Introducing the Statistical Redundancy of Instantaneous Phases of the Seismic Signal to Isolate Persistent Sources

We introduce a new method based on pairwise comparisons among a set of synchronous time-series to detect signal redundancies in the seismic ambient wavefield. This approach is based on instantaneous phase coherence statistics, assuming the ergodicity property of a random signal. Both theory and synthetic experiments show that, for perfect phase randomness, the theoretical values of the mean and variance are equal to 0 and 1 2=, respectively. Any departure from these values signs the presence of a redundant phase in the raw continuous signal. The previously detected 26 s period microseismic source is used to illustrate one of the possible ways of handling phase coherence statistics. The dataset is composed of continuous vertical component during the month of August 2004, recorded at four stations. Each 31 day length seismogram is split into 372 2 h time windows to be cross-correlated among all possible station pairs. We observe that, for all station pairs, the mean overall coherence value is close to zero for most time lags, except for specific time windows. Using a constant group velocity, each mean overall coherence value is converted into a geographical location and points out a redundant source signal located in the Gulf of Guinea, as previously found in the literature. This result demonstrates that this approach enables to point out persistent sources, and to quantify their contribution to the overall seismic ambient wavefield. Further improvements to better constrain the strength of the repetitiveness