Omnidirectional plane-wave destruction

Introduction

Seismic wavefields can be approximated by local plane waves, and the local slope field of these plane waves has been a significant parameter in seismic analysis. Plane-wave destruction (PWD) is one of the most popular tools to estimate the slope field. The linear PWD proposed by Claerbout (1992) uses explicit finite differences and obtains the slope field by least-squares estimation. The nonlinear PWD proposed by Fomel (2002) uses the maxflat fractional delay filter (Thiran, 1971; Zhang, 2009) to approximate a linear phase operator (or phase shift operator) and to provide a polynomial equation for the local slope (Chen et al., 2013). When the nonlinear PWD is applied iteratively, its first iteration corresponds to the linear PWD.

Local slope field has been widely applied in seismic applications. In applications such as model parameterization (Fomel et al., 2007; Fomel and Guitton, 2006), trace interpolation (Bardan, 1987) and wavefield separation and denoising (Harlan et al., 1984) in prestack datasets, seismic events usually have moderate slopes. However, in other applications, there might be steep or even vertical structures in the data and the slopes might be large or even infinite. Some common examples are: (1) migrated datasets, where geological structures can be steeply dipping, and attribute analysis may require the slope field (Marfurt et al., 1999); (2) time slices, where azimuths can follow any directions (Marfurt, 2006, Figure 2a is a good example); (3) profiles with insufficient horizontal sampling interval, causing dip aliasing problems (Barnes, 1996). Hale (2007) has shown that neither linear nor nonlinear PWD can cope with these steep structures well. In this case, the PWD-based slope estimation may be inaccurate.

In order to handle steep structures, several methods have been proposed to improve the linear PWD: Davis (1991) and Noye (2000) introduced other finite-difference methods to obtain a better phase-shift response. Hale (2007) applied the linear PWD in both horizontal and vertical directions, to construct the directional Laplacian operator. Schleicher et al. (2009) proposed total least-squares estimation to improve the least-squares estimation.

In this paper, we propose to interpret the phase shift operator in the nonlinear PWD as a 1D wavefield interpolator (vertical interpolation in a seismic trace). In order to handle omnidirectional structures, we introduce a 2D interpolator, which interpolates the wavefield along a circle instead of a vertical line. Circle interpolation can avoid aliasing problems and enable efficient modeling of steep structures.

We design a 2D maxflat fractional delay filter to implement circle interpolation. This 2D filter can be decoupled into a cascade of two 1D filters applied in different directions. Using the polynomial design of the maxflat fractional delay filter (Chen et al., 2013), we propose an omnidirectional plane-wave destruction (OPWD). We use a synthetic example to demonstrate the omnidirectional modeling ability and apply OPWD to improve events picking for a field dataset.

Omnidirectional plane-wave destruction