Nonlinear structure-enhancing filtering using plane-wave prediction

Introduction

Extracting structural information is the most important goal of seismic interpretation. A number of approaches have been proposed to preserve and enhance structural information. Hoeber et al. (2006) applied nonlinear filters, such as median, trimmed mean, and adaptive Gaussian, over planar surfaces parallel to the structural dip. Fehmers and Höcker (2003) and Hale (2009) applied structure-oriented filtering based on anisotropic diffusion. Fomel and Guitton (2006) suggested the method of plane-wave construction. AlBinHassan et al. (2006) developed 3-D edge-preserving smoothing (EPS) operators to reduce noise without blurring sharp discontinuities. Traonmilin and Herrmann (2008) used a mix of finite-impulse-response (FIR) and infinite-impulse-response (IIR) filters, followed by f-x filtering, to perform structure-preserving seismic processing. Whitcombe et al. (2008) introduced a frequency-dependent, structurally conformable filter. Random noise attenuation and structure protection are always ambivalent problems in seismic data processing. The main challenge in designing effective structure-enhancing filters is controlling the balance between noise attenuation and signal preservation.

Mean filter (stacking) plays an important role in improving signal-to-noise ratio in seismic data processing (Yilmaz, 2001). Conventional stacking is a simple and effective method of denoising, but it is optimal only when noise has a Gaussian distribution (Mayne, 1962). Therefore, alternative stacking methods were proposed. Robinson (1970) proposed a signal-to-noise-ratio-based weighted stack to further minimize noise. Tyapkin and Ursin (2005) developed optimum-weighted stacking. To eliminate artifacts in angle-domain common-image gathers, Tang (2007) presented a selective-stacking approach, which applied local smoothing of envelope function to achieve the weighting function. Rashed (2008) proposed ``smart stacking,'' which is based on optimizing seismic amplitudes of the stacked signal by excluding harmful samples from the stack and applying more weight to the center of the samples population. Liu et al. (2009a) introduced time-dependent smooth weights to design a similarity-mean stack, which is a nonstationary, nonlinear operator.

Lower-upper-middle (LUM) filters (Hardie and Boncelet, 1993) are a class of rank-order-based filters that generalize the concept of the median filter. They combine the characteristics of two subclasses, LUM smoothers and LUM sharpeners, and find a variety of signal and image-processing applications. A special LUM smoother, probably still the most widely used, is a simple median of the points within a window. The median filter is a well-known method that can effectively suppress spike-like noise in nonstationary signal processing. Median filters find important applications in seismic data analysis. Mi and Margrave (2000) incorporated noise reduction using median filter into standard Kirchhoff time migration. Zhang and Ulrych (2003) used a hyperbolic median filter to suppress multiples. Liu et al. (2009b,2006) implemented random-noise attenuation using 2-D multistage median filter and nonstationary time-varying median filter. However, in many cases the median filter introduces too much smoothing. LUM sharpeners have excellent detail preserving characteristics because of their ability to pass small details with minimal distortion. For a given window size and shape, the parameters of LUM filter can be adjusted independently to yield a wide range of characteristics.

In this paper, we combine structure prediction (Fomel, 2008) with either nonlinear similarity-mean filtering or lower-upper-middle (LUM) filtering to define a structure-enhancing filter. Structure prediction generates structure-conforming predictions of seismic events from neighboring traces, whereas a similarity-mean filtering or an LUM filtering reduces several predictions to optimal output values. We test the proposed method on synthetic and field data examples to demonstrate its ability to enhance structural details of seismic images.

Nonlinear structure-enhancing filtering using plane-wave prediction