Weighted compressive sensing applied to seismic interferometry

Seismic interferometry retrieves the waves that propagate between sensors, any one of which acts as a virtual source. To retrieve accurate wavefields, one often requires months or years of seismic noise records for noise interferometry, or seismic records from a perfect source distribution for active source interferometry. In practice, such recordings may not be fully available. The computational storage and cost of seismic interferometry can also be expensive, especially for the long-term seismic records. Compressive sensing, as a wavefield reconstruction technique that can operate on incomplete data, may alleviate these issues. In a numerical example, we use a linear receiver array with missing sensors surrounded by sources. We compute interferometric surface wavefields for all available virtual sources using cross-correlation before the compressive sensing reconstruction. Using a Fourier basis for a sparse transform, we show that one can reconstruct the interferometric wavefields at the locations where seismometers are unavailable or inoperative, reducing the data storage required for seismic interferometry. In practice, the wavefields obtained by interferometry may contain spurious arrivals that do not correspond to the surface waves that propagate between sensors. We develop a weighted compressive sensing technique that suppresses these arrivals.