Some analyses of 2-D median f-k filters

Two‐dimensional median filters can be designed so that they have properties similar to f-k fan filters. This is done by using the coefficients of a truncated impulse response of an f-k filter as the weight coefficients for the weighted median process. The filter is called a median f-k filter and can be used to discriminate between events on the basis of apparent velocity. The filter appears suitable as a poststack coherency filter because it produces less distortion at wavefield terminations than conventional f-k fan filters. One‐dimensional weighted median filters that include negative coefficients are a logical starting point for the analysis of median f-k filters since simple numerical techniques may be used to analyze the behavior of these filters. We show that median filters with negative coefficients do not provide an unbiased estimate of the mean and can misplace the position of steps. Faults on a stacked section may be modeled by steps, and therefore applying a median f-k filter to stacked seismic data could change the position of faults. However, the distortion of steps introduced by median f-k filters is shown to be less than the distortion produced by the corresponding linear f-k filter, and the error in step placement is small. We present simple model examples and a seismic field data example to illustrate differences between linear f-k filters and median f-k filters.