Abstract:
The coherence attribute computation is typically carried out as a poststack application on 3D prestack migrated seismic data volumes. However, since its inception, interpreters have applied coherence to bandpass-filtered data, azimuthally limited stacks, and offset-limited stacks to enhance discontinuities seen at specific frequencies, azimuths, and offsets. The limitation of this approach is the multiplicity of coherence volumes. Of the various coherence algorithms that have evolved over the past 25 years, the energy ratio coherence computation stands apart from the others, being more sensitive to the seismic waveform changes rather than changes in their amplitude. The energy ratio algorithm is based on the crosscorrelation of five or more adjacent traces to form a symmetric covariance matrix that can then be decomposed into eigenvalues and eigenvectors. The first eigenvector represents a vertically variable, laterally consistent pattern that best represents the data in the analysis window. The first eigenvalue represents the energy of the data represented by this pattern. Coherence is then defined as the ratio of the energy represented by the first eigenvalue to the sum of the energy of the original data. An early generalization of this algorithm was to compute the sum of two covariance matrices, one from the original data and the other from the 90° phase rotated data, thereby eliminating artifacts about low-amplitude zero crossings. More recently, this concept has been further generalized by computing a sum of covariance matrices of traces represented by multiple spectral components, by their azimuthally limited stacks, and by their offset-limited stacks. These more recently developed algorithms capture many of the benefits of discontinuities seen at specific frequencies, azimuths, and offsets, but they present the interpreter with a single volume. We compare the results of multispectral, multiazimuth, and multioffset coherence volumes with the traditional coherence computation, and we find that these newer coherence computation procedures produce superior results. Introduction Coherence is a discontinuity detection attribute, which is applied to stacked migrated seismic data volumes to facilitate the interpretation of geologic structural or stratigraphic discontinuities. In general, coherence is applied to data stacked after migration, and it is available in most workstation interpretation software packages. Various implementations of coherence algorithms have evolved over the past 25 years including crosscorrelation-based (Bahorich and Farmer, 1995), semblance-based (Marfurt et al., 1998), variance-based (Pepper and Bejarano, 2005), Sobel filter-based (Luo et al., 1996, 2003), eigenstructure-based (Gersztenkorn and Marfurt, 1999), and gradient structure tensor-based (Bakker, 2003) algorithms. The algorithms most commonly available on workstation software packages are the semblance and some form of eigenstructure decomposition of covariance matrices. We restrict our analysis to the application of the energy ratio algorithm (Chopra and Marfurt, 2008), which is a variation of the eigenstructure approach. We discussed in detail the applications of coherence attribute to seismic data in Chopra and Marfurt (2007, 2018a, 2018b). The interpretation of stratigraphic features on seismic data is dependent on their bandwidth. In general, seismic data that have a higher bandwidth also provide greater lateral resolution, resulting in sharper coherence images. However, because of tuning, some frequencies may be more sensitive to a given lateral stratigraphic discontinuity than others. Likewise, a given seismic wavelet may show two different horizons to be “aligned” across a fault (e.g., Libak et al., 2017), whereas a wavelet at a different frequency may be misaligned. For these reasons, sometimes interpreters run spectral decomposition (Partyka et al., 1999) or compute spectral voice components prior to computing coherence (Chopra and Marfurt, 2016). In general, TGS, Calgary, Alberta, Canada. E-mail: satinder.chopra@tgs.com (corresponding author). The University of Oklahoma, Norman, Oklahoma, USA. E-mail: kmarfurt@ou.edu. Manuscript received by the Editor 15 May 2018; revised manuscript received 30 October 2018; published ahead of production 05 December 2018; published online 15 March 2019. This paper appears in Interpretation, Vol. 7, No. 2 (May 2019); p. SC21–SC32, 13 FIGS. http://dx.doi.org/10.1190/INT-2018-0090.1. © 2019 Society of Exploration Geophysicists and American Association of Petroleum Geologists. All rights reserved. t Special section: Seismic geometric attributes Interpretation / May 2019 SC21 D ow nl oa de d 05 /0 6/ 19 to 2 05 .1 96 .1 79 .2 37 . 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 / higher frequency spectral magnitudes or voice components highlight lateral variation in thinner beds, whereas lower frequency magnitude or voice components highlight lateral changes in thicker beds. Another tool at their disposal is the red-green-blue blending of three frequency components, which allows interpreters to corender the information content at different scales. Although useful, this color display tool has a limitation Figure 1. A vertical slice through a 3D seismic amplitude volume from the Montney-Dawson area of northeast British Columbia. The data had been put through one pass of structure-oriented filtering, and the interpreted horizons are shown in green and yellow (data courtesy of TGS, Calgary). Figure 2. Stratal slices 36 ms above the yellow horizon shown in Figure 1 through (a) coherence volume generated on the fulloffset stack and (b) multispectral coherence volume generated by using 12 selected voice component (20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, and 75 Hz) volumes. Similar stratal slices generated along the yellow horizon though the (c) full-offset stack and (d) multispectral coherence volume. The seismic data are from the Montney-Dawson area in British Columbia, Canada. Notice the overall better definition of faults (indicated by the yellow, cyan, and green arrows) and the paleochannels (indicated with the magenta arrows) on the multispectral coherence volume shown in Figure 3b and 3c (data courtesy of TGS, Calgary). SC22 Interpretation / May 2019 D ow nl oa de d 05 /0 6/ 19 to 2 05 .1 96 .1 79 .2 37 . 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 / in that it can show only three components at a time (Henderson et al., 2008). Obviously, if a given spectral component highlights a feature of interest, one can delineate edges in such volumes using coherence. The same argument applies to azimuthally limited, offset-limited, or angle-limited partial stacks of the migrated data. Because of amplitude variation with offset effects, lithologic “edges” may be stronger on coherence computed on the far-offset stack. Similarly, faults and other discontinuities will be better illuminated by a perpendicular rather than a parallel azimuthally limited partial stack (Chopra and Marfurt, 2007). Unfortunately, there are two major drawbacks to this “component analysis” workflow. First, each spectral component or partial stack has a lower signal-to-noise content than the broadband or full-stack data volume. Second, the interpreter is now faced with interpreting multiple coherence images, one for each component, which (because of their lower signal-to-noise ratio) can be tedious and very time consuming. Marfurt (2017) describes a way to construct a multispectral covariance matrix by summing the covariance matrices for all the input spectral components each of which is oriented along the structural dip using analytic voice components. The energy ratio coherence computed using this approach is referred to as multispectral coherence. Qi et al. (2017) extend this concept to azimuthally limited and offset-limited partial stacks, resulting in “multiazimuth” and “multioffset” coherence. Recall that the seismic response across offsets is sensitive to changes in lithology, porosity, and fluid content. Therefore, we expect that the attribute images generated from offset-limited volumes will show some sensitivity to these changes. In fact, the stratigraphic effects have the maximum influence on the near-offset range, and the lithology and fluid have the greatest effect on the longer offsets. When the seismic amplitudes are stacked over all offsets, we obtain some average of all these responses. Although the presence of hydrocarbons can cause changes in seismic response with offset or incident Figure 4. A segment of a seismic section from the Montney-Dawson area in northeast British Columbia in Canada. Stratal slices have been generated between two horizons in black and are shown in red. Displays along stratal slices numbered 8, 12, and 14 are shown in Figure 5 (data courtesy of TGS, Calgary). Figure 3. Stratal slices 38 ms above a horizon at approximately 1400 ms through (a) coherence volume generated on the full-offset stack, (b) multispectral coherence volume generated by using 12 selected voice component (20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, and 75 Hz) volumes, and (c) multispectral coherence volume generated by using six selected voice component (50, 55, 60, 65, 70, and 75 Hz) volumes. The seismic data are from the Montney-Dawson area in British Columbia, Canada. Notice the overall better definition of faults (indicated with the yellow, cyan, and green arrows) and the paleochannels (indicated with the magenta arrows) on the multispectral coherence volume shown in (b) (data courtesy of TGS, Calgary). Interpretation / May 2019 SC23 D ow nl oa de d 05 /0 6/ 19 to 2 05 .1 96 .1 79 .2 37 . 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 / angle, aligned vertical fa
