Abstract:
A 3D seismic image contains structural and stratigraphic features such as reflections, faults, and channels. When smoothing such an image, we want to enhance all of these features so that they are easier to interpret. Most smoothing methods aim to enhance reflections but may blur faults and channels in the image. A few methods smooth seismic reflections while preserving faults and channel boundaries. However, it has not well-discussed to smooth simultaneously along the seismic reflections and channels, which are linear features apparent within dipping reflections. In addition, to interpret faults and channels, extra steps are required to compute attributes or mappings of faults and channels from a seismic image. Such fault and channel attributes are often sensitive to noise because they are typically computed as discontinuities of seismic reflections. In this paper, we have developed methods to simultaneously enhance seismic reflections, faults, and channels while obtaining mappings of the faults and channels. In these methods, we first estimate the orientations of the reflections, faults, and channels directly in a seismic image. We then use the estimated orientations to control the smoothing directions in an efficient iterative diffusion scheme to smooth a seismic image along the reflections and channels. In this iterative scheme, we also efficiently compute mappings of faults and channels, which are used to control smoothing extents in the diffusion to stop smoothing across them. This diffusion scheme iteratively smooths a seismic image along reflections and channels while updating the mappings of faults and channels. By doing this, we will finally obtain an enhanced seismic image (with enhanced reflections and channels and sharpened faults) and cleaned mappings of faults and channels (discontinuities related to noise are cleaned up). We have examined the methods using 2D and 3D real seismic images. Introduction Seismic interpretation often includes extracting structural and stratigraphic features such as horizons, faults, and channels from a seismic image (Wu and Hale, 2016b). The seismic horizons can be directly extracted from a seismic image by following reflections, which are dominant linear (2D) or planar (3D) features in the seismic image (Wu and Hale, 2015). The seismic faults and channels are recognized as the lateral discontinuities of reflections in a seismic image (Gersztenkorn andMarfurt, 1999; Chopra and Marfurt, 2007). In a 3D seismic image, channels are also spatially apparent as linear features that are aligned within dipping reflections (Wu, 2017). To extract seismic faults and channels, we often need to compute an extra attribute image from a seismic image so that the faults and channels are the most prominent features in the attribute image (Wu and Hale, 2016a; Wu, 2017). In practice, such structural and stratigraphic features may not be obvious to track in a seismic image because of noise or limitations in seismic imaging methods. Therefore, a helpful step before seismic interpretation is to first enhance the structural and stratigraphic features in the seismic image so that the reflections are more continuous in areas away from faults and channels, the reflection discontinuities near faults and channels are more obvious, and the channels are spatially more continuous along dipping horizons or reflections. Some methods (e.g., Bakker et al., 1999; Fehmers and Höcker, 2003; Lavialle et al., 2007; Hale, 2009, 2011; Liu et al., 2010) have been proposed to enhance seismic reflections while preserving reflection discontinuities near faults and channel boundaries. To enhance the linear or planar reflections, most authors (Fehmers and Höcker, 2003; Lavialle et al., 2007; Hale, 2009) construct structure-oriented filters to smooth a seismic image along reflections by using anisotropic diffusion (Weickert, 1997, 1999). Some other authors construct structureoriented filters using the steered Kuwahara filter (Bakker et al., 1999; AlBinHassan et al., 2006), plane-wave prediction (Liu et al., 2010), and steered bilateral filter The University of Texas at Austin, Bureau of Economic Geology, Austin, Texas, USA. Central South University, Changsha, China. E-mail: guozhenwei@csu.edu.cn. Manuscript received by the Editor 21 September 2017; revised manuscript received 6 July 2018; published ahead of production 18 September 2018; published online 21 December 2018. This paper appears in Interpretation, Vol. 7, No. 1 (February 2019); p. T155–T166, 14 FIGS., 3 TABLES. http://dx.doi.org/10.1190/INT-2017-0174.1. © 2019 Society of Exploration Geophysicists and American Association of Petroleum Geologists. All rights reserved. t Technical papers Interpretation / February 2019 T155 D ow nl oa de d 05 /0 4/ 19 to 1 28 .8 3. 63 .2 0. R ed is tr ib ut io n su bj ec t t o SE G li ce ns e or c op yr ig ht ; s ee T er m s of U se a t h ttp :// lib ra ry .s eg .o rg / (Hale, 2011). To preserve reflection discontinuities near faults, all the methods require computing some fault image to stop the smoothing at the faults. To preserve computational efficiency, some authors (Bakker et al., 1999; Hale, 2009) do not update the fault image during the smoothing. However, such a fault image is often sensitive to noise, some other authors (Fehmers and Höcker, 2003; Lavialle et al., 2007; Liu et al., 2010; Hale, 2011) therefore prefer to iteratively update the fault image to obtain a more accurate detection of faults and to better preserve faults during the smoothing. Although structure-oriented smoothing methods have been proposed to enhance seismic reflections while preserving faults and channel boundaries, it is not discussed to simultaneously enhance or smooth along seismic stratigraphic features such as channels. In addition, the efficiency of the previous structure-oriented smoothing methods can be further improved. In this paper, we discuss fast cyclic explicit diffusion methods to simultaneously enhance reflections, faults, and channels in a seismic image while computing enhanced images of faults and channels. In the methods, we first estimate the orientations of reflections, faults, and channels from a seismic image. We also compute fault and channel mappings from the seismic image and apply faultand channel-oriented smoothing to enhance the fault and channel features in these mappings. We then use the orientations of reflections and channels to control the smoothing directions in an iterative diffusion scheme to smooth along reflections and channels in the seismic image. The fault and channel mappings are used to control the smoothing extents in the diffusion scheme so that the smoothing is performed along reflections and channels but not across faults and channels. In the diffusion scheme, we iteratively update the fault and channel mappings together with the seismic image. The finally updated fault and channel imageswill display enhanced faults and channels, whereas the finally updated seismic image will display enhanced reflections, channels, and sharpen discontinuities near faults and channel boundaries. To accelerate the diffusion, we use the fast explicit diffusion (FED) method proposed by Grewenig et al. (2010) and Weickert et al. (2016), which requires fewer iterations than the conventional explicit diffusions schemes. We demonstrate the proposed methods using 2D and 3D examples with many faults and channels. Structural and stratigraphic orientations Several methods, such as the structure tensor (Van Vliet and Verbeek, 1995; Weickert, 1997; Fehmers and Höcker, 2003), coherence scanning (Marfurt, 2006), plane-wave destruction (Fomel, 2002), and dynamic image warping (Arias, 2016), have been proposed to estimate seismic reflection orientations or slopes. However, the latter three methods are not applicable to estimate orientations of seismic stratigraphic features such as channels that are generally aligned within dipping reflections. In this paper, we use the structure tensormethod to estimate orientations of structural features (reflections) and stratigraphic features (channels). Structure tensors A structure tensor T at each seismic image sample can be constructed as a smoothed outer product of image gradient g∶T 1⁄4 hgg⊤i, where h·i denotes the smoothing for each element of the outer product or structure tensor. This smoothing, often implemented as a Gaussian filter, helps to construct structure tensors with stable estimations of seismic structural and stratigraphic orientations. For each image sample in a 2D image, a structure tensor T is a 2 × 2 symmetric positive-semidefinite matrix T 1⁄4 hgg⊤i 1⁄4 hg1g1ihg1g2i hg1g2ihg2g2i ; (1) where g 1⁄4 1⁄2g1g2 represent the 2D image gradients with first derivatives computed in the vertical (g1) and horizontal (g2) directions and h·i denotes the smoothing of whatever is inside the angle brackets. As shown by Fehmers and Höcker (2003), the seismic reflection orientation at each image sample can be estimated from the eigendecomposition of the structure tensor T at that sample T 1⁄4 λuuu þ λvvv; (2) where λu and λv are the eigenvalues corresponding to eigenvectors u and v of T. If we label the eigenvalues λu ≥ λv ≥ 0, then the corresponding eigenvectors u will be perpendicular to locally linear features (seismic reflections) in an image and the eigenvectors v will be parallel to such features. Figure 1a shows a 2D seismic image, and the cyan segments in Figure 1b represent the eigenvectors v that are aligned with the seismic reflections in the image. Although we display the eigenvectors v only at some image samples in Figure 1b, we actually compute eigenvectors u and v for all image samples from the eigendecomposition of 2D structure tensors. Figure 1. (a) A 2D seismic image is displayed with the (b) eigenvectors v (the cyan segments) of structure tensors. T156 Interpretation / February 2019 D ow nl oa de d 05 /0 4/ 19 to 1 28 .8 3. 63 .2 0. R ed is tr ib ut io n su bj ec t t o
