Summary
Seismic interferometry is a technique that allows one to estimate the wavefields accounting for the wave propagation between seismometers, any of which can act as a virtual source. Interferometry, particularly noise interferometry, has been applied to several geophysical disciplines such as passive monitoring and distributed acoustic sensing. In practice, one requires long recordings of seismic noise for noise interferometry. Additionally, one can have missing seismic interferometric traces because some receivers in seismic arrays may be absent or inoperative due to issues of receiver installation and malfunction. Thus, filling the gap of seismic interferometric profile requires wavefield reconstruction and regularization techniques. Compressive sensing is one such method that can reconstruct seismic interferometric wavefields and help mitigate the limitations by exploiting the sparsity of seismic waves. In our work, we use compressive sensing to reconstruct missing seismic interferometric wavefields. One can interpolate interferometric wavefields using correlograms provided by one virtual source. We call this method of reconstructing an individual virtual source gather single-source wavefield reconstruction. We propose an alternative technique called multi-source wavefield reconstruction, which applies compressive sensing to reconstruct multiple interferometric wavefields using a volume of virtual source gathers provided from all available virtual sources. Using numerical examples, we show that one can apply compressive sensing to recover interferometric wavefields resulting from interferometry of a linear seismic array. To exploit the sparsity of interferometric wavefields, we apply the Fourier and Curvelet transforms to the two reconstruction schemes. Using the signal-to-noise ratio (SNR) to compare reconstruction of interferometric wavefields, the Fourier multi-source method improves the recovery of interferometric wavefields by approximately 50 dB compared to the Fourier and Curvelet single-source wavefield reconstructions.
