Data-based diffraction kernels for surface waves from convolution and correlation processes through active seismic interferometry

We investigated the construction of diffraction kernels (DKs) for surface waves using two-point convolution and/or correlation from land active seismic data recorded in the context of exploration geophysics. The high density of controlled sources and receivers, combined with the application of the reciprocity principle, allows us to retrieve 2-D phase-oscillation DKs of surface waves between any two source or receiver points in the medium at each frequency (up to 15 Hz, at least). These DKs are purely data based as no model calculations and no synthetic data are needed. They naturally emerge from the interference patterns of the recorded wavefields projected on the dense array of sources and/or receivers. The DKs are used to obtain multimode dispersion relations of Rayleigh waves, from which near-surface shear velocity can be extracted. Using convolution versus correlation with a grid of active sources is an important step in understanding the physics of the retrieval of surface wave Green's functions. This provides the foundation for future studies based on noise sources or active sources with a sparse spatial distribution