Scale invariant property in Walsh frequency domain and a multifractal model for geophysical data processing in GIS environment
Walsh列率域中多维分形模型与GIS环境下地球物理信号处理

Geophysical fields present scale invariant property in multiple scale ranges.This is originated from the self-similarity or self-affine attributes of geological,geophysical,geochemical,and mineralization processes.To separate geophysical signals of these types into mono-scale invariant patterns reflecting simple geological,geophysical,geochemical or mineralization processes is useful for mineral exploration and environment assessment.The fractal and multifractal attributes between power spectrum and frequency of geophysical data in Walsh domain are investigated.A wide variety of geophysical well logging data from Ocean Drilling Program(ODP),oil bearing,and coal bed section is tested and approved of multifractal property in Walsh domain.Multifractal Walsh Spectrum Area(W-A) accumulation model is proposed and implemented for extracting geophysical anomalies for mineral exploration in GIS environment.Using the W-A method,Walsh power spectrum density "thresholds" or "breaks" could be defined by means of Least Square(LS) and these breaks can be further used in filter design.W-A filter can be used to decompose geophysical data into signals with distinct local self-similarity with the anisotropy attributes of the original geophysical data retained.W-A has some advantages over the S-A a filtering technique in the Fourier Domain,such as suitable for detecting local features of sharp edges,linear or curvilinear,and weak signals.Further more,W-A is much faster than Fourier based method because Fast Walsh Transformation(FWT) and Inverse Fast Walsh Transformation(IFWT) require only addition and subtraction operation whereas Fourier based methods need complex multiplying in Fast Fourier Transformation(FFT) and Inverse Fast Fourier Transformation(IFFT).Therefore,W-A is suitable for real time geophysical processing or in situ fast data processing.The Bouguer anomaly of southeast Nova Scotia,Canada is processed using W-A method and the results showing good agreement with the known spatial distribution of lithology units,and mineral deposits and occurrences.