In this work, we present a new technique for the decomposition of multivariate data, which we call Multivariate Fast Iterative Filtering (MvFIF) algorithm. We study its properties, proving rigorously that it converges in finite time when applied to the decomposition of any kind of multivariate signal. We test MvFIF performance using a wide variety of artificial and real multivariate signals, showing its ability to: separate multivariate modulated oscillations; align frequencies along different channels; produce a quasi–dyadic filterbank when decomposing white Gaussian noise; decompose the signal in a quasi–orthogonal set of components; being robust to noise perturbation, even when the number of channels is increased considerably. Finally, we compare it and its performance with the main methods developed so far in the literature, proving that MvFIF produces, without any a priori assumption on the signal under investigation and in a fast and reliable manner, a uniquely defined decomposition of any multivariate signal.

The short-term prediction of earthquakes is an essential issue connected with human life protection and related social and economic matters. Recent papers have provided some evidence of the link between the lithosphere, lower atmosphere, and ionosphere, even though with marginal statistical evidence. The basic coupling is hypothesized as being via the atmospheric gravity wave (AGW)/acoustic wave (AW) channel. In this paper we analyze a scenario of the low latitude earthquake (Mw = 6.9) which occurred in Indonesia on 5 August 2018, through a multi-instrumental approach, using ground and satellites high quality data. As a result, we derive a new analytical lithospheric–atmospheric–ionospheric–magnetospheric coupling model with the aim to provide quantitative indicators to interpret the observations around 6 h before and at the moment of the earthquake occurrence.