RESIDUAL STATICS BY CDP‐LOCALIZED STACK OPTIMIZATION¹

Many conventional schemes of automated residual statics estimate time lags between prestack traces (sorted as CDP gathers) and a model section, and transform the collected lags into surface‐consistent residuals. The method discussed in this paper aims at improving the lag estimator. ‘Externally generated’ reference traces are avoided and a principle of localized stack optimization is introduced whereby application of a multichannel filter to the stack and evaluation of the normalized power of every filtered trace gives a measure of the stack quality. One may consider the power as a function of all variable (inconsistent) shifts applied to the prestack traces. To obtain a set of optimal lag estimates the power function must be maximized. This power function is complex and the number of its variables prohibits a straightforward search for the maximum. Thus an iterative method must be employed, and steepest descent schemes have proved the most satisfactory. In the actual calculation, the repeated evaluation of the objective can be replaced by the computation of certain cross‐correlations. At the last iteration (after five to ten coordinate sweeps), the global behaviour of this correlation gives some indications of how well a prestack trace is adapted to the filtered stack. This information is used to compute a weighting factor to be stored with the lag estimate. At this stage simple statistical procedures are run to eliminate the most unlikely estimates. The remaining ones are transformed to surface‐consistent residuals by means of a weighted least‐squares inversion according to a model which takes into account the fact that the lags have no fixed reference datum.

The efficiency of the method is demonstrated by a field data example into which synthetic anomalies were introduced, and the effect of the new process is compared with that of a ‘classical’ production program using field data with genuine static problems.