Abstract

Kriging, the geostatistical interpolation technique, calculates an interpolation function that minimizes the estimation variance. Kriging is very flexible and can be used to filter white noise (Error Cokriging) or coloured noise (Factorial Kriging) out of stacking velocity data (for instance). On the other hand, splines calculate the interpolation function that minimizes a regularisation operator such as the average curvature (thin plate splines). Smoothing splines can also be used to filter noise out of the data. Conditional simulation is a geostatistical technique which consists of sampling realisations from the a priori variogram-based model. Geostatistical inversion is an extension of conditional simulation, where acoustic impedance realisations are generated which also match (after convolution) the seismic data. We will see that close relationships exist between geostatistical and optimisation techniques such as splines