The role of the background velocity model for the Marchenko focusing of reflected and refracted waves

TL;DR

This paper investigates how the accuracy of background velocity models affects the Marchenko focusing of reflected and refracted waves, demonstrating that detailed models are necessary for refracted wave retrieval.

Contribution

It provides a systematic comparison of Green's functions retrieved with different velocity models and clarifies the model accuracy needed for effective Marchenko focusing.

Findings

Green's functions correlate over 90% with exact functions using approximate models

Refracted waves are only retrieved if the velocity model is sufficiently detailed

Approximate models are effective near the receiver aperture edges

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 three 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 give correlation coefficients with the exact Green's function larger than 90% on average except near the edges of the receiver aperture. We also examine the presence of refracted waves in the retrieved Green's function. We show with a numerical example that the 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.