Principal components analysis of spectral components

Abstract

Summary Spectral decomposition methods help illuminate lateral changes in porosity and thin bed thickness. Typically, an interpreter may generate 80 or more spectral components spanning the useable seismic bandwidth at 1 Hz intervals. However, most of these images contain redundant information. The most common means of displaying these components is by simply animating through them. By observing how bright and dim areas of the response move laterally with increasing frequency, a skilled interpreter can determine whether a channel or other stratigraphic feature of interest is thickening or thinning. Principal component analysis is a well-established means of reducing a multiplicity of data into a more manageable number of components. By construction, each principal component is mathematically orthogonal to other components. In addition the importance of each principal component is proportional to its corresponding eigenvalue. In this manner, we can reduce the 80 or more input spectral components to a more manageable 12 principal components. If the data are normalized with respect to amplitude, the first principal component represents the most common spectral variation seen along an interpreted horizon. The second principal component best represents that part of the spectrum not represented by the first principal component, and so on. Given typical depositional processes, principal components are therefore ideally suited to identify geologic features that give rise to anomalous spectra. Principal components implicitly remove random noise by throwing out those components having small eigenvalues. Equally important, by mapping the three largest principal components against Red, Green, and Blue, we can represent 75% of our spectral information with a single colored image.