Retrieving Higher-mode Surface Waves Using Seismic Interferometry by Multidimensional Deconvolution

Virtual-source surface-wave responses can be retrieved using the crosscorrelation of wavefields observed at two receivers. Higher-mode surface waves cannot be properly retrieved when there is a lack of subsurface sources, which is often the case. In this paper, we present a multidimensional-deconvolution scheme that introduces an additional processing step in which the crosscorrelation result is deconvolved by a point-spread function. The scheme is based on an approximate convolution theorem that includes point-force responses only, which is advantageous for applications with contemporary field-acquisition geometries. The point-spread function captures the imprint of the lack of subsurface sources and quantifies the associated smearing of the virtual source in space and time. The function can be calculated from the same wavefields used in the correlation method, provided that one or more vertical arrays of subsurface receivers are present and the illumination is from one side. We show that the retrieved surface-wave response, including the higher modes, becomes much more accurate. The waveforms are properly reconstructed and there is only a small amplitude error, which is due to non-canceling cross terms in the employed approximate convolution theorem. The improved retrieval of the multi-mode surface waves can facilitate dispersion analyses and near-surface inversion algorithms.