Defining channelized reservoirs can sometimes be problematic in highly heterogeneous plays, and the channel sands in the Blackfoot field of southern Alberta, Canada, are no exception. Here, the producing Lower Cretaceous Glauconite Member contains shales and quartz sands of lacustrian and channel origin, with oil and gas present. The hydrocarbon reservoirs typically occur where the porous sands pinch out against impermeable sands or shales. Three channel phases have deposited sands with up to 18% porosity. However, the channel sands can be difficult to differentiate from the adjacent low-permeability strata because the lithotypes share similar P-wave impedances. By applying several spectral decomposition methods to the Blackfoot data, we were able to visualize the channel facies at greater resolution and extract geological details beyond the limits of conventional seismic analysis.

Overview of spectral decomposition
Spectral decomposition enables the interpreter to visualize seismic data in the time-frequency domain. First introduced to industry in the late '90s, spectral decomposition is now becoming an integral part of the interpreter's toolkit for investigating complex plays. Typically used in thin bed analysis, spectral decomposition is based on the concept that a thin bed reflection in the frequency domain has a unique spectral response that can qualitatively indicate bed thickness in the time domain. The method breaks down the seismic signal into its frequency components and generates amplitude and phase maps tuned to specific frequencies (i.e. a tuning cube). The resulting amplitude maps can help to estimate bed thickness, while phase maps aid in defining lateral stratigraphic discontinuities. By viewing amplitude and phase maps at various frequencies (i.e. by scrolling through the tuning cube), the interpreter can identify subtle events that would otherwise be overlooked in full bandwidth displays.

The workflow
Spectral decomposition can be applied directly to poststack amplitude data and its attributes. However, in our Glauconite channel study, we first applied a "strata-grid" calculation to our poststack interval of interest. A strata-grid is essentially a sample volume that has been extracted from the original seismic volume, but the poststack data in a strata-grid is reorganized into proportional slices. This removes structural bias and allows the interpreter to render through the slices to visualize paleo-surfaces. Based on well log data and previously published reports from the Blackfoot survey area, we picked two stable horizons to generate the strata-grid. We generated a tuning cube by applying one of four available spectral decomposition algorithms to the strata-grid. A section view of the strata-grid spectral decomposition results (Figure 1a) reveals a high energy anomaly within the channel facies.
We then generated a frequency gather (Figure 1b) to see the distribution of frequency on a single trace along the target horizon. High energy signals in the frequency gather correspond to frequencies where we may expect to visualize channel sands in the tuning cube - from 50 Hz to 90 Hz. Scrolling through the resulting frequency slices revealed distinct channel morphology at about 70 Hz (Figure 2). After determining the optimal frequency for visualizing the channel sands, we narrowed down the zone of interest for further investigation with multiple spectral decomposition techniques. By running the computationally intensive algorithms on a smaller volume, the interpreter can reduce the time it takes for the tuning cubes to be generated.

Comparison of methods
We applied four spectral decomposition methods to the zone of interest: Short Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT), Time Frequency Continuous Wavelet Transform (TFCWT) and S-Tansform (ST). All the methods provided better resolution of the channel morphology in comparison to the poststack amplitude map, but each offered a different spectral response at 70 Hz (Figure 3).
In the STFT method, the user specifies the length of a time window, where the signal represents the acoustic properties and bed thicknesses within the window. With the fixed window approach, one can select a shorter window length to resolve high-frequency events and to separate events with similar or closely spaced dominant frequencies. However, the use of these shorter windows can overlook events at lower frequency and compromise map resolution. If the window length is increased to sample a wider range of wavelets, the results may be a better statistical representation of the acoustic properties, but they can also overlook fine-scale events.
Figure 3b shows spectral decomposition result via STFT with a window size of 30 milliseconds (ms). Longer window size results are not given because structures of interest are only seen at higher frequencies based on the frequency gather analysis (Figure 1b) and the other spectral decomposition maps in Figure 3.
Compared to the STFT method, CWT is far superior in preserving reflection events. The CWT samples wavelets using a moving, scalable time window and allows for finer sampling of the seismic trace. While it provides better frequency resolution at lower frequencies, CWT cannot adequately resolve low-frequency events that are closely spaced in the time domain. TFCWT overcomes this issue by generating a time-frequency map, whereas the CWT method outputs a time-scale map. The time-frequency conversion in TFCWT provides higher resolution than CWT for a broader frequency spectrum. Both methods provide high-frequency resolution at low frequencies and high temporal resolution at high frequencies. However, TFCWT is computationally intensive, and generating spectral decomposition maps with this method can be time-consuming. Figures 3c and 3d demonstrate that CWT and TFCWT provide better time-frequency resolution than STFT.
Like TFCWT, S-Transform generates a time-frequency map, but it samples wavelets using a frequency-dependent window length. It is faster to calculate than TFCWT but gives a similar result, with only slightly less resolution (Figure 3e). Overall, the TFCWT map resolves the channel morphology with greater detail in comparison to all other methods.

A closer look
Generally speaking, thin events appear as high amplitudes at higher frequencies in spectral decomposition maps. So it is possible to observe the spatial variation of the target by looking through the different frequency cubes. Sometimes, if channel or bed thickness increases or decreases spatially, it can be observed by scrolling through the frequency slices (Figure 4).

Conclusions
Spectral decomposition can greatly improve visualization and interpretation workflows by revealing thin beds, lateral discontinuities and subtle anomalies not readily identified in poststack data. In imaging the Glauconite channel sands, running multiple spectral decomposition methods helped to resolve the channel morphology and bed thickness relationships within the channel facies. By correlating the spectral maps back to well logs and attribute relationships, the technique can help the interpreter to better understand complex reservoir plays and plan drilling strategies with greater confidence.
For more information, please visit www.geomodeling.com.