Fast interpolation method for surfaces with faults by multi-scale second-derivative optimization

Abstract : We present a smooth surface interpolation method enabling to take discontinuities (e.g. faults) into account that can be applied to any dataset defined on a regular mesh. We use a second-derivative multi-scale minimization based on a conjugate gradient method. Our multi-scale approach allows the algorithm to process millions of points in a few seconds on a single-unit workstation. The interpolated surface is continuous, as well as its first derivative, except on some lines that have been specified as discontinuities. Application in geosciences are numerous, for instance when a structural model is to be built from points picked on seismic data. The resulting dip of interpolation extends the dip of the input data. The algorithm also works if faults are given by broken lines. We present results from a synthetic and real examples taking into account fault network.