A noise‐optimized objective method for predictive deconvolution

Predictive deconvolution filters are designed to remove as much predictable energy as possible from the input data. It is generally understood that temporally correlated geology can cause problems for these filters. It is perhaps less well appreciated that uncorrelated random noise can also severely affect filter performance. The root of these problems is in the objective function being minimized; in addition to minimizing predictable multiple energy, the filter is attempting to simultaneously minimize the temporally correlated geology and the random‐noise energy. Instead of minimizing the input trace energy, an alternative objective function for minimization can be defined that is the result of a linear operator acting on the input data. Ideally this alternative objective function contains only the targeted noise (e.g., multiples). The linear operator that creates this objective function is designated as the “noise‐optimized objective” (NOO) operator. The filter that minimizes this new objective function is the NOO filter. Useful NOO operators for multiple suppression are those that maximize multiple energy and/or minimize primary or random noise energy in the data. Examples of such linear operators include stacking, bandpass filtering, dip filtering, and muting or scaling. Simply scaling down the primary‐containing portion of the objective function can address the problematic removal of correlated geology. Stacking can also be a useful NOO operator. By minimizing the predictable energy on a stacked trace, the prestack filters are less affected by random noise. The NOO stacking method differs from a standard poststack filter design because the filters are designed to be applied prestack. Further, this method differs from a standard prestack prediction filter because it minimizes the predictable energy on the stacked trace. The standard prestack filter has reduced multiple suppression because the filter must compromise between minimizing the multiple energy and minimizing the random noise energy. Minimizing the impact of random noise can be quite important in prediction filtering. At a signal‐to‐random‐noise ratio of one, for example, half the multiple remains after filtering. This random noise‐related degradation might help to explain the common observation that prediction filters tend to leave multiple energy in the data. A time‐varying gap implementation of a stacking NOO filter addresses these random noise effects while also addressing data aperiodicity issues.