Anisotropic Scale Invariance Quantification Models And Their Applications In Sn-Cu Geochemical

Scale invariance is basic property of nature. A lot of nature phenomenon and process, like turbulence, rains, floods, earthquake, are scaling. Although scale invariance is widely studied in geoscience, most researches focus on self-similarity (isotropic) and self-affine (stratification), and don’t pay much attention to anisotropic scale invariance, which is more accurate, detailed, sophisticated and more close the reality. In fact, almost no scaling phenomenon and process is exactly isotropic. Studying their anisotropic properties is of great importance.A series of researches indicate that most geological process and mineralization process are anisotropic scaling process. Studying their anisotropic scaling properties provides a new idea for mineral resource prediction and assessment. So far geoscientists have developed some anisotropic scale invariance quantification techniques, but they are mainly applied in meteorology studies. Applying these techniques to the mineral resource exploration and studying mineralization’s anisotropic scaling properties become a promising research area.Anisotropic scale invariance based prediction and assessment methods usually handle geochemical and geophysical data, which are two types of basic data that have been extensively used in exploration geosciences. These data usually contain the accumulative effect generated by multiple geological processes with different scales. The geochemical and geophysical data of this kind are called mixing data. Strictly speaking, these data can only be utilized properly provided that different components in the data have been properly identified or separated. So studying mixing data (pattern) decomposition based on anisotropic scale invariance is necessary.This paper thoroughly studied the Generalized Scale Invariance (GSI) theory system and the Scale Invariant Generator (SIG) model and the Spectrum-Area (S-A) model. The GSI theory system states the most ordinary situation different scales are related. The SIG model quantifies anisotropies by estimating the generalized scale invariance (GSI) generator parameters in frequency domain, which represent how a scaling field is stratified and how it rotates. Also based on the2D GSI, the spectrum-area (S-A) model quantifies anisotropies by estimating the anisotropic scaling exponent in2D frequency domain and decomposes multi-component data into separate patterns based on their distinct anisotropic scaling properties. The combined model of S-A and SIG is proposed, which is also improved in three aspects.The application of the combined model of S-A and SIG to stream sediment geochemical data from the Gejiu mineral district, not only separates Sn-Cu anomaly pattern from background, but also characterize the anomaly pattern’s anisotropic scale invariance properties such as differential compression and rotational scaling through estimating the GSI generator parameters (e、f、c). Understanding the combined effects of slight rotational and differential compressional scaling representing by these parameters infer that the geochemical field analyzed is generally elongated in N-S orientation or generally compressed in E-W orientation. This further suggests that fault systems generally oriented S-N to NNE likely controlled Sn-Cu mineralization and the spatial distribution of associated geochemical anomalies especially the background patterns. Moreover, the decomposed anomalous pattern is apparently affected by intersection of other fault systems.In this research, anisotropic scale invariance quantification theories and models are applied to mineral resource prediction and assessment for the first time. The combined model of SIG and S-A not only decomposed the Sn-Cu anomaly pattern from background, but also successively quantified the anisotropic scale invariance of the anomaly pattern and infer the mineralization process and controlling factors behind. It provides a new method for better understanding the formation of anomaly pattern. Since it is applicable for any2D fields or patterns, it has the potential to become a general model for anisotropic scale invariance quantification and mixing pattern decomposition in geo-science and some other fields.