Interferometric redatuming of autofocused primaries and internal multiples

摘要

Recently, an iterative scheme has been introduced to retrieve the down- and upgoing Green's functions at an arbitrary level A_F inside an acoustic medium as if there were a source at the surface. This scheme requires as input the reflection response acquired at the surface and the direct arrival of the transmission response from the surface to level A_F. The source locations of these Green's functions can be effectively redatumed to level AF by interferometric redatuming, which requires solving a multidimensional deconvolution problem, essentially being a Fredholm integral equation of the first kind. We show how this problem can be simplified by rewriting it as a Fredholm integral equation of the second kind that can be expanded as a Neumann series. Redatumed data can be used for multiple-free true-amplitude imaging at or in the vicinity of AF. For imaging the closest reflector to AF only, the Neumann series can be truncated at the first term without losing accuracy.