Seismic dip estimation based on the two-dimensional Hilbert transform and its application in random noise attenuation

introduction

Random noise, which refers to any unwanted features in data, commonly contaminates seismic data. Random noise sources in seismic exploration are roughly divided into three categories. First, there are external disturbances such as wind and human activities. Second, there is electronic instrument noise. Third, there is the irregular interference owing to seismic explosions. Random noise attenuation is a significant step in seismic data processing. In particular, the extent of noise suppression in poststack data directly affects the accuracy of subsequent processing and interpretation. Presently, several different random noise attenuation methods are available. Liu et al. (2006) presented a 2D multilevel median filter for random noise attenuation, whereas Liu et al. (2009b) used a 1D time-varying window median filter. Bekara and van der Baan (2009) used the empirical mode decomposition (EMD) method and proposed a filtering technique for random noise attenuation in seismic data. Liu et al. (2009a) proposed a high-order seislet transform for random noise attenuation. Li et al. (2012) applied morphological component analysis to suppress random noise and Liu et al. (2012) proposed a novel method of random noise attenuation based on local frequency-domain singular value decomposition (SVD). Maraschini and Turton (2013) assessed the effect of nonlocal means random noise attenuator on coherency. Li et al. (2013) used time-frequency peak filtering to suppress strong noise in seismic data. Liu and Chen (2013) used f-x regularized nonstationary autoregression to suppress random noise in 3D seismic data. The abovementioned random noise attenuation methods are limited by their lack of protection of structural information. For example, improper filtering may blur small faults, which may also make the displacement of larger fault continuous and consequently make layers appear continuous instead of faulted. Obviously, this hinders fault interpretation, and makes denoising and protecting structural information important. Fehmers and Hocker (2003) applied structureoriented filtering to fast structural interpretation. Hoeber et al. (2006) applied nonlinear filters, such as median, trimmed mean, and adaptive Gaussian, over planar surfaces parallel to the structural dip. Fomel and Guitton (2006) suggested the method of plane-wave construction by using model reparameterization. Liu et al. (2010) applied nonlinear structure-enhancing filtering by using plane-wave prediction to preserve structural information. Liu et al. (2011b) proposed a poststack random noise attenuation method by using weighted median filter based on local correlation and tried to balance the protection of fault information and noise attenuation.

Structure-oriented filtering includes structure prediction and filtering. Seismic dip is at the core of structure prediction; for, we can use seismic dip to determine structural trends and achieve structure protection. Ottolini (1983) used local slant stack to formulate a local seismic dip estimation method. Fomel (2002) proposed a seismic dip estimation method based on the plane-wave destruction (PWD) filter. Schleicher et al. (2009) compared different methods of local dip computations. The selection of filtering methods in structure-oriented filters is critical and polynomial fitting has been successfully applied to seismic data denoising. Lu and Lu (2009) used edge-preserving polynomial fitting to suppress random seismic noise. This method achieves better results when the trajectories of seismic events are linear or the amplitudes along the trajectories are not constant. Liu et al. (2011a) proposed a novel seismic noise attenuation method by using nonstationary polynomial fitting (Fomel, 2009) and shaping regularization (Fomel, 2007) for constraining the smoothness of the polynomial coefficients.

In this paper, we discuss the two-dimensional (2D) Hilbert transform and use it to derive the formula for the dip in the plane wave, construct a stable algorithm for estimating the dip, and improve the computational efficiency of Fomel's method (Fomel, 2002) without minimizing the precision of the dip estimation. Finally, we use synthetic model and field seismic data to demonstrate the applicability of the proposed method.

Seismic dip estimation based on the two-dimensional Hilbert transform and its application in random noise attenuation