Neural networks for seismic principal components analysis

The neural network, using an unsupervised generalized Hebbian algorithm (GHA), is adopted to find the principal eigenvectors of a covariance matrix in different kinds of seismograms. We have shown that the extensive computer results of the principal components analysis (PCA) using the neural net of GHA can extract the information of seismic reflection layers and uniform neighboring traces. The analyzed seismic data are the seismic traces with 20-, 25-, and 30-Hz Ricker wavelets, the fault, the reflection and diffraction patterns after normal moveout (NMO) correction, the bright spot pattern, and the real seismogram at Mississippi Canyon. The properties of high amplitude, low frequency, and polarity reversal can be shown from the projections on the principal eigenvectors. For PCA, a theorem is proposed, which states that adding an extra point along the direction of the existing eigenvector can enhance that eigenvector. The theorem is applied to the interpretation of a fault seismogram and the uniform property of other seismograms. The PCA also provides a significant seismic data compression.