Principal component spectral analysis

Abstract

Spectral decomposition methods help illuminate lateral changes in porosity and thin-bed thickness. For broadband data, an interpreter might generate 80 or more somewhat redundant amplitude and phase spectral components spanning the usable seismic bandwidth at [Formula: see text] intervals. Large numbers of components can overload not only the interpreter but also the display hardware. We have used principal component analysis to reduce the multiplicity of spectral data and enhance the most energetic trends inside the data. Each principal component spectrum is mathematically orthogonal to other spectra, with the importance of each spectrum being proportional to the size of its corresponding eigenvalue. Principal components are ideally suited to identify geologic features that give rise to anomalous moderate- to high-amplitude spectra. Unlike the input spectral magnitude and phase components, the principal component spectra are not direct indicators of bed thickness. By combining the variability of multiple components, principal component spectra highlight stratigraphic features that can be interpreted using a seismic geomorphology workflow. By mapping the three largest principal components using the three primary colors of red, green, and blue, we could represent more than 80% of the spectral variance with a single image. We have applied and validated this workflow using a broadband data volume containing channels draining an unconformity, which was acquired over the Central Basin Platform, Texas, U.S.A. Principal component analysis reveals a channel system with only a few output data volumes. The same process provides the interpreter with flexibility to remove any unwanted high-amplitude geologic trends or random noise from the original spectral components by eliminating those principal components that do not aid in delineation of prospective features with their interpretation during the reconstruction process.