3D-reconstruction of complex geological interfaces from irregularly distributed and noisy point data

In this paper we introduce a new, precise and adaptive method for the implicit reconstruction of faulted surfaces with complex geometry from scattered, unorganized points as obtained from seismic data or laser scanners. We embed the point set into a 3d-complex on which a 3d-implicit function is interpolated. The 3d-complex is a set of tetrahedrons and the implicit function represents a surface that lies as close as possible to the input data points. The density of the 3d-complex can be adapted to efficiently control both the precision of the implicit function and the size of triangles of the reconstructed surface. Discontinuities in the topology of the tetrahedral mesh make it possible to reconstruct discontinuous, bounded surfaces and very close parallel patches without introducing unwanted connections (topological “handles”) between these regions. To compute the implicit function we use the discrete smooth interpolation (DSI) method with a set of boundary, off-boundary and smoothness constraints. The interpolation problem does not primarily depend on the number of input data points but on the magnitude of the 3d-complex. This method can be applied to the construction of faulted horizons and salt-top surfaces.