Signal and noise separation in prestack seismic data using velocity-dependent seislet transform

Introduction

Signal and noise separation is a persistent problem in seismic exploration. Sometimes noise is divided into random noise and coherent noise. Many authors have developed effective methods of eliminating random noise. Ristau and Moon (2001) compared several adaptive filters, which they applied in an attempt to reduce random noise in geophysical data. Karsli et al. (2006) applied complex-trace analysis to seismic data for random-noise suppression, recommending it for low-fold seismic data. Some transform methods were also used to deal with seismic random noise, e.g., the discrete cosine transform (Lu and Liu, 2007), the curvelet transform (Neelamani et al., 2008), and the seislet transform (Fomel and Liu, 2010). If seismic events are planar (lines in 2D data and planes in 3D data) or locally planar, one can predict seismic events by using prediction techniques in the $f$-$x$ domain (Canales, 1984; Liu and Liu, 2013; Sacchi and Kuehl, 2001) or the $t$-$x$ domain (Claerbout, 1992; Sacchi and Naghizadeh, 2009; Fomel, 2002; Liu et al., 2015).

Multiple reflections are one kind of coherent noise, especially in marine environments. Wave-equation based algorithms for attenuating multiples have rapidly developed since 1990s and usually consist of two steps, namely multiple prediction (Verschuur et al., 1992; Weglein et al., 1997; Berkhout and Verschuur, 1997) and adaptive subtraction (Fomel, 2009a; Wang, 2003b; Guitton and Verschuur, 2004). However, these algorithms need to calculate a full wavefield, which is often a computational bottleneck for their application, especially in the 3D case. Another popular class of demultiple techniques is based on variants of the Radon transform (Foster and Mosher, 1992). Several revised Radon transforms have been proposed for multiple attenuation (Hargreave et al., 2003; Hunt et al., 1996; Zhou and Greenhalgh, 1996; Wang, 2003a). Radon-transform based methods often fail to provide accurate separation because of their non-sparsity in characterizing seismic data, although they can be improved by high-resolution methods (Sacchi and Ulrych, 1995; Herrmann et al., 2000; Trad et al., 2003). Despite their usual classification as noise, multiples can penetrate deeply enough into the subsurface to illuminate the prospect zone. In this sense, multiples can also be viewed as a viable signal, rather than noise (Berkhout and Verschuur, 2006; Reiter et al., 1991; Youn and Zhou, 2001). Brown and Guitton (2005) proposed a least-squares joint imaging of pegleg multiples and primaries and discussed separation of pegleg multiples and primaries in prestack data.

In seismic data analysis, it is common to represent signals as sums of plane waves by using multidimensional Fourier transforms. The discrete wavelet transform (DWT) is often preferred to the Fourier transform for characterizing digital images, because of its ability to localize events in both time and frequency domains (Mallat, 2009; Jensen and la Cour-Harbo, 2001). However, DWT may not be optimal for describing data that consist of plane waves. Wavelet-like transforms that explore directional characteristics of images have found important applications in seismic imaging and data analysis (Herrmann et al., 2008; Chauris and Nguyen, 2008). Fomel (2006) investigated the possibility of designing a wavelet-like transform tailored specifically to seismic data and introduced it as the seislet transform. Fomel and Liu (2010) further developed the seislet framework and proposed additional applications. The original 2D seislet transform utilizes local data slopes estimated by plane-wave destruction (PWD) filters (Chen et al., 2013b; Fomel, 2002; Chen et al., 2013a). However, a PWD operator can be sensitive to strong interference, which makes the seislet transform based on PWD (PWD-seislet transform) occasionally fail in characterizing noisy signals.

In this paper, we develop a velocity-dependent (VD) concept (Liu and Liu, 2013), where local slopes in prestack data are evaluated from moveout parameters estimated by conventional velocity-analysis techniques. We implement a VD-seislet transform and propose its application for signal and noise separation. We expect the new VD-seislet transform to provide better compression ability for reflection events away from interference of strong random noise. We also provide an application of VD-seislet transform for separating primaries from pegleg multiples of different orders. We test the performance of VD-seislet transform using synthetic and field data.

Signal and noise separation in prestack seismic data using velocity-dependent seislet transform