Delaunay triangulation structured kriging for surface interpolation

Surface interpolation is an essential tool in surveying and geographical information systems projects. For example, given a list of observations (e.g. elevations, gravity or magnetic field values, and underground-water levels), a prediction of a value at an unobserved location is made. Surveyors and engineers commonly use Triangulated Irregular Network (TIN) based linear interpolation for surface interpolation. TIN interpolation is computationally very efficient, utilizing a Delaunay triangulation algorithm and simple mathematical function. However, the TIN method uses only three local data points. Therefore, it is often less accurate and will yield a higher Mean Square Prediction Error (MSPE). Kriging is a relatively new, accurate interpolation method which yields a smaller Mean Square Prediction Error (MSPE). Nevertheless, kriging is computationally inefficient and requires the inversion of an nxn matrix where n is the number of data points. A unique approach is presented here that combines these two techniques such that the Delaunay triangulation data-structure is used to determine the interpolation neighborhood of a kriging prediction process. The new TIN-based kriging algorithm is used to interpolate aeromagnetic data for a geographical information system developed in West Antarctica. A comparison is made between global kriging, TIN linear interpolation, and the TIN-structured kriging.