Marchenko without up/down decomposition on the Marmousi model and retrieval of the refracted waves: Are they caused by the Marchenko algorithm?

Abstract

Marchenko algorithms retrieve the Green’s function for arbitrary subsurface locations, and the retrieved Green’s function includes the primary and multiple reflected waves. The Marchenko algorithms require the estimate of the direct arrivals and the reflected waves; however, most previous Marchenko algorithms also require the up/down components of the Marchenko equation for the Green’s function retrieval. We use the Marmousi model to retrieve the Green’s function without using the up/-down components of the Marchenko equation and show that the retrieved Green’s function matches with the numerically modeled Green’s function. We also show that the refracted waves can be successfully produced independently from the acquisition geometry, i.e., singlesided or two-sided; however, the retrieval of refracted waves that arrive before the first primary waves is inconsistent with the requirement that the Green’s function vanishes before the direct wave. Even though we retrieve such refracted waves, they are caused by the injection of the direct wave into suciently detailed background velocity and density models instead of operations of the Marchenko algorithm on the recorded wavefields.