Modification of the pattern informatics method for forecasting large earthquake events using complex eigenvectors

Recent studies have shown that real-valued principal component analysis can be applied to earthquake fault systems for forecasting and prediction. In addition, theoretical analysis indicates that earthquake stresses may obey a wave-like equation, having solutions with inverse frequencies for a given fault similar to those that characterize the time intervals between the largest events on the fault. It is therefore desirable to apply complex principal component analysis to develop earthquake forecast algorithms. In this paper we modify the Pattern Informatics method of earthquake forecasting to take advantage of the wave-like properties of seismic stresses and utilize the Hilbert transform to create complex eigenvectors out of measured time series. We show that Pattern Informatics analyses using complex eigenvectors create short-term forecast hot-spot maps that differ from hot-spot maps created using only real-valued data and suggest methods of analyzing the differences and calculating the information gain.Comment: 13 pages, 1 figure. Submitted to Tectonophysics on 30 August 200

Multivariate and 2D Extensions of Singular Spectrum Analysis with the Rssa Package

Implementation of multivariate and 2D extensions of singular spectrum analysis (SSA) by means of the R package Rssa is considered. The extensions include MSSA for simultaneous analysis and forecasting of several time series and 2D-SSA for analysis of digital images. A new extension of 2D-SSA analysis called shaped 2D-SSA is introduced for analysis of images of arbitrary shape, not necessary rectangular. It is shown that implementation of shaped 2D-SSA can serve as a basis for implementation of MSSA and other generalizations. Efficient implementation of operations with Hankel and Hankel-block-Hankel matrices through the fast Fourier transform is suggested. Examples with code fragments in R, which explain the methodology and demonstrate the proper use of Rssa, are presented