A Demonstration of the Application of Quantized Spatial Transforms in the Scaled and Optimized Separation of Scalar Potential Source Contributions for Use in Education, Research and Resource Exploration

Abstract

An approach to the inverse Fast Fourier Transform (IFFT) isolation and identification of geological source contributions to surface gravitational and magnetic attractions is demonstrated. The techniques were developed from considerations of the scaling and linearity of the continuous Fourier transform and the properties of the classical potential fields. The approach exploits the characteristics of the discrete vertical spectral components of the FFT and their equivalent IFFT representations. The results depend upon absolute and relative quantitative comparisons over scaled regions represented within the digitized transform of the grid-based surface interpolated from the original field measurements. They provide for quantified estimates of parameters related to equivalent source contributions to anomalies identified within the surface. The techniques can be optimized with respect to the goals and resources associated with a particular investigation. Anomalies within FFT/IFFT filtered spatial residuals from a transformed digital surface are defined in terms of localized reference levels over scaled central sub-regions of a surveyed area. Iterative methods lead to particular subsets of the discrete depth components viewed over scaled spatial regions which contribute to identifiable features. Such identification can yield information related to the physical properties of sources responsible for regional and localized anomalies. The depth, spatial extent, and density or magnetization associated with these contributions can be estimated directly from the scaled views. These methods can be applied with predictable accuracy over orders of magnitude in physical scale. The quantitative information derived from the techniques provides for a scaled reduction in the ambiguity associated with any subsequent interpretation.