Marchenko Focusing Without Up/Down Decomposition

Current Marchenko algorithms require up/down separation, and solving the Marchenko equation enables one to retrieve the up/down components of the Green's function. We propose an iterative scheme to relax the need for up/down separation for focusing. By presenting a visual tour, we show how to retrieve the Green's function in the subsurface at a pre-defined location without requiring component decomposition. Our retrieved Green's function contains accurate primary and multiple events of the heterogeneous subsurface and forms the basis for obtaining an image of the subsurface without the need for up/down decomposition.Accepted author manuscriptImPhys/Medical ImagingApplied Geophysics and Petrophysic

A modified Marchenko method to retrieve the wave field inside layered metamaterial from reflection measurements at the surface

With the Marchenko method, it is possible to retrieve the wave field inside a medium from its reflection response at the surface. To date, this method has predominantly been applied to naturally occurring materials. This study extends the Marchenko method for applications in layered metamaterials with, in the low-frequency limit, effective negative constitutive parameters. It illustrates the method with a numerical example, which confirms that the method properly accounts for multiple scattering. The proposed method has potential applications, for example, in non-destructive testing of layered materials.ImPhys/Medical ImagingApplied Geophysics and Petrophysic

A single-sided representation for the homogeneous Green's function of a unified scalar wave equation

Applied Geophysics and Petrophysic

The Marchenko method for evanescent waves

With the Marchenko method, Green’s functions in the subsurface can be retrieved from seismic reflection data at the surface. State-of-the-art Marchenko methods work well for propagating waves but break down for evanescent waves. This paper discusses a first step towards extending the Marchenko method for evanescent waves and analyses its possibilities and limitations. In theory both the downward and upward decaying components can be retrieved. The retrieval of the upward decaying component appears to be very sensitive to model errors, but the downward decaying component, including multiple reflections, can be retrieved in a reasonably stable and accurate way. The reported research opens the way to develop new Marchenko methods that can handle refracted waves in wide-angle reflection data.ImPhys/Medical ImagingApplied Geophysics and Petrophysic

Wave-field representations with Green's functions, propagator matrices, and Marchenko-type focusing functions

Classical acoustic wave-field representations consist of volume and boundary integrals, of which the integrands contain specific combinations of Green's functions, source distributions, and wave fields. Using a unified matrix-vector wave equation for different wave phenomena, these representations can be reformulated in terms of Green's matrices, source vectors, and wave-field vectors. The matrix-vector formalism also allows the formulation of representations in which propagator matrices replace the Green's matrices. These propagator matrices, in turn, can be expressed in terms of Marchenko-type focusing functions. An advantage of the representations with propagator matrices and focusing functions is that the boundary integrals in these representations are limited to a single open boundary. This makes these representations a suitable basis for developing advanced inverse scattering, imaging and monitoring methods for wave fields acquired on a single boundary.Applied Geophysics and Petrophysic

Single-sided Marchenko focusing of compressional and shear waves

In time-reversal acoustics, waves recorded at the boundary of a strongly scattering medium are sent back into the medium to focus at the original source position. This requires that the medium can be accessed from all sides. We discuss a focusing method for media that can be accessed from one side only. We show how complex focusing functions, emitted from the top surface into the medium, cause independent foci for compressional and shear waves. The focused fields are isotropic and act as independent virtual sources for these wave types inside the medium. We foresee important applications in nondestructive testing of construction materials and seismological monitoring of processes inside the Earth.Geoscience & EngineeringCivil Engineering and Geoscience

Nonreciprocal Green’s function retrieval by cross correlation

The cross correlation of two recordings of a diffuse acoustic wave field at different receivers yields the Green’s function between these receivers. In nearly all cases considered so far the wave equation obeys time-reversal invariance and the Green’s function obeys source-receiver reciprocity. Here the theory is extended for nonreciprocal Green’s function retrieval in a moving medium. It appears that the cross correlation result is asymmetric in time. The causal part represents the Green’s function from one receiver to the other whereas the acausal part represents the time-reversed version of the Green’s function along the reverse path.GeotechnologyCivil Engineering and Geoscience

Pre-stack migration in two and three dimensions

Civil Engineering and Geoscience

Reciprocity and Representation Theorems for Flux- and Field-Normalised Decomposed Wave Fields

We consider wave propagation problems in which there is a preferred direction of propagation. To account for propagation in preferred directions, the wave equation is decomposed into a set of coupled equations for waves that propagate in opposite directions along the preferred axis. This decomposition is not unique. We discuss flux-normalised and field-normalised decomposition in a systematic way, analyse the symmetry properties of the decomposition operators, and use these symmetry properties to derive reciprocity theorems for the decomposed wave fields, for both types of normalisation. Based on the field-normalised reciprocity theorems, we derive representation theorems for decomposed wave fields. In particular, we derive double- and single-sided Kirchhoff-Helmholtz integrals for forward and backward propagation of decomposed wave fields. The single-sided Kirchhoff-Helmholtz integrals for backward propagation of field-normalised decomposed wave fields find applications in reflection imaging, accounting for multiple scattering.ImPhys/Acoustical Wavefield ImagingApplied Geophysics and Petrophysic