Quantifying the Generalized Self-Similarity of Spatial Patterns for Mineral Resource Assessment

Scale invariance, including self-similarity (isotropic), self-affinity (stratification), and generalized self-similarity (anisotropy), is a common property of spatial patterns generated from various geological processes and events. Scale invariance can be described by means of fractal and multifractal models. Quantifying the scale invariance properties of spatial patterns may provide a powerful tool for characterizing geological processes and events. For example, the clustering distribution of hydrothermal mineral deposits can be characterized by means of local singularity analysis. The identification of distinct generalized self-similarity in the Fourier domain can be used to decompose spatial patterns into separate components such as anomalies from background patterns. The current paper introduces a number of relevant multifractal models and methods, including a linear model for generalized scale invariance (GSI); a spectrum-area method (S-A) for anomaly separation; a local singularity analysis method; and methods for predicting undiscovered mineral deposits on the basis of fractal and multifractal properties. Some of these methods have been applied in various case studies. The case study introduced in the current paper demonstrates the application of S-A anomaly separation and local anomaly enhancement in analyzing lake sediment geochemical data (As, Pb, Zn and Cu) for gold mineral resource prediction. It has been shown that the areas delineated by a strong singularity in As, Pb, Zn and Cu are spatially associated with the location of known gold mineral deposits.