SMOOTHING SEISMICALLY DERIVED VELOCITIES

It is often very useful to be able to smooth velocity fields estimated from exploration seismic data. For example seismic migration is most successful when accurate but also smooth migration velocity fields are used. Smoothing in one, two and three dimensions is examined using No rth Sea velocity data. A number of ways for carrying out this smoothin g are examined, and the technique of locally weighted regression (LOES S) emerges as most satisfactory. In this method each smoothed value is formed using a local regression on a neighbourhood of points downweig hted according to their distance from the point of interest. In additi on the method incorporates 'blending' which saves computations by usin g function and derivative information, and 'weighting and robustness' which allows the smooth to be biased towards reliable points, or away from unreliable ones. A number of other important factors are also con sidered: namely, the effect of changing the scales of axes, or of thin ning the velocity field, prior to smoothing, as well as the problem of smoothing on to irregular subsurfaces.