Plane-wave Sobel attribute for discontinuity enhancement in seismic images |

Bahorich and Farmer (1995) proposed the first celebrated discontinuity enhancement attribute and coined the term ``coherence". The attribute produces images of the normalized local cross-correlations between adjacent seismic traces and combines them to estimate coherence. This algorithm provided the framework for semblance, the generalization to an arbitrary number of traces, proposed by Marfurt et al. (1998). Using multidimensional correlations, this approach improves vertical resolution. Both of these correlation-based methods can be sensitive to lateral amplitude variations, which may obscure features such as faults and channels.

The local covariance matrix measures the uniformity of a seismic image in each dimension. Decomposing this matrix into its eigenvectors and eigenvalues provides a quantitative measure of local variations of seismic structures. Gersztenkorn and Marfurt (1999) propose to compute the ratio of the largest eigenvalue and the sum of all eigenvalues of the covariance matrix at each sample, highlighting areas where there is no dominant texture in the seismic image. This attribute is commonly called ``eigenstructure coherence" and is only sensitive to lateral changes in phase. A similar decomposition can be applied to the structure-tensor which measures the local covariance of the image in each dimension (Randen et al., 2001; Bakker, 2002; Randen et al., 2000). Local linearity and planarity can be computed from the eigenvalues of the structure-tensor. Wu (2017) proposes to modify the traditional structure-tensor decomposition by orienting the image gradient along seismic structures. Discontinuous features are highlighted further by smoothing along discontinuities.

Information about reflection dip in seismic images allow filters to be oriented along seismic reflections. Variance is a simple, but effective attribute which highlights unpredictable signal associated with discontinuous features. The local variance calculation is oriented along structure using the eigenvectors of the structure-tensor (Randen et al., 2001). Hale (2009) also orients semblance along seismic reflections using the eigenvectors of the structure-tensor, and additionally applies smoothing along directions perpendicular to the reflections to provide an enhanced image. Karimi et al. (2015) uses predictive painting (Fomel, 2010) to generate multiple predictions of local structures in seismic images. The difference between the predicted and real data provides an image with isolated discontinuities.

To compute a discontinuity enhancement image for detection and extraction of fault surfaces, semblance can be computed along fault strike and dip orientations. Cohen et al. (2006) use the normalized differential entropy attribute to enhance faults. Local fault planes are separated and extracted using an adaptive image-binarization-and-skeletonization algorithm. This method effectively extracts fault surfaces by segmenting the coherence image. Hale (2013) and Wu and Hale (2016) propose to scan through fault strikes and dips to maximize the semblance attribute. Fault surfaces are constructed by picking along the ridges of the likelihood attribute. Additionally, images can be unfaulted by estimating fault throws using correlations of seismic reflections across fault surfaces (Wu et al., 2016).

In image analysis, the traditional Sobel filter can be used to efficiently compute an image with enhanced discontinuities (Sobel and Feldman, 1968). The Sobel filter is an edge detector which computes an approximation of the gradient of the image intensity function at each point by convolving the data with a zero-phase discrete differential operator and a perpendicular triangular smoothing filter. This 2D filter is small and integer-valued in each direction, making it computationally inexpensive to apply to images (O'Gorman et al., 2008). Luo et al. (1996) first proposed the applications of Sobel filters to seismic images. Since, modifications of the Sobel filter have been proposed for edge detection in seismic images by orienting the filter along local slopes estimated by maximizing local cross-correlation and dynamically adapting the size of the filter based on local frequency content (Aqrawi et al., 2011; Aqrawi, 2014; Aqrawi and Boe, 2011). Dip-oriented Sobel filters can be applied directly to a seismic image to compute an image with enhanced edges, or to coherence images to further sharpen previously enhanced edges (Chopra et al., 2014).

We propose to modify the definition of the Sobel filter to follow seismic structures. We modify the Sobel filter by replacing the discrete differential operator with linear plane-wave destruction (Fomel, 2002) and triangular smoothing with plane-wave shaping (Phillips et al., 2016; Fomel, 2007; Swindeman, 2015). This method is particularly efficient because it does not require computation of the eigenvectors of the covariance matrix or structure-tensor. Local slopes are instead estimated using accelerated plane-wave destruction (Chen et al., 2013). We further modify the Sobel filter by orienting the filter along the azimuth perpendicular to discontinuities by implementing an azimuth scanning workflow (Merzlikin et al., 2017b). Merzlikin et al. (2017a) demonstrate the successful application of plane-wave Sobel filtering in the data domain to highlight seismic diffractions before imaging discontinuous features. We test our modification on benchmark 3D seismic images from offshore New Zealand and Nova Scotia, Canada and compare the results with those from alternative coherence attributes.

Plane-wave Sobel attribute for discontinuity enhancement in seismic images |

2018-11-15