Fractal Singular-Value (Egin-Value) Decomposition Method for Geophysical and Geochemical Anomaly Reconstruction

Geochemical and geophysical anomalies are originated from geological processes. These processes involve a great deal of complexity temporally and spatially. It is critical to improve the current anomaly extraction methods from the standpoint of the association of geophysical and geochemical anomalies for mineral exploration. The fractal singular-value-decomposition (MSVD) in GIS environment developed in this study is demonstrated superb in extracting linear and circular geophysical and geochemical anomalies as well as the detailed structural and textural information from 2D geochemical and geophysical maps. The MSVD method constructs a self-contained orthogonal basis using the outer product of left and right eigenvector matrixes decomposed from 2D geochemical or geophysical maps. A power-law relationship based on fractal theory has been suggested to associate the spectrum density and spectrum radius (or spectrum scale) defined in the paper. Multiple power-law relationships observed between the spectrum density and spectrum radius can help to group singular values and their corresponding eigenvectors. Each of these groups can be used to reconstruct the geophysical and geochemical maps to reflect decomposed components. The component reconstructed with relative large singular values may correspond to background and those obtained with relatively small singular values may represent anomalies. This method has been demonstrated using datasets from Nova Scotia, Canada. The results obtained for As and other elements from lake sediment samples, gravity anomalies and airborne magnetic anomalies have shown that the power-law relationship might exist between spectrum density and spectrum radius. Several different exponents are observed from the datasets which can be based to separate the anomalies from background.