Trend surface fitting of airborne gamma-ray spectrum based on 2D-AsLS

The trend surface analysis is one of the important methods for processing radioactive element concentration data of airborne gamma-ray spectrum. At present, the fitting of trend surface is mainly based on the polynomial least-squares method. Due to the degree of limitation of polynomial functions, the polynomial least-squares method is imprecise in describing the trend surface. Therefore, as an alternative approach, we considered the 2D asymmetric least squares (2D-AsLS) developed under 2D tensor product of a P-spline. 2D-AsLS can make full use of the spatial characteristics of radioactive element concentration data to fit trend surfaces. 2D-AsLS can adjust the fitting effect of the trend surface by modifying smoothness, and can evaluate the fitting effect through the parameters (i.e. fitting coefficient, error variance, coefficient of variation, and degree of deviation). Gamma-ray spectrum data acquired by an unmanned aerial vehicle was used in the experiment. The results showed that 2D-AsLS can completely distinguish regional trend and residual values. Moreover, the trend surface fitted by 2D-AsLS can describe the regional radioactive background in detail.