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The Marchenko method retrieves the responses to virtual sources in the Earth's subsurface from reflection data at the surface, accounting for all orders of multiple reflections. The method is based on two integral representations for…
To enhance monitoring of the subsurface, virtual sources and receivers inside the subsurface can be created from seismic reflection data at the surface of the Earth using the Marchenko method. The response between these virtual sources and…
We aim to monitor and characterize signals in the subsurface by combining these passive signals with recorded reflection data at the surface of the Earth. To achieve this, we propose a method to create virtual receivers from reflection data…
The Marchenko method is a powerful tool for reconstructing full-wavefield Green's functions using surface-recorded seismic data. These Green's functions can then be utilized to produce subsurface images that are not affected by artifacts…
We implement the 3D Marchenko equations to retrieve responses to virtual sources inside the subsurface. For this, we require reflection data at the surface of the Earth that contain no free-surface multiples and are densely sampled in…
Marchenko redatuming is a novel scheme used to retrieve up- and down-going Green's functions in an unknown medium. Marchenko equations are based on reciprocity theorems and are derived on the assumption of the existence of functions…
We consider reflection data that have been subsampled by 70% and use Point-Spread-Functions to reconstruct the original data. The subsampled, original and reconstructed reflection data are used to image the medium of interest with the…
In seismic monitoring, one is usually interested in the response of a changing target zone, embedded in a static inhomogeneous medium. We introduce an efficient method which predicts reflection responses at the earth's surface for different…
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…
An example of full solution of the inverse scattering problem on the half line is presented. For this purpose, a simple analytically solvable model system (Morse potential) is used, which is expected to be a reasonable approximation to a…
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…
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…
In recent years, a variety of Marchenko methods for the attenuation of internal multiples has been developed. These methods have been extensively tested on 2D synthetic data and applied to 2D field data, but only little is known about their…
The Marchenko algorithm can suppress the disturbing effects of internal multiples that are present in seismic reflection data. To achieve this, a set of coupled equations with four unknowns is solved. These coupled equations are separated…
This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…
In this paper, we investigate iterative methods that are based on sampling of the data for computing Tikhonov-regularized solutions. We focus on very large inverse problems where access to the entire data set is not possible all at once…
Incorporating information about the target distribution in proposal mechanisms generally produces efficient Markov chain Monte Carlo algorithms (or at least, algorithms that are more efficient than uninformed counterparts). For instance, it…
We have seen many developments in Marchenko equation-based methods for internal multiple attenuation in the past years. Starting from a wave-equation based method that required a smooth velocity model, there are now Marchenko equation-based…
Acoustic imaging methods often ignore multiple scattering. This leads to false images in cases where multiple scattering is strong.Marchenko imaging has recently been introduced as a data-driven way to deal with internal multiple…
Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of…