Analysis of tsunami signals from tide gauges and ocean-bottom pressure gauges through Iterative Filtering

Time-series from coastal tide gauges and ocean-bottom pressure gauges play a fundamental role in the study and monitoring of tsunami. A typical tsunami record is the result of the superposition with the tsunami itself of different physical phenomena, such as tides, and seismic waves that relatively close to the earthquake source may overlap with the tsunami. In the case of coastal gauges, nonlinear interactions with local bathymetric and coastal morphology features characterize the tsunami evolution. In this study, we apply the recently developed Iterative Filtering (IF) technique, specifically tailored to non-stationary and non-linear signals, to tsunami time-series. IF is a data-driven algorithm that decomposes signals into elementary oscillatory components, called Intrinsic Mode Functions (IMFs), each containing distinct frequency bands. This technique attempts to separate different physical phenomena present in the time-series into different IMF.

To complement the decomposition, a time-frequency analysis technique called IMFogram is used. The IMFogram relies on computing for each IMF the local frequency, computed based on the distribution of zero-crossings, and local amplitude, computed interpolating the absolute values of relative maxima. Despite their simplicity, these definitions produce a time-frequency representation that generalizes the traditional spectrogram. The output of the IMFogram algorithm, given in matrix form, can be used to pinpoint time and amplitude of special features of the signal both graphically and quantitatively.

The ability to separate the different components of a measured record into different IMFs and analyze their spectral properties is shown by applying the technique to available real-world data, for tsunami of different “intensity” and frequency content. The results are compared to other techniques, such as classical filtering techniques and the Empirical Mode Decomposition (EMD). It is shown that IF results, unlike classical linear filters, do not depend on experts’ choice and, unlike the EMD, are stable w.r.t. to noise. Special attention is given to recent events in the Mediterranean Sea, where robust analysis of each signal is needed to remedy the  absence of deep sea tsunami sensors, the sparsity of coastal tide gauges, and the morphological complexity. At last, the possibility of real-time application in early warning system is considered.