelength content of the fractal innovation. Deconvolution of the modified data produces the system function, which is removed from the original data to produce the near-surface magnetic source distribution. This distribution serves as a susceptibility map which can be used for enhancing magnetic field anomalies and geological mapping. Thus, the statistical descriptions of near-surface magnetic sources are useful for modelling airborne magnetic data in "shield-type" geologic environments.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.74300 |
| Date | January 1989 |
| Creators | Gregotski, Mark Edward |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Geological Sciences.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001067254, proquestno: AAINN63546, Theses scanned by UMI/ProQuest. |
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