Automatic estimation of optimal autoregressive filters for the analysis of volcanic seismic activity

Abstract. Long-period (LP) events observed on volcanoes provide important information for volcano monitoring and for studying the physical processes in magmatic and hydrothermal systems. Of all the methods used to analyse this kind of seismicity, autoregressive (AR) modelling is particularly valuable, as it produces precise estimations of the frequencies and quality factors of the spectral peaks that are generated by resonance effects at seismic sources and, via deconvolution of the observed record, it allows the excitation function of the resonator to be determined. However, with AR modelling methods it is difficult to determine the order of the AR filter that will yield the best model of the signal. This note presents an algorithm to overcome this problem, together with some examples of applications. The approach described uses the kurtosis (fourth order cumulant) of the deconvolved signal to provide an objective criterion for selecting the filter order. This approach allows the partial automation of the AR analysis and thus provides interesting possibilities for improving volcano monitoring methods.