Time Characterization of Seismic Signals by Optimal Filter Selection

The characterization of earthquake records as samples of an underlying stochastic process can be roughly subdivided into two parts: frequency content description and time characterization. In fact, even in the uncommon case of a completely non-stationary coupled time-frequency approach, different model parameters are often evaluated as uncoupled. In this work, the attention is steered towards the time characterization with care to the illustration and assessment of quantities commonly used in the definition of amplitude-modulated random processes: the envelope function, the modulating function, and the detection and localization of the equivalent stationary duration of an earthquake time history. The importance of these time quantities comes from the fact that their evaluation gives a complete identification of the energy distribution in a seismic signal in terms of length (duration), position in time and the associated mean intensity value of the quasi-stationary portion. A signal analysis approach is followed in this work developed on the basis of some common methods for defining the envelope function of time-histories samples. A recently proposed relation between a modulating function and the related equivalent stationary duration is recalled and estimated for different cases. A new definition of modulating function is then proposed formulating a straight condition for the implementation of a simple optimal filtering selection, able to strictly relate the natural meaning of an amplitude modulated stationary stochastic process with the time distribution of the released energy and therefore the value and position along the time axis of the equivalent stationary duration. The approach proves to be free from a priori definitions of any arbitrary parameter or amount. The proposed model is applied in the numerical example to three natural records that can be considered as representative samples extracted from the most significant seismic Italian events of a few past decades.