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.

Seismic trace interpolation in the f‐x‐y domain

“…If a f-x rather than the f-xy interpolator was applied within a shot gather, representation of curved events would have difficult. The f-x-y domain prediction, however, can relax the requirement that events be linear (Chase, 1992;Abma and Claerbout, 1995;Gülünay, 2000). Events that are nonlinear in one direction but linear in another may be predicted exactly with the f-x-y prediction filter.…”

“…These divided operators (with L = 5, for example), as shown schematically in Figure 3c, have the forms of has zero phase in the wavenumber space. The spectral properties of such a noncausal spatial prediction filter were described by Claerbout (1992) and Gülünay (2000). The LP system consisting of equations (5) and (6) may be represented in vector-matrix notation as…”

Multicomponent f-x seismic random noise attenuation via vector autoregressive operators

“…For instance, prediction filters are used by Canales (1984) and Spitz (1991) in the f-x domain for denoising and data interpolation, respectively. Other methods such as projection filters (Soubaras, 1994), noncausal prediction filters (Gulunay, 2000), singular value decomposition (Trickett, 2003), Cadzow denoising (Cadzow and Ogino, 1981;Trickett and Burroughs, 2009), and singular spectrum analysis (Oropeza and Sacchi, 2009) have also been used for random noise attenuation in the f-x domain. All of the f-x denoising methods are based on the assumption that the spatial signals at each single frequency are composed of a superposition of a limited number of complex harmonics (Sacchi and Kuehl, 2000).…”

Noncausal spatial prediction filtering based on an ARMA model

“…He designed and applied a 2-D prediction filter for each temporal frequency slice of the 3-D data volume. Gulunay (2000) systematically discussed the differences between pseudononcausal (PNC) and noncausal (NC) prediction fi ltering in 2-D and 3-D seismic data processing. He pointed out the NC prediction fi lters derived from symmetric YuleWalker normal equations can preserve more signal.…”