The Design of High-Resolution Digital Filters

Seismic recordings made with standard filters often afford insufficient resolution for overlapping reflected events. In this treatment we apply least squares Wiener theory to the design of high-resolution digital time-domain filters. Under the assumption that estimates of the seismic pulse shape are available, we present techniques that allow one to calculate digital filters which transform this pulse into one which is sufficiently sharp so that it can be distinguished against a background of noise. The two design criteria governing filter performance are filter lag and filter memory function duration. The performance of a Wiener filter is numerically measurable by a quantity which we call the filter performance parameter P, where 0 ¿ P ¿ 1. The quality of the filter output improves as P approaches unity. We thus seek that combination of lag and memory function duration that maximizes P. This goal can be accomplished by the study of a two-dimensional display of P vs. lag and memory function duration. The proposed design techniques are illustrated by means of numerical examples.