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In this work, we address the following question: can we use modern, cutting-edge techniques conceived for the analysis of nonlinear non-stationary signals to measure scale-wise lags? To this scope, we propose a novel technique, called intrinsic mode cross correlation (IMXC) method, which leverages on the decomposition of nonlinear non-stationary signals by the multivariate fast iterative filtering (MvFIF) technique and the computation of a scale-by-scale cross correlation. We evaluate this technique on artificial signals (whose ground truth is known) and plasma density data provided by the Langmuir probes onboard the Swarm satellites. We show that this technique allows indeed to reconstruct the lag dependence on the involved spatio/temporal scales for the artificial dataset (even in the presence of high levels of noise) and to estimate them in a real-life signal. This can pave the way to future uses of this technique in contexts in which the causation chain can be hidden in a complex, multiscale coupling of the investigated features.

Intrinsic Mode Cross Correlation: A Novel Technique to Identify Scale-Dependent Lags Between Two Signals and Its Application to Ionospheric Science