Multivariate interpolation of large sets of scattered data
ACM Transactions on Mathematical Software (TOMS)
Modeling of geological surfaces using finite elements
An international conference on curves and surfaces on Wavelets, images, and surface fitting
Vertical fault detection from scattered data
Journal of Computational and Applied Mathematics - Special issue on scattered data
Data Structures for Range Searching
ACM Computing Surveys (CSUR)
The detection and recovery of discontinuity curves from scattered data
Journal of Computational and Applied Mathematics
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We propose a method for the localization of unknown fault lines of a surface only known at scattered data. Our detection scheme is divided into three steps: first, a nearest-neighbor searching procedure is applied; second, all the nodes near a fault line are picked out and collected in a set; then, a polygonal curve approximation the fault line is obtained. To select the nodes near the faults we use a cardinal radial basis interpolation formula. Numerical results are given, which show the efficiency of our scheme in comparison with similar ones. The method has important applications in several fields, for example in the oil industry, where automatic algorithms are required for the detection of faults form geological scattered data. Furthermore, the output of our algorithm is the natural impute of a method, that we proposed [4], for representing faulted surfaces by means of radical near-interpolants.