Vertical fault detection from scattered data (Q1815885)

This paper contains the problem of detecting vertical faults in explicit surfaces from sets of data points. In geology or geophysics, the reconstruction of a faulted surface from a set of scattered data points is a common problem. In this paper, the focus is on a method to detect vertical faults, modelled as jump discontinuities of the function \(f\) on the set \(F\). First, the authors establish a characterization of jump discontinuities for bivariate functions. Next, the authors derive a detection method of vertical faults in surfaces which takes as input a set of scattered data points. Finally, some numerical and graphical examples are given.