Data limitations - and solutions

I feel that the data used here has been stretched to the limits of its inherent usefulness. In my estimation, the following attributes (not an exhaustive list) describe ``ideal'' data for this problem:

1.

Dense, wide-area seismic coverage.

2.

20 or more wells inside seismic coverage.

3.

Five or more picked seismic horizons.

4.

Access to stacking velocities.

I combine ``Conclusions'' and ``Future Work'' into one section, because SEP is in the process of acquiring a large group of North Sea data from Mobil that will better allow us to develop and test new ideas, thanks to a collaboration with the Stanford Center for Reservoir Forecasting (SCRF). The data consists of five densely sampled seismic horizons and over twenty wells with well log data.

Verification of the validity of the final model $\tilde{\bold H}_i(x,y)$ is a difficult and ill-defined task. The method of cross-validation seems most promising. The optimization problem of Equation (8) is solved, but one of more of the well logs is disregarded. At the disregarded well locations, compare the depth to the actual horizon from the well log and that predicted by $\tilde{\bold H}_i(x,y)$. Since the first and second ``ideal data attributes'' should be satisfied to make this scheme viable, I do not utilize it in this paper, but I think the Mobil data is well-suited for the task. One can imagine a more complicated cross-validation scheme, in which many values of $\tilde{\bold H}_i(x,y)$ are determined from Equation (8) by removing different well logs. The result is a map of cross-validation errors, which is then minimized in another least-squares scheme.