arXiv subjects

Roel Snieder

Publications and source records attributed to Roel Snieder.

3 recordsLinked to original sources

arXiv2023

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

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.

physics.geo-ph↗

arXiv2023

Propagator and transfer matrices, Marchenko focusing functions and their mutual relations

Many seismic imaging methods use wave field extrapolation operators to redatum sources and receivers from the surface into the subsurface. We discuss wave field extrapolation operators that account for internal multiple reflections, in particular propagator matrices, transfer matrices and Marchenko focusing functions. A propagator matrix is a square matrix that `propagates' a wave-field vector from one depth level to another. It accounts for primaries and multiples and holds for propagating and evanescent waves. A Marchenko focusing function is a wave field that focuses at a designated point in space at zero time. Marchenko focusing functions are useful for retrieving the wave field inside a heterogeneous medium from the reflection response at its surface. By expressing these focusing functions in terms of the propagator matrix, the usual approximations (such as ignoring evanescent waves) are avoided. While a propagator matrix acts on the full wave-field vector, a transfer matrix (according to the definition employed in this paper)`transfers' a decomposed wave-field vector (containing downgoing and upgoing waves) from one depth level to another. It can be expressed in terms of decomposed Marchenko focusing functions. We present propagator matrices, transfer matrices and Marchenko focusing functions in a consistent way and discuss their mutual relations. In the main text we consider the acoustic situation and in the appendices we discuss other wave phenomena. Understanding these mutual connections may lead to new developments of Marchenko theory and its applications in wave field focusing, Green's function retrieval and imaging.

physics.geo-ph↗

arXiv2021

Green's function representations for Marchenko imaging without up/down decomposition

Marchenko methods are based on integral representations which express Green's functions for virtual sources and/or receivers in the subsurface in terms of the reflection response at the surface. An underlying assumption is that inside the medium the wave field can be decomposed into downgoing and upgoing waves and that evanescent waves can be neglected. We present a new derivation of Green's function representations which circumvents these assumptions, both for the acoustic and the elastodynamic situation. These representations form the basis for research into new Marchenko methods which have the potential to handle refracted and evanescent waves and to more accurately image steeply dipping reflectors.

physics.geo-ph↗