Assessing the precision of gridding techniques for creating surfaces and calculating volumes through different hypothetical terrains

The objective of this study is to assess the precision of various gridding methods and numerical integration approaches in accurately representing surfaces and calculating volumes between two surfaces. Three hypothetical surface categories were generated and volumes were computed using analytical integration in Python. These surfaces served as benchmarks for comparison with other surface forms and computed volumes. Various gridding methods available in Surfer software were compared, and the computed volumes were compared to those obtained from Python analytical integration. Statistical metrics such as Absolute Error, Squared Error, and Absolute Percentage Error were used to assess the precision of each approach. The results showed that methods like Kriging, Inverse Distance to A Power, Triangulation with Linear Interpolation, Minimum Curvature, Nearest Neighbor, Radial Basis Function, and Modified Shepard's Method exhibited the highest precision across all surface types. The Natural Neighbor method was inconsistent across all surface groups, whereas, the Local Polynomial Method had varying results. Polynomial Regression, Moving Average, and Data Metrics methods were excluded. The first two methods suffer from a lack of precision in representing terrain natures, whereas the third method resulted both invalid volume estimates and terrain shape representation.