Testing Rayleigh–Schuster hodographs using time series models and earthquake flows

The paper considers features and peculiarities of Rayleigh−Schuster hodographs designed for detailed investigation of changes in the phase of quasiperiodic signals in time series. The method allows a researcher to estimate the statistical significance of analyzed periodicities and visualize a change in the signal phase. The method is tested using various models, in particular, flows of random events, earthquake flows, periodic signals, and noise-contaminated periodic signals of earthquake flows. The equations for estimating errors in the resulting vector phase are given. It is clearly demonstrated that the hodographs of random signals can in some cases be similar to nonrandom ones. This effect contradicts intuitive concepts and creates the illusion of nonrandom signals. Possible causes of the phenomenon are discussed. A methodology for hodograph analysis ensuring a more feasible interpretation is proposed.