Vertical and oblique fault detection in explicit surfaces

The purpose of this paper is to study the problem of detection of vertical and oblique faults in explicit surfaces. First, we characterize the finite jump discontinuities of a univariate function in terms of the divergence of sequences related to the slopes of least-squares polynomial approximations of the function. Then, we propose an algorithm to locate the finite jump discontinuities of a univariate function and its first derivative from a finite set of scattered data values of the function. As a consequence, we derive a method to detect vertical and oblique faults in explicit surfaces when the data sets are distributed along lines. We finally present some numerical and graphical examples.