A single-sided homogeneous Green's function representation for holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval

作者：Wapenaar Kees^*; Thorbecke Jan; van der Neut Joost

来源：Geophysical Journal International, 2016, 205(1): 531-535.

DOI：10.1093/gji/ggw023

• Interferometry
• Controlled source seismology
• Wave scattering and diffraction

Green's theorem plays a fundamental role in a diverse range of wavefield imaging applications, such as holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval. In many of those applications, the homogeneous Green's i.e. the Green's function of the wave equation without a singularity on the right-hand side) is represented by a closed boundary integral. In practical applications, sources and/or receivers are usually present only on an open surface, which implies that a significant part of the closed boundary integral is by necessity ignored. Here we derive a homogeneous Green's function representation for the common situation that sources and/or receivers are present on an open surface only. We modify the integrand in such a way that it vanishes on the part of the boundary where no sources and receivers are present. As a consequence, the remaining integral along the open surface is an accurate single-sided representation of the homogeneous Green's function. This single-sided representation accounts for all orders of multiple scattering. The new representation significantly improves the aforementioned wavefield imaging applications, particularly in situations where the first-order scattering approximation breaks down.

• 出版日期2016-4