Characterization of the complexity in short oscillating time series: An application to seismic airgun detonations

Extracting frequency-derived parameters allows for the identification and characterization of acoustic events, such as those obtained in passive acoustic monitoring applications. Situations where it is difficult to achieve the desired frequency resolution to distinguish between similar events occur, for example, in short time oscillating events. One feasible approach to make discrimination among such events is by measuring the complexity or the presence of non-linearities in a time series. Available techniques include the delay vector variance (DVV) and recurrence plot (RP) analysis, which have been used independently for statistical testing, however, the similarities between these two techniques have so far been overlooked. This work suggests a method that combines the DVV method with the recurrence quantification analysis parameters of the RP graphs for the characterization of short oscillating events. In order to establish the confidence intervals, a variant of the pseudo-periodic surrogate algorithm is proposed. This allows one to eliminate the fine details that may indicate the presence of non-linear dynamics, without having to add a large amount of noise, while preserving more efficiently the phase-space shape. The algorithm is verified on both synthetic and real world time series.