The reflection strength, frequency and phase of a seismic trace all serve to quantify key components of the seismic reflection pattern that can be examined not only on vertical slices but also on time and horizon slices through the seismic data volume. Because phase displays emphasize continuity or discontinuity in the seismic reflection pattern, the instantaneous phase and its cosine have long been used as an aid in mapping faults and unconformities including onlaps, offlaps and downlaps that form the basis of a seismic stratigraphic analysis. By construction, the cosine of instantaneous phase is insensitive to the seismic strength and therefore does not carry any information as to how strong such continuities and discontinuities may be. In this article, we show that corendering the cosine of instantaneous phase with relative acoustic impedance provides improved delineation of architectural elements of a complex turbidite system from the Taranaki Basin, New Zealand.
The Goal of Seismic Stratigraphic Analysis
Much of seismic interpretation is based on the identification of stratigraphically significant edges. For example, the time slice through coherence in figure 1 clearly delineates the architectural elements of a complex channel from the Romney survey in New Zealand’s Taranaki Basin, described in this article. In contrast, vertical slices through the same coherence volume (figure 2a) fail to accurately represent the stratigraphic terminations seen in the same slice through the seismic amplitude volume (figure 2b).
The identification of such stratigraphic boundaries is the goal of seismic stratigraphic analysis, specifically, to map geologic terminations such as onlap, offlap, downlap and erosional truncation surfaces. These mapped terminations can then be used to identify stratigraphic surfaces such as unconformities and maximum flooding surfaces. The interpreter then uses these surfaces to define relative stratigraphic ages that can be used to reconstruct the environment of deposition. It was shown earlier on that with sufficient well control an interpreter can construct a chronostratigraphic record of the area. Such geochronostratigraphic analysis has been vastly facilitated by software that (with interpreter guidance) autopicks each surface in a target area to map “relative geologic time”. Although there is research to automate the interpretation of surfaces where these horizons terminate, at present most interpreters simply pick those horizon terminations interactively.
In figure 2b, our goal is to delineate the separate architectural elements of this system, allowing us to use our understanding of depositional processes to better understand the evolution of the channel system and define components that may be more sand- rather than shale-prone.
Phase
On land data, a seismic trace can be considered to consist of the measured data from a geophone (related to the kinetic energy of the seismic event) and a 90-degree phase-rotated version of the data computed using a Hilbert transform weighted average of neighboring samples (related to the potential energy of the seismic event). In the 1970s, a suite of “instantaneous” attributes were introduced to quantitatively measure different components of the seismic reflection at each pixel (in 2-D) or voxel (in 3-D), one of which is the instantaneous phase. Because the instantaneous attributes are computed from the original measured data and its Hilbert transform, they should be interpreted as being localized rather than instantaneous measurements. The instantaneous phase is commonly displayed using a cyclical color bar that rotates around the color wheel (figure 3a) with voxel values of ±180 degrees assigned to the same color. It is an established fact that the human eye is more sensitive to spatial edges using a monochrome color bar. Although one could carefully construct a monochrome color bar with equal colors at ±180 degrees, it is much simpler to compute the cosine of the instantaneous phase, which has an added benefit of varying more slowly about 0 degrees and ±180 degrees, thereby emphasizing the contribution of peaks and troughs on zero-phase seismic amplitude volumes. In our gray-scale color bar, the cos(0 degrees), or a peak, will map to white, whereas the cos(±١٨٠ degrees), or a trough, will map to black, as shown in figure 3b.
Traditionally, interpreters map faults, sequence boundaries and other discontinuities directly on the cosine of instantaneous phase volume shown in figure 3b. By construction, the phase is insensitive to the strength of the seismic reflection event, such that noise associated with low amplitude events can overprint our image. This limitation is addressed by weighing the cosine of instantaneous phase by the envelope. An alternative is to corender the cosine of instantaneous phase with the seismic amplitude as shown in figure 3c. This later approach is unsatisfying, which motivates the construction of the workflow described in this article. In summary, we make the following observations:
- For well-defined horizons and a zero-phase source wavelet, reflector peaks and troughs map interfaces between geologic layers.
- The cosine of the instantaneous phase, cosφ, maps these peaks with a value of +1 and troughs with a value of -1.
- Relative acoustic impedance rotates the seismic amplitude by -90 degrees and increases the low-frequency component of the data. As such, it better represents the impedances of the layers that fall between the interfaces mapped by peaks and troughs of the original seismic amplitude volume.
We therefore hypothesize that corendering the relative acoustic impedance with the cosine of the instantaneous phase on vertical slices will generate improved delineation of geologic units.
Corendering the Cosine of Instantaneous Phase, Relative Acoustic Impedance
The primary goal of corendering is to combine the information content of two or more seismic attribute volumes, with the resulting image providing greater interpretational insight to either attribute by itself. A secondary (and not insignificant) goal is to provide images that are more easily (and perhaps more quickly) understood by teammates, partners, management and government regulators who are nowhere near as intimate with the seismic data than the seismic interpreter who generated them.
The first issue with figure 3c is that it is difficult to see the black and white extrema of the cosφ volume on top of the RAI volume using a yellow-red-white-blue-cyan amplitude color bar. Clearly, we don’t wish to use white for the zero crossing of an amplitude or relative acoustic impedance volume. Furthermore, the white peak of cosφ is difficult to see on yellow, as is the black trough of cosφ on blue (figure 4a). We therefore modify our relative impedance color bar as indicated by Figure 4b to generate the vertical slices of RAI shown in figure 5a and RAI corendered with cosφ in figure 5b where we can now more easily follow the peak and trough values of the cosφ attribute. For zero-phase data, the peaks and troughs of seismic amplitude represent the interfaces between geologic layers. In contrast, the RAI better represents the relative acoustic impedance of the layers themselves, at least within the limits of seismic resolution.
- Interpolation to a finer sample increment
Close inspection of figure 5b reveals discontinuous cosφ anomalies that limit their value in delineating the seismic facies indicated by the RAI. The spectrum of these data range between 5 and 85 hertz, such that reflectors with a dominant frequency of 50 hertz (or period of 20 milliseconds) will be sampled only six times, potentially missing the extrema of |cosφ|>0.8. To address this display issue, figure 6a shows the same corendered attributes computed from the data resampled to a 1 millisecond sample increment. Figure 6b and c show zoomed images of the data that fall in the yellow rectangles in figures 5b and 6a. Note the improved continuity of the cosφ attribute indicated by the yellow, green and orange arrows achieved by simple interpolation. This improvement is only because of display at discrete samples with no increase in seismic resolution.
The original seismic data exhibit time-variant spectra that range between 10 and 55 hertz (figure 7a). We subjected these data to a spectral balancing algorithm, as described in the March 2015 installment of Geophysical Corner, to obtain the “flatter” (more constant with frequency) spectrum shown in figure 7b that now ranges from 5 to 80 hertz. Figure 8a shows line AA’ through the original seismic amplitude volume whereas figure 8b shows the same line after spectral balancing. Arrows indicate areas within the channel of improved vertical resolution.
Improving the vertical resolution of the seismic amplitude volume also improves the vertical resolution of the resulting attributes where figure 9a shows line AA’ through cosφ and figure 9b through the corendered RAI and cosφ volumes. Arrows indicate the same locations shown in the previous figure. Note the improvement in resolution of these two figures over those computed from the original data volume (before balancing) shown in figures 3b and 6a.
As a final figure, we display a time slice though the corendered RAI and cosφ after spectral balancing in figure 10. Here, we find the images to be not as useful as the vertical slice images. We have obtained similar results on stratal slices through the corendered volumes. Basically, where we anticipated seeing sharp boundaries between impedance values on time slices like we did on vertical slices, we instead obtain white and black smears. Further examination reveals that these results accurately represent boundaries that are subparallel to the time and stratal slices.
Conclusions
Seismic stratigraphy is key to defining the depositional environment not only in frontier basins, but also in basins where lithologic and biostratigraphic data are available. We have shown how two attributes available in most interpretation workstation software - the instantaneous phase and relative acoustic impedance, can be corendered to delineate geologic packages important to seismic stratigraphic interpretation. Effective display requires the use of a carefully constructed color bar for relative acoustic impedance and interpolation of the data to a finer sample increment for cosφ. Spectral balancing further enhances the resolution of stratigraphic boundaries. Clearly, alternative “stratigraphic edge” algorithms are available with the most sophisticated being the automatic picking of chronostratigraphic horizons. Whatever the technique, our results accurately delineate stratigraphic images on vertical sections where attributes like coherence have limited value. We therefore suggest using corendered RAI and cosφ on vertical sections along with coherence on time and horizon slices to provide the greatest possible detail.
Acknowledgements
Thanks to New Zealand Petroleum and Minerals for providing access to their Romni3D data volume. All attributes were computed and displayed using software provided by the OU AASPI consortium.