The Radial Basis Function (RBF) interpolation method has emerged as a powerful geostatistical tool for mineral resource estimation, offering flexibility and robustness in modeling complex orebody geometries and grade distributions. Unlike traditional estimation techniques such as Inverse Distance Weighting (IDW) or Ordinary Kriging, RBF utilizes a smooth mathematical function that fits through known data points while minimizing interpolation error. This property enables the method to capture both global and local grade variability with high precision. In this study, the RBF approach was applied to a gold deposit using drillhole assay data to generate a continuous three-dimensional grade model. Various kernel functions—such as multiquadric, Gaussian, and thin-plate spline—were tested to optimize model accuracy and performance. Cross-validation results demonstrated that the RBF model effectively reproduced spatial grade trends and provided smoother, geologically realistic surfaces compared to conventional methods. The resulting block model was validated against composited data and geological interpretations, showing strong correlation and reduced estimation bias. The RBF method proves particularly advantageous in deposits with irregular sampling patterns or non-stationary grade distributions. Consequently, RBF interpolation represents a valuable alternative for modern resource estimation workflows, especially when integrated within advanced 3D geological modeling software such as Leapfrog Geo.

Radial Basis Functions (RBFs) are used in resource estimation, particularly for spatial interpolation and implicit modeling in geological and mining applications. They offer an alternative when traditional methods like ordinary kriging are not feasible due to challenges in variogram calculation. RBFs are also used in implicit modeling, a technique that uses RBFs to define the boundaries of geological models. How RBFs are used in Resource Estimation: Spatial Interpolation: RBFs are employed to estimate values at unknown locations based on known data points, like drillhole data. This is crucial for creating continuous surfaces or volumes for resource estimation. Implicit Modeling: RBFs are used to define the shape and boundaries of geological formations. This approach offers a flexible way to model complex geological structures, especially when traditional methods are difficult to apply. Grade Estimation: In mining, RBFs can be used to estimate ore grades at different locations within a deposit, aiding in reserve estimation and mine planning. Overcoming Limitations of Traditional Methods: RBFs can be a good alternative when traditional methods like ordinary kriging are challenging, such as when experimental variograms cannot be reliably calculated. Key Concepts: Radial Basis Functions: These are functions that depend on the distance from a central point. Implicit Modeling: This approach uses RBFs to define the geometry of a 3D model by representing surfaces and volumes as level sets of a distance function. Interpolation: Estimating values at unknown locations based on known data points. Advantages of using RBFs in Resource Estimation: Flexibility: RBFs can model complex shapes and surfaces. Simplicity: RBF networks have a simpler structure compared to other neural network models. Speed: RBF networks can have a faster training process than some other methods. Robustness: RBFs can provide reasonable estimates even with limited data or when dealing with skewed distributions.

Comparing implicit and explicit geological modeling in the context of resource estimation involves examining how each approach handles the complexities of geology and impacts the accuracy of resource assessments. Here are the key differences: 1. Implicit Geological Modeling: - In implicit geological modeling, geological features are represented using implicit functions to define their boundaries and properties. - It is useful for modeling complex geological structures where the boundaries are not clearly defined or where data uncertainty is high. - Implicit modeling allows for more flexible interpretation of geological data and can capture intricate geological relationships. - Resource estimation based on implicit geological modeling may be more robust in areas with complex geology as it considers the layered structure and relationships within the model. 2. Explicit Geological Modeling: - Explicit geological modeling involves the direct representation of geological features using explicit geometries, such as surfaces, faults, and rock units. - It is suitable for modeling simpler geological structures. - Explicit modeling provides a more straightforward visual representation of the geology, making it easier for interpretation and communication. - Resource estimation based on explicit geological modeling may be simpler and faster for well-defined geological structures, but it may overlook subtle relationships and complexities present in the geology. Differences in Resource Estimation: 1. Data Integration: - Implicit modeling allows for more seamless integration of various data sources and types, which can lead to more comprehensive resource estimation. - Explicit modeling may rely more on manual interpretation and input, which could result in limitations in incorporating all available data for resource estimation accuracy. 2. Geological Complexity: - Implicit modeling can capture complex geological relationships and uncertainties more effectively, leading to potentially more accurate resource estimation in geologically complex areas. 3. Interpretation Flexibility: - Implicit modeling allows for greater flexibility in interpreting geological data and relationships, which can lead to more nuanced resource estimation. In resource estimation, the choice between implicit and explicit geological modeling depends on the complexity of the geology being modeled, the available data, and the level of detail required for accurate estimation. Explicit modeling may be more suitable for straightforward geological settings, while implicit modeling offers advantages in handling complex geology and uncertainties for robust resource estimates.