Some analyses of 2-D median f-k filters

Abstract

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.

Large explosive shot gathers along the SinoProbe deep seismic reflection profile and Moho depth beneath the Qiangtang terrane in central Tibet

“…The median filter is a simple and effective method in signal processing that can suppress noise (especially spikes), especially in non-stationary signal processing. The method has been applied in seismic prospecting (Bednar 1983;Duncan and Beresford 1995). Based on the recent research, this filter can effectively separate the signal from noise, preserve detailed structure, and then reduce the random noise (Liu et al,2006;Huo et al,2012).…”

Median filtering in Kirchhoff migration for noisy data

“…Stewart (1985) showed that F-K domain median filters can tremendously reduced noise in VSP data. Duncan and Beresford (1995) applied F-K median filtering to surface seismic data and obtained very good results.…”

Swell Noise Attenuation Using a Cascade of F-X Filter and Median Filter

“…파랑잡음과 같은 돌출값 형태로 존재하는 잡음을 제거하기 위해 주로 사용하는 방법으로 중앙값 필터(median filter)가 있 다. 중앙값 필터는 간단하지만 매우 효과적이며 (Bednar, 1983;Duncan and Beresford, 1995), 잡음의 특성에 따라 보다 복잡 한 형태의 중앙값 필터도 제시되고 있다 (Mi and Margrave, 2000;Liu et al, 2006). 불규칙 잡음을 제거하기 위한 다른 방 법으로는 비인과(noncausal) 예측필터를 이용한 잡음제거법 (Gulunay, 2000), 적응필터를 통한 잡음제거법 (Ristau and Moon, 2001), 복소 트레이스 분석(complex-trace analysis)을 통한 잡음제거법 (Karsli et al, 2006) Ma 경에 이르러 섭입이 중단된 것으로 알려져 있다 (Kim et al, 1995;Larter et al, 1997;Livermore et al, 2000).…”