An Improved GWR Approach for Exploring the Anisotropic Influence of Ore-Controlling Factors on Mineralization in 3D Space

Spatial non-stationarity is a common geological phenomenon, and the formation of orebodies is a typical non-stationary process. Therefore, a quantitative study of the non-stationary relationships between mineralization and its controlling factors in 3D space is of great significance for metallogenic prediction. Geographically weighted regression (GWR) is an effective method for exploring spatial non-stationarity by measuring the nearness between factors in the data. However, non-stationarity is affected not only by distances but also by factors related to direction. Traditional GWR cannot address the non-stationarity that arises from differences in direction. To address this issue, we propose an improved GWR method to characterize the directional characteristics of non-stationary relationships by introducing a direction weight to the GWR. The anisotropic influence of factors can be obtained by comparing the performance of models with different weights on direction terms. A case study of the Xiadian and Dayingezhuang gold deposits, Jiaodong Peninsula, Eastern China was carried out to verify the anisotropic nature of ore-controlling factors. First, multi-collinearity and OLS (ordinary least squares) diagnosis for the variables were performed and the necessity of the non-stationarity exploration was demonstrated. Second, GWR was applied to explore the spatial non-stationarity of the relationships among the variables by comparing the global R2 value with that of OLS, evaluating the local R2, values testing the t-statistic values, analyzing and comparing the spatial autocorrelation of residuals with that of OLS, and calculating the spatial stationary index of the parameter estimates of explanatory variables. Third, the improved GWR method was applied, and the directional characteristics of the non-stationary relationship were analyzed. Finally, the anisotropic influence of the controlling factors on mineralization was validated by comparing the performance of the improved GWR model with different bandwidths and different kernels, and the importance of the direction of the fault zone to mineralization was further verified.