Noncausal spatial prediction filtering for random noise reduction on 3-D poststack data

Abstract

A common practice in random noise reduction for 2-D data is to use pseudononcausal (PNC) 1-D prediction filters at each temporal frequency. A 1-D PNC filter is a filter that is forced to be two sided by placing a conjugate‐reversed version of a 1-D causal filter in front of itself with a zero between the two. For 3-D data, a similar practice is to solve for two 2-D (causal) one‐quadrant filters at each frequency slice. A 2-D PNC filter is formed by putting a conjugate flipped version of each quadrant filter in a quadrant opposite itself. The center sample of a 2-D PNC filter is zero. This paper suggests the use of 1-D and 2-D noncausal (NC) prediction filters instead of PNC filters for random noise attenuation, where an NC filter is a two‐sided filter solved from one set of normal equations. The number of negative and positive lags in the NC filter is the same. The center sample of the filter is zero. The NC prediction filters are more center loaded than PNC filters. They are conjugate symmetric as PNC filters. Also, NC filters are less sensitive than PNC filters to the size of the gate used in their derivation. They can handle amplitude variations along dip directions better than PNC filters. While a PNC prediction filter suppresses more random noise, it damages more signal. On the other hand, NC prediction filters preserve more of the signal and reject less noise for the same total filter length. For high S/N ratio data, a 2-D NC prediction filter preserves geologic features that do not vary in one of the spatial dimensions. In‐line and cross‐line vertical faults are also well preserved with such filters. When faults are obliquely oriented, the filter coefficients adapt to the fault. Spectral properties of PNC and NC filters are very similar.