Biharmonic Trend Modeling with Sequential Gaussian Simulation for Geospatial Estimation of Soil Thickness

An integrated approach for soil thickness estimation is developed and evaluated. The method combines a biharmonic trend model with a stochastic Sequential Gaussian Simulation (SGS) component. Numerical experiments are first carried out in one dimentional synthetic data to provide a controlled enviroment for testing the methodology, investigating interpolation behavior, and determining parameter sensitivity. The approch is then extended to a two dimensional synthetic domain to see how well it captures spatial variability that is more representative of real-world applications. In both settings, the large-scale structure of the soil thickness field is approximated using a biharmonic equation, while the small-scale variability is represented by SGS applied to the residuals. This decomposition enables the method to preserve global smoothness imposed by the PDE model while simultaneously reproducing local heterogeneity through stochastic simulation. The results demonstrate that the hybrid method reduces prediction error relative to the PDE model or ordinary kriging alone, and that it provides a flexible approach for uncertainty quantification, making it suitable for realistic soil thickness mapping problems.