Green’s function estimation by seismic interferometry from limited frequency samples

Green’s function estimation is an important application of seismic interferometry but can require cross-correlating very long time series that are difficult to gather, store, and transmit in resource-constrained scenarios. We derive a compressive approach for estimating a Green’s function using only a small number of random frequency samples from each signal. We bound the maximum error between this estimator and the original cross-correlation and show how this error decreases as the number of samples increases. We demonstrate the application of this technique to a numerical one-dimensional reflected wave case and to estimation of surface wave Green’s functions for the western United States using USArray data. We show that the compressive approach can be extended to deconvolution as well, and we illustrate this with pressure and displacement data recorded on a volcano. We also provide guidelines for implementing the technique.