Crosscorrelation kernels in acoustic Green's function retrieval by wavefield correlation for point sources on a plane and a sphere

Abstract

S U M M A R YThe far-field approximation is commonly assumed in the derivation of Green's function retrieval by wavefield correlation using reciprocity theorems. This approximation can result in erroneous amplitude of the retrieved seismic phases and generate artificial arrivals. In an open system, we show that the far-field approximation can be removed by the exact integral equation method and this leads to the crosscorrelation kernel. In previous work, kernels in 2-D space had been explicitly constructed. With the kernel, we can construct the Green's function by crosscorrelation even when the sources are not in the far field. Here we extended the 2-D case to 3-D for acoustic waves for point sources on a plane and on a sphere. For the spherical case, the kernel is expressed by spherical harmonics and it degenerates to the Dirac Delta distribution under the high-frequency case; however, for a fixed frequency, if we increase the radius of the sphere, it reduces to that of the plane boundary.

Green's theorem in seismic imaging across the scales

“…The main approximation is that evanescent waves are neglected (Zheng et al, 2011;Wapenaar et al, 2011). In the following sections we discuss different imaging methods.…”

Green's theorem in seismic imaging across the scales

“…The main approximation is that evanescent waves are neglected at S (Zheng et al, 2011;Wapenaar et al, 2011). The latter representation forms the starting point for discussing a number of applications in the next sections.…”

Supplementary material to "Green's theorem in seismic imaging across the scales"

“…The main approximation is that evanescent waves are neglected at S (Zheng et al, 2011;Wapenaar et al, 2011).…”