Spectral decomposition
Spectral decomposition is an innovative way of utilizing seismic data. Seismic data is rarely dominated by simple blocky and resolved reflections. Also, it is rare that true geological boundaries fall along fully resolved seismic peaks and troughs. By transforming seismic data into the frequency domain with the Discrete Fourier Transform (DFT), short-window amplitude and phase spectra localize thin bed reflections and define bed thickness variability within complex rock strata.
Fourier analysis is based on the assumption that the frequency content of the seismic trace does not change with time. However, we know that the spectral content of the trace varies with time through the earth - higher frequencies getting preferentially lost. It is desirable to have a frequency spectrum that adjusts its resolution depending on the frequency content of the signal. The Continuous Wavelet Transform (CWT) method directly extracts the frequency content at each time location, eliminating windowing problems and results in high-resolution spectral analysis.
Besides the traditional Fourier transform, SamiGeo offers the CWT, and Matching Pursuit Decomposition (MPD) for transformation of data to frequency domain. The latter technique offers more accurate analysis.
Voice components of seismic data
The voice component, which is a simple function of spectral magnitude, m, and phase ø at each time-frequency sample, is given by
The real part of the sum over all frequencies, f, of all these voice components reconstructs the original trace.
Because the voice components are band-pass-filtered versions of the original seismic data, the application to map subtle hydrocarbon features can be viewed as analysis of spectral voices. After choosing an appropriate mother wavelet, the scaled members of the wavelet family are defined by simple scaling and shifting of the mother wavelet. Crosscorrelating the member wavelets with the original seismic trace generates the spectral-voice components. For the continuous-wavelet transform, the voice components are equivalent to narrow bandpass-filtered versions of the input seismic data. We show the 30-Hz voice-component section in the figure below, along with the magnitude spectrum of the 30-Hz wavelet.
A vertical slice through the 30 Hz voice component after spectral decomposition with spectral balancing and its amplitude spectrum. Notice the frequency width on both sides of the amplitude maxima seen at 30 Hz. (Adapted from Chopra and Marfurt, (2016); Data courtesy: TGS, Calgary)
Such voice components offer more information that subsequently can be processed and interpreted. In the figure below, we show a vertical slice through a 3D seismic volume from north-central Alberta, Canada, as well as the equivalent slices through the spectral magnitude, phase, and voice components at 65 Hz, which highlight fault discontinuities not seen in the original broadband data (or in most of the lower spectral components).
Notice that the vertical-discontinuity information is not seen clearly on the spectral magnitude but is clear on the phase component.
Vertical slices through (a) original 3D seismic amplitude and corresponding 65 Hz (b) spectral magnitude, (c) spectral phase, and (d) spectral voice component volumes. Notice the vertical discontinuities in the highlighted portion are poorly seen in the original broadband data, are not seen in the spectral magnitude component, but are clearly seen in the spectral phase and voice components. The voice component has the advantage that it can be easily interpreted and processed (e.g. using coherence) as one would the original seismic amplitude data. (Adapted from Chopra and Marfurt, (2016); Data courtesy: TGS, Calgary)
The voice components combine both attributes and nicely delineate the discontinuities. This observation could be exploited to our advantage by interpreting the discontinuity information as such or by running discontinuity attributes such as coherence on the voice-component volume. Since their introduction to the 3D interpretation community by Partyka et al. (1999), spectral-magnitude components have been used routinely to delineate stratigraphic features at or below the limits of seismic resolution. If a stratigraphic feature exhibits an approximately constant interval velocity, the tuning thickness is inversely proportional to the spectrally balanced peak frequency. More detailed information on seismic geo-morphology can be gained by visualizing data at multiple frequencies, either through animation or by combining different spectral components using red-green-blue (RGB) color schemes.
References
Partyka, G., J. Gridley, and J. A. Lopez, 1999, Interpretational applications of spectral decomposition in reservoir characterization: The Leading Edge, 18,353–360.
Chopra, S., and K. J. Marfurt, 2016, Spectral decomposition and spectral balancing of seismic data, The Leading Edge, 35,936–939.