Spectral decomposition is a valuable analytical technique with applications in direct hydrocarbon detection, thickness determination and the measurement of attenuation, lithology and fluid type. Despite this impressive list of applications, spectral decomposition generates a large number of volumes for analysis which can overwhelm the seismic interpreter.
The geology illuminated by these volumes can be visualized by animating across spectral magnitudes on time, depth or horizon slices, a process that is both laborious and time-consuming. During animation, interpreters may identify two or three spectral component volumes that exhibit spatial patterns indicative of subsurface geological features. When three spectral magnitude components uniquely respond to certain geologic features, they are co-rendered using a red-green-blue (RGB) color combination. Efforts have been made to reduce the dimensionality of the numerous spectral components through principal component or independent component analysis. An alternative to color blending and dimensionality reduction is the use of statistical measures derived from the spectrum’s histogram.
It is a common observation that as the thickness of a formation decreases, the associated peak frequency slightly increases. This finding was expanded by applying a short-window discrete Fourier transform to the seismic data, demonstrating that the frequency corresponding to the peak spectral magnitude effectively describes formation thickness. Specifically, a low peak frequency indicates thick channels, while a high peak frequency suggests thin channels.
From such initial observations, we can generate several statistical measures that extract key components of the seismic spectrum. These attributes include peak magnitude, peak frequency and peak phase. An additional effective attribute is the measurement of peak magnitude above the mean spectrum, which is useful for delineating high amplitude tuning events. Similarly, the bandwidth is defined as the frequency distance between the leftmost and rightmost values of 1/√2 of the peak magnitude.
Figure 1 defines some of the aforementioned terms for a typical magnitude spectrum, where the peak frequency, or the mode of the spectrum, indicates the location of the peak spectral magnitude and is often associated with the tuning thickness. The mean magnitude represents the average of all computed magnitudes. The peak magnitude above the mean is calculated by subtracting the mean magnitude spectrum for each sample from the peak magnitude.
Application
Let us now investigate the application of these attributes to actual seismic data and examine their utility for seismic interpreters. We aim to show how peak frequency and peak magnitude volumes can be effectively co-rendered, and how the inclusion of multispectral energy ratio coherence in these co-rendered displays can enhance context and add value to their interpretation. These displays are produced for both the input seismic data and its spectrally balanced counterpart.
Availability of Seismic Data
For our current study, we have chosen the Romney 3-D seismic data volume from the deepwater Taranaki Basin, located off the northwest coast of New Zealand. We had earlier used this data volume to showcase a deepwater turbidite channel in terms of unsupervised seismic facies classification. More details about the seismic data can be found in the October 2022 Geophysical Corner. Figure 2a displays a segment of a seismic section from this dataset, along with its frequency spectrum. A significant Miocene deepwater channel is visible in the center of the section.
An exploration well was drilled on this 3-D seismic volume to a depth of 4,575 meters below the sea surface. It did not intersect the Miocene deepwater channel, but it provided valuable lithology information. The Miocene strata comprise claystone, siltstone and limestone. When correlated with the seismic data, these lithoelements show strong amplitude, high-continuity reflections at limestone to mudstone interfaces and weaker amplitudes within the mudstone deposits. The bright seismic amplitudes within the channel correspond to shingled reflections, suggesting sandy fill during migration of the channel.
The Work Plan
As is well known, the wavelet in seismic data changes with depth. To ensure accurate extraction of geological information in terms of tuning effects, and to avoid bias toward the spectral characteristics of the seismic wavelet, the data must undergo spectral balancing.
The peak frequency of the unbiased data volume is biased toward the peak frequency of the seismic wavelet. If the tuning frequency falls within the spectrally balanced part of the spectrum, the peak frequency often correlates with the temporal tuning thickness.
It is also important to consider that tuning thickness estimates from peak frequency in areas of anomalously low reflectivity are less meaningful than those from areas of high reflectivity where the result is modified by the overprinted noise spectrum. As a result, when peak frequency is plotted against hue and modulated by peak magnitude (plotted against saturation), areas of low reflectivity are represented by grayer tones.
In scenarios in which mapping of high reflectivity channels within a lower reflectivity matrix is required, a composite plot of peak frequency and peak magnitude above mean can highlight the highly tuned channels. Composite plots combining any two of the three attributes (peak frequency, peak magnitude and peak magnitude above mean) can be effectively integrated with the coherence attribute. This integration allows the spectral attributes to represent channel thickness, while coherence indicates channel width.
Therefore, the data at hand was spectrally balanced, followed by the generation of coherence and spectral attributes, as will be discussed in the next section.
Conditioning Seismic Data for Attribute Analysis
Traditional seismic data typically preserve information up to 50 or 60 hertz at the high end of the bandwidth. While this could suffice for thicker conventional reservoirs, it often lacks the necessary resolution for deepwater turbidite reservoirs. However, advancements in seismic data acquisition and processing, along with increased computer capacities and speeds, offer cost-effective solutions for enhancing resolution. In addition to the reasons stated above as to why spectral balancing is necessary, to improve the vertical and lateral resolution of a decade-old vintage seismic dataset, an amplitude-friendly post-stack spectral balancing procedure is required. Our preferred method for spectral balancing was first introduced by Marfurt and Matos and has been described in the May 2014 Geophysical Corner.
Figures 2a and 2b present a comparison of seismic section segments crossing a deepwater channel complex before and after frequency balancing, including their frequency spectra. The reflections appear well-defined both outside and within the channel complex in figure 2b, and the frequency spectra look flatter compared to the input seismic volume.
The frequency balanced seismic data volume then underwent structure-oriented filtering and attribute computation. To highlight the benefits of this process, attribute computation was also repeated on the input seismic data volume, and comparative results will be displayed in the following section.
Coherence Attribute
Encouraged with the higher-frequency content of the seismic data, we first generated the coherence attribute. Much has been written about this attribute and the usefulness of its application.
Coherence applied to band-pass filtered or spectral voice components often delineates edges at or near the tuning frequency of a particular formation. Typically, higher frequencies better reveal shorter, more vertically confined faults and channel edges, whereas lower frequencies more effectively delineate through-going faults. Furthermore, besides computing a covariance matrix for each bandpass filtered data set and then calculating coherence for each, an alternative and efficient way would be to sum the covariance matrices and use it to derive coherence, leading to the concept of multispectral coherence computation. More details on multispectral coherence and its applications can be found in the July 2018 Geophysical Corner. We employ multispectral coherence for creating corendered displays that integrate spectral attributes calculated from both the input and frequency-balanced seismic data volumes.
Spectral Decomposition
Various methods exist for computing spectral decomposition, such as the traditional short-window discrete Fourier transform, continuous wavelet transform, S-transform and matching pursuit. More details on spectral decomposition methods can be found in the December 2013, March 2014 and March 2015 installments of Geophysical Corner. In this study, we utilize the matching pursuit method, known for its high-resolution attribute production.
Beyond creating spectral magnitude components, we also produce attributes such as peak frequency, peak magnitude and peak magnitude above the mean spectrum. The subsequent section will explore the creation of composite plots using these spectral peak attributes in conjunction with coherence.
Generation of Composite Displays
Because the peak frequency of a spectrally balanced seismic data volume can often be correlated to the temporal tuning thickness, a composite plot is generated with peak magnitude. As is shown on time slices at 2.784 seconds in figure 3, peak frequency is plotted against hue and is modulated by peak magnitude plotted against saturation, for both the attributes generated from the input seismic data (figure 3a) as well as the input data after spectral balancing (figure 3b). In figure 3b, notice the detailed definition of the point bars indicated by the two white block arrows, the crisp boundaries of the smaller channel to the right as indicated by the magenta and pink block arrows, both enclosed in the highlighting black dashed ellipses. For stratigraphic objectives, stratal slice displays are typically used; however, in this case, the structural dip is so low that the horizon slice is nearly parallel to the time slice at the channel level. Therefore, time slice displays are used for all attribute displays to avoid any bias that might arise from horizon picking.
An equivalent comparison of composite displays generated with peak frequency and peak magnitude above mean spectrum is shown in figure 4. These displays are particularly insightful, as the color seen in figure 4b gives a clear indication of the thickness of the channels, with the bluish hues suggesting thinner channels and the reddish hues indicating thicker channels.
Finally, figure 5 shows an equivalent set of displays with peak frequency and peak magnitude corendered with multispectral energy ratio coherence. Figure 5b depicts a variety of channel features from point bars to thick and thin channels, while their thickness can be read off in terms of the color they enclose.
Conclusions
We have showcased the use of spectral attributes like peak frequency, peak magnitude and peak magnitude above the mean amplitude spectrum to identify high amplitude tuning events. This showcase was conducted using the Romney 3-D seismic data volume from New Zealand, focusing on the deepwater turbidite channel system. Following the spectral balancing of seismic data and the creation of spectral attributes, we constructed composite displays of peak frequency and peak magnitude for both the original seismic data and its spectrally balanced counterpart. Once defined, the interpreter can use the value of the peak frequencies seen in targeted channels to extract three spectral components centered on the peak frequency value and then display the results using RGB. Additionally, multispectral energy ratio coherence was introduced as another attribute for co-rendering. This approach led to a more precise definition of point bars, improved delineation of smaller channels and visual cues of their thicknesses in the spectrally balanced spectral attributes. These displays enhance the effective interpretation of channel systems, which was the ultimate goal.
Acknowledgements
The first author would also like to thank the subsurface AI (formerly Geomodeling Technology Corporation), Calgary, for making the Attribute Studio software available, which has been used for some visualization displays shown in this paper, as well as the Attribute-Assisted Seismic Processing and Interpretation Consortium, University of Oklahoma, for access to their software, which has been used for all attribute computation and corendering displays. The data courtesy for Romney 3-D seismic volume is extended to New Zealand Petroleum and Minerals department.