Design of Sub‐optimum Filter Systems for Multi‐trace Seismic Data Processing*

Abstract

Using optimum filter theory as a starting point, we describe a method for the design of practical multi-trace seismic data processing systems. We assume the inputs to be the superposition of signal, coherent noise, and incoherent noise. The signal and coherent noise moveouts are described statistically by their probability densities. Our approach is to split the system into two stages. The first stage achieves optimum noise suppression but distorts the signal. The signal distortion is reduced in the second stage by an optimum finite memory inverse filter.The system that is obtained using our method of design depends upon the form of the probability density functions. We show two examples, ghost suppression and velocity filtering.In ghost suppression we choose a model with moveouts known exactly, which corresponds to delta functions for the probability densities.In velocity filtering the signal and coherent noise moveouts are equally probable within non-overlapping ranges.The resulting system in each case is both simple and effective. In ghost suppression a simple shift and subtract cancels the coherent noise. The signal distortion is reduced by an inverse filter. The velocity filter system consists of differentiated moving averages applied to each trace, followed by a go' phase shift and a low pass filter. DESIGN OF SUB-OPTIMUM FILTER SYSTEMS FOR MULTI-TRACE SEISMIC DATA PROCESSING I. IlztroductionThe use of Wiener optimum filter theory in multi-trace seismic data processing was proposed by Robinson (1954) and applied by Burg (1962). In this theory economic constraints are not imposed and the resulting filters are costly to construct and apply. Our purpose is to describe a method which goes beyond the optimum theory, producing practical filters whose performance is excellent. We begin by selecting a basic system which is optimum for high noise levels. For actual data this system effectively suppresses the noise but badly distorts the signal. We then apply an inverse filter to reduce the signal distortion.

Principles of Digital Wiener Filtering*

“…Simpson et al, 1961Simpson et al, -1964Foster et al, 1964;Schneider et al, 1964, and many others). Its usefulness will depend on the ultimate degree of success that it can yield in unraveling an actual seismogram.…”

“…Particular cases of this model have, however, been successfully used in a very wide variety of seismic problems over the past decade (see e.g. Simpson et al, 1961Simpson et al, -1964Foster et al, 1964;Schneider et al, 1964, and many others). Our present purpose is to show some of its potential uses in actual seismic analysis, but for the sake of brevity we shall not give examples using real seismic data.…”

Three‐dimensional Optimum Multichannel Velocity Filters*

“…Filters computed in this way are difficult to obtain with other techniques. The class designed with this particular procedure includes, for instance, ghost suppression filters (Schneider, Larner, Burg, Backus rg64), suboptimum velocity filters (Foster, Sengbush, Watson 1964), optimum multichannel velocity filters (Sengbush, Foster 1968) and optimum multichannel stacking filters (Galbraith and Wiggins 1968). The design principle is basically the same in all cases.…”

Studies of the Effect of Depth of Focus on Seismic Pulses: Estimation Procedure for Focal-Depth Determination of Seismic Disturbances

“…These assumptiens are probably not true fot the seismic data generation process, but are nevertheless appropriate when no further knowledge concerning the noise statistics are available (Foster et al, 1964).…”

“…An inverse operate-designed for a specific R and R combination may be modified for any delay time T, simply by making the spacing between filter points equal to that of the desired delay time. This is true because the inverse filter is a sampled function (sampled at 0.1 second intervals) which is zero everywhere except at multiples of T (Foster et al, 1964). Appendix II contains diagrams ot the filter arrays used in this thesis.…”