A SEMBLANCE‐GUIDED MEDIAN FILTER1

Abstract

AbstractReiter, E.C., Toksoz, M.N. and Purdy, G.M. 1992. A semblance‐guided median filter. Geophysical Prospecting41, 15–41.A slowness selective median filter based on information from a local set of traces is described and implemented. The filter is constructed in two steps, the first being an estimation of a preferred slowness and the second, the selection of a median or trimmed mean value to replace the original data point. A symmetric window of traces defining the filter aperture is selected about each trace to be filtered and the filter applied repeatedly to each time point. The preferred slowness is determined by scanning a range of linear moveouts within the user‐specified slowness passband. Semblance is computed for each trial slowness and the preferred slowness selected from the peak semblance value. Data points collected along this preferred slowness are then sorted from lowest to highest and in the case of a pure median filter, the middle point(s) selected to replace the original data point. The output of the filter is therefore quite insensitive to large amplitude noise bursts, retaining the well‐known beneficial properties of a traditional 1D median filter. Energy which is either incoherent over the filter aperture or lies outside the slowness passband, may be additionally suppressed by weighting the filter output by the measured peak semblance.This approach may be used as a velocity filter to estimate coherent signal within a specified slowness passband and reject coherent energy outside this range. For applications of this type, other velocity estimators may be used in place of our semblance measure to provide improved velocity estimation and better filter performance. The filter aperture may also be extended to provide increased velocity estimation, but will result in additional lateral smearing of signal. We show that, in addition to a velocity filter, our approach may be used to improve signal‐to‐noise ratios in noisy data. The median filter tends to suppress the amplitude of random background noise and semblance weighting may be used to reduce the amplitude of background noise further while enhancing coherent signal.We apply our method to vertical seismic profile data to separate upgoing and downgoing wavefields, and also to large‐offset ocean bottom hydrophone data to enhance weak refracted and post‐critically reflected energy.