f 3D Interpolation of geophysical parameters - The GOCAD approach

There are many applications in geology which require to know the distribution of physical parameters (velocities, porosities,...) in a region of the 3D space corresponding to the subsurface. Most of the time, these applications require to know the values of these parameters at the nodes of a regular 3D grid which must be interpolated from scattered data points. Classical methods, like for example Krigging, have the following drawbacks - they are numerically unstable as soon as data are clustered, and this is often the case in geophysics - they are mathematically unable to account for discontinuities generated by complex surfaces corresponding to horizons or faults, and it is necessary to use "programming tricks" ; - they are often too slow for initializing huge grids having for example a size of 500³ nodes like it is often the case in seismic migration methods!