Quantization Within the Spectral and Spatial Transforms of Sampled Source Contributions to Geophysical Scalar Potential Fields and Its Significance for Education, Research, and Resource Exploration

Conventional application of fast Fourier transform (FFT) methods in the spectral separation and analysis of surface gravity and magnetization measurements has evolved from the traditional perspective that a continuous spectrum of source contributions overlaps an associated range of wave numbers (frequencies). The FFT algorithm is array-based and the interpolated measurements can be decomposed into a unique and complete set of discrete and disjoint matrices representing vertical components which contribute to the values at each element in the original surface array. The scaling and superposition properties of these components can be exploited in order to develop an alternative approach to the spectral separation of the interpolated surface. The approach has been applied to a variety of interpolated surface arrays, each representing a unique geological region and sampling event. A simulated generalized potential distribution has been designed in order to test and refine analytical methods suggested by the approach. The methods rely upon a principle of optimized scaling of the parameters associated with the field survey. The methods exploit the physical characteristics of the associated potential fields and the mathematical properties of the basis set of vertical spectral components and their equivalent spatial arrays. The approach permits the isolation of spectral components contributed by particular sources within well-defined spatial volumes beneath an associated planar sub-region of the original interpolated surface. Analysis based upon estimates of spatial characteristics for sources represented within the array elements contribute to reduced or minimized ambiguity in interpretations concerned with equivalent-source contributions to the original field measurements.