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

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...

Robust estimation of primaries by sparse inversion and Marchenko equation-based workflow for multiple suppression in the case of a shallow water layer and a complex overburden: A 2D case study in the Arabian Gulf

Suppression of surface-related and internal multiples is an outstanding challenge in seismic data processing. The former is particularly difficult in shallow water, whereas the latter is problematic for targets buried under complex, highly scattering overburdens. We have developed a two-step, amplitude- and phase-preserving, inversion-based...

A field data example of Marchenko multiple elimination

Internal multiple reflections have been widely considered as coherent noise in measured seismic data, and many approaches have been developed for their attenuation. The Marchenko multiple elimination (MME) scheme eliminates internal multiple reflections without model information or adaptive subtraction. This scheme was originally derived from...

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...

Theory for 1D full waveform inversion of surface GPR data

In one dimension, full waveform inversion is shown to be a linear problem under several conditions. I show that if the magnetic permeability can be assumed constant and electric conductivity to be zero, measuring the magnetic field at the surface or in the air suffices as input data. I present the theory using integral equations that describe...

A tour of Marchenko redatuming: Focusing the subsurface wavefield

Marchenko redatuming can retrieve the impulse response to a subsurface virtual source from the single-sided surface reflection data with limited knowledge of the medium. We illustrate the concepts and practical aspects of Marchenko redatuming on a simple 1D acoustic lossless medium in which the coupled Marchenko equations are exact. Defined...

Source-receiver Marchenko redatuming on field data using an adaptive double-focusing method

We have developed an adaptive double-focusing method that is specifically designed for the field-data application of source-receiver Marchenko redatuming. Typically, the single-focusing Marchenko method is combined with a multidimensional deconvolution (MDD) to achieve redatuming. Our method replaces the MDD step by a second focusing step...

A lossless earth Green's function representation between any two subsurface points from surface reflection GPR data

We present a three-dimensional scheme that can be used to compute the electromagnetic impulse response between any two subsurface points from surface reflection data measured at a single surface of a lossless medium. The scheme first computes a virtual vertical radar profile using the Marchenko scheme from which focusing wavefields are...

Beyond Marchenko: Obtaining virtual receivers and virtual sources in the subsurface

By solving the Marchenko equations, the Green’s function can be retrieved between a virtual receiver in the subsurface to points at the surface (no physical receiver is required at the virtual location). We extend the idea of these equations to retrieve the Green’s function between any two points in the subsurface; i.e, between a virtual source...

Marchenko equations for acoustic Green's function retrieval and imaging in dissipative media

We present a scheme for Marchenko imaging in a dissipative heterogeneous medium. The scheme requires measured reflection and transmission data at two sides of the dissipative medium. The effectual medium is the same as the dissipative medium, but with negative dissipation. We show how the measured double-sided data can be combined to obtain the...

Marchenko wavefield redatuming, imaging conditions, and the effect of model errors

Recently, a novel method to redatum the wavefield in the sub-surface from a reflection response measured at the surface has gained interest for imaging primaries in the presence of strong internal multiples. A prerequisite for the algorithm is an accurate and correct estimate of the direct-wave Green's function. However, usually we use an...

An interferometric interpretation of Marchenko redatuming including free-surface multiples

We present an interferometric interpretation of the iterative Marchenko scheme including both free-surface multiples and internal multiples. Cross-correlations are used to illustrate the combination of causal and acausal events that are essential for the process of multiple removal. The first 4 steps in the scheme are discussed in detail, where...

Creating virtual vertical radar profiles from surface reflection ground penetrating radar data

Internal multiple suppression by adaptive Marchenko redatuming

Recently, a novel iterative scheme was proposed to retrieve Green's functions in an unknown medium from its single-sided reflection response and an estimate of the propagation velocity. In Marchenko imaging, these Green's functions are used for seismic imaging with complete wavefields, including internal multiple reflections. In this way, common...

Autofocusing imaging: Imaging with primaries, internal multiples and free-surface multiples

Recent work on autofocusing with the Marchenko equation has shown how the Green's function for a virtual source in the subsurface can be obtained from reflection data. The response to the virtual source is the Green's function from the location of the virtual source to the surface. The Green's function is retrieved using only the reflection...

Data-driven Green's function retrieval and application to imaging with multidimensional deconvolution

An iterative method is presented that allows one to retrieve the Green's function originating from a virtual source located inside a medium using reflection data measured only at the acquisition surface. In addition to the reflection response, an estimate of the travel times corresponding to the direct arrivals is required. However, no detailed...

Computing the vertical density and seismic velocity profiles from multi-angle reflection data: Error analysis

Numerical models were used to recursively compute the density profile and the seismic velocity profile of three different artificial models of the underground from primary reflection images obtained from multi-angle incident plane wave reflection data. The aim is to investigate the effect of errors in the obtained primary reflection amplitudes...

Focusing one dimensional models by using the ‘Single-sided’ autofocusing procedure of Rose for layered materials