Three‐dimensional Optimum Multichannel Velocity Filters*

Abstract

Design procedures and characteristics of three stacking filters are discussed which may find application in various three‐dimensional velocity filtering problems. These filters are derived in the time‐domain as optimum multichannel Wiener filters. Random stationary functions are assumed as stochastic models for the seismic traces. All power and crosspower spectra which are the basic elements of the multichannel normal equations are statistically averaged according to specific three‐dimensional considerations. Various properties of the input traces may be incorporated in the design of the optimum filters. With fairly general assumptions about the input these filters are deterministic in the sense that they are applicable to a broad class of input traces with similar statistics in amplitudes and arrival times of signals.