INTRODUCTION

Many powerful velocity estimation programs have been written based on intuition and exhaustive experience. It is not easy to improve such programs. Recently we presented a more formal approach showing how directional interpolation in interval velocity can exploit null-spaces in order to build more ``geologically pleasing'' velocity models Clapp et al. (1997).

Here we build the velocity model from surface seismology while retaining the null-space aspect. We begin from fundamental concepts in Geophysical Estimation Theory Claerbout (1997) and we define the simplest interval velocity estimation method we can that includes the notion of null-space. Generally, we minimize interval velocity ``wiggliness'' where we don't have good quality reflections.

The method presented here is linear (almost). Although this simple approach may perform badly on certain practical tests (such as with multiple reflections) it should be a useful beginning in areas where careful statistical averaging is essential. Since the approach is a systematic interpretation of a general theory, the pathways to further improvements rely more on logic than on intuition and experience. An attractive feature of this simple method is that it readily extends towards estimation of the lateral variation in interval velocity. It also leads towards a logically consistent way of combining well velocities and seismic velocities.