The Role of the Background Velocity Model for the Marchenko Focusing of Reflected and Refracted Waves

Abstract

Marchenko algorithms retrieve the wavefields excited by virtual sources in the subsurface, these are the Green’s functions consisting of the primary and multiple reflected waves. The requirements for these algorithms are the same as for conventional imaging algorithms; they need an estimate of the velocity model and the recorded reflected waves. We investigate the dependence of the retrieved Green’s functions using the Marchenko equation on the background velocity model and address the question: “How well do we need to know the velocity model for accurate Marchenko focusing?”. We present different background velocity models and compare the Green’s functions retrieved using these models. We show that these retrieved Green’s functions using the Marchenko equation match the exact Green’s function with a high accuracy. We also examine the presence of refracted waves in the retrieved Green’s function. Marchenko focusing algorithm produces refracted waves only if the initial velocity model used for the iterative scheme is sufficiently detailed to model the refracted waves. We show with numerical examples that the average slowness between the surface and the depth of the focal point is required for an accurate reflected wave retrieval. However, substantially more accurate velocity model knowledge is required in the presence of refracted waves.