A poly-Gaussian regression model to locate and quantify multiple anomalies in 3D geochemical exploration data

Abstract

A non-linear regression method has been developed to fit multiple anomalies in geochemical data obtained from sampling in three dimensions from drill holes, trenches and surface geochemical surveys. A heuristic description of the method is given. Related to trend surface analysis, it uses a set of Gaussian functions (negative exponentials of quadratic functions of coordinates) instead of the polynomial or Fourier series used in classical trend surface analysis. Isosurfaces of Gaussian functions are ellipsoids. Their combinations are capable of giving adequate approximations of much more complicated surfaces. Location, size and form of the anomalies are modelled by including the ellipsoid axes and orientation angles as variables to be fitted. Using lithogeochemical data, the method further allows quantitative estimation of the resources within each anomaly or in other limits of interest, by integration of the fitted function for response values above a defined cutoff concentration. A case study is provided, from exploration geochemical data in the area around the Pokrovsky mine in the Amur region of far eastern Russia.