Spectral decomposition is a powerful analysis technique that provides direct measurement of thin-bed tuning effects. One limitation in using spectral decomposition in volumetric analysis is the shear size of the spectral component volumes that are generated. For this reason, peak amplitude, peak frequency, and peak phase, which represent the mode of the complex spectra have proven to be three of the most useful volumetric spectral attributes. While estimates of the spectral mean, bandwidth, skewness, and kurtosis have been available in commercial formationBased spectral decomposition software for almost a decade, few if any case studies have been presented showing its value. Since many spectra are bi- vs. unimodal we find the mean spectra, bandwidth and kurtosis to have only limited interpretation value. In contrast, spectral skewness estimates quantify the asymmetry of the spectra which in turn can be correlated to multimodal behaviour due to channels, as well as the presence of upward fining, and upward coarsening sequencies.
First applied to 3D seismic volumes by Partyka et al. (1999), spectral decomposition has since become a routine interpretation analysis tool. The more common applications include identification of tuning thickness (e.g. Marfurt and Kirlin, 2001; Tirado, 2004) and direct hydrocarbon detection (Castagna et al., 2003). Unfortunately, the 4D spectral decomposition volumes obtained from 3D data are unwieldly, presenting both visualization and data management problems. For this reason, we seek to identify a small suite of 3D volumes that represent key spectral features of the 4D volume.
The most straightforward and broadly used attributes associated with spectral decomposition are peak amplitude, peak frequency, and peak phase (Liu et al., 2007; Matos and Johann, 2007). Measures of peak amplitude above the average spectrum provide added delineation of highamplitude tuning events (Blumentritt, 2008). However, it isnaive to think that one frequency can fully represent the complete spectrum.
Several commercial implementations of formation-based spectral decomposition provide measures of the spectral mean, bandwidth (proportional to the standard deviation), skewness, and kurtosis. These measures are excellent in defining moderate spectral variations away from what is otherwise a Gaussian distribution. However, we found that some of the features of most interest were bimodal, thereby violated the Gaussian assumption. Futhermore, our analysis is done after (statistical) spectral flattening (Liu and Marfurt, 2007), such that the average spectrum is by definition flat (and non-Gaussian) within the frequencyband analyzed. Nevertheless, we find skewness to be a spectral measurement that is statistically applicable to an univariate continuous spectra. A spectra is skewed if one of its tails is longer than the other. A symmetric frequency spectrum at a given time sample has zero skewness. An asymmetric spectrum with a long tail extending to the high frequency direction has a positive skewness, and vice versa.
Theoretically, skewness is sensitive to the shift of the dominant energy of the spectrum along the temporal and spatial directions of the seismic data, which enables us to map structural and stratigraphic variation on seismic time and horizon slices.
