Applications of autoregressive models and time–frequency analysis to the study of volcanic tremor and long-period events

Volcanic tremor and long-period (LP) events are characterized by sharp spectral peaks that generally result from resonance effects at the source and which concentrate most of the radiated energy. The understanding of these seismovolcanic phenomena requires good descriptions of the distribution in time and frequency of the different spectral components included in the signals, as well as a separation of the resonance effects from less energetic effects such as excitation and propagation. We address the issue of extracting from individual records information as detailed as possible on the physical processes involved at the source. We introduce and compare several time–frequency analysis methods, and we describe the application of autoregressive modeling and deconvolution methods to the characterization and separation of the main spectral components. We propose a signal analysis approach based on the joint use of a set of complementary methods, and we present applications to several examples of volcanic tremor and LP events. The time–frequency analysis of some of the LP events taken as examples reveals short-duration components at the seismogram onsets with energy concentrated at frequencies either higher or lower than the main resonance frequencies. These seismic phases are probably related to the excitation processes of the volcanic resonators. In several cases, the arrival of the main spectral peak has a delay of a few tenths of a second with respect to the first arrival. The residual signals obtained by deconvolving and eliminating the main spectral components contain information about the excitation, such as duration, delay, or frequency band. The residual signals are short for LP events, and continuous for volcanic tremor. The autoregressive modeling of the sample records gives precise estimations of the frequency and quality factor of the main spectral peaks. The measured parameters cover a wide range of values, which is consistent with the great variety of fluids filling resonating cavities in volcanoes.