There is a similar form of Kriging, called Dual Kriging (Chilès & Delfiner, 1999), that also computes the weights once. Additionally, Kriging often computes weights for each estimate using a local search neighborhood RBFs conventionally use all samples to compute the weights once. A key difference between RBFs and Kriging is that RBFs use a positive definite basis function and Kriging uses the covariance function for interpolation (Cowan et al., 2003). The development of RBFs was in parallel to the work of Matheron on regionalized variables (Matheron, 1963). RBFs were first mentioned in the geological literature by (Hardy, 1971). Signed distance functions have been widely used for implicit surface inference (Osher & Fedkiw, 2003). To supplement manual interpretation, several mathematical approaches have been developed for implicit modeling a common method is the interpolation of signed distance functions using Radial Basis Functions (RBF) (Cowan et al., 2003).
Different interpretations of the same boundary modeling problem (between red and blue) There could be different interpretations in presence of widely spaced data (Silva & Deutsch, 2012) and these can be time-consuming and difficult to reproduce. Historically, a manual interpretation of the domain boundaries was considered based on the experience and knowledge of the geologist. These domains can be based on grade, lithology, alteration, mineralization, structure or a combination of these factors. This is performed to satisfy the decision of stationarity used in geostatistical workflows. Compare RBF interpolation and dual krigingĪ critical task in geostatistical modeling is the delimitation of domain boundaries.Review the framework of radial basis functions (RBF).Review the importance of stationary domains.University of Alberta Learning Objectives Implicit Boundary Modeling with Radial Basis Functions Sebastian Sanchez
Domain Delimitation with Radial Basis Functions.
Cite this lesson as: Sanchez, S., & Deutsch, C.V.
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