Path integral calculation of relativistic Green’s functions for particles in the field of the plane wave

A method to perform bosonization of a fermionic theory in (1+1) dimensions in a path integral framework is developed. The method relies exclusively on the path integral property of allowing variable shifts, and does not depend on the explicit form of Green's functions. Two examples, the Schwinger model and the massless Thirring model, are worked out.

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Marchenko redatuming, imaging and multiple elimination, and their mutual relations

Geophysics ◽

10.1190/geo2020-0854.1 ◽

2021 ◽

pp. 1-103

Author(s):

Kees Wapenaar ◽

Joeri Brackenhoff ◽

Marcin Dukalski ◽

Giovanni Meles ◽

Chris Reinicke ◽

...

Keyword(s):

Plane Wave ◽

Green's Functions ◽

Green’S Functions ◽

Mathematical Framework ◽

Reflection Data ◽

Efficient Alternative ◽

Internal Multiples ◽

Mutual Relations ◽

Double Focusing ◽

Multiple Elimination

With the Marchenko method it is possible to retrieve Green's functions between virtual sources in the subsurface and receivers at the surface from reflection data at the surface and focusing functions. A macro model of the subsurface is needed to estimate the first arrival; the internal multiples are retrieved entirely from the reflection data. The retrieved Green's functions form the input for redatuming by multidimensional deconvolution (MDD). The redatumed reflection response is free of internal multiples related to the overburden. Alternatively, the redatumed response can be obtained by applying a second focusing function to the retrieved Green's functions. This process is called Marchenko redatuming by double focusing. It is more stable and better suited for an adaptive implementation than Marchenko redatuming by MDD, but it does not eliminate the multiples between the target and the overburden. An attractive efficient alternative is plane-wave Marchenko redatuming, which retrieves the responses to a limited number of plane-wave sources at the redatuming level. In all cases, an image of the subsurface can be obtained from the redatumed data, free of artefacts caused by internal multiples. Another class of Marchenko methods aims at eliminating the internal multiples from the reflection data, while keeping the sources and receivers at the surface. A specific characteristic of this form of multiple elimination is that it predicts and subtracts all orders of internal multiples with the correct amplitude, without needing a macro subsurface model. Like Marchenko redatuming, Marchenko multiple elimination can be implemented as an MDD process, a double dereverberation process, or an efficient plane-wave oriented process. We systematically discuss the different approaches to Marchenko redatuming, imaging and multiple elimination, using a common mathematical framework.

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Fast image-domain target-oriented least-squares reverse time migration

Geophysics ◽

10.1190/geo2018-0033.1 ◽

2018 ◽

Vol 83 (6) ◽

pp. A81-A86 ◽

Cited By ~ 3

Author(s):

Zeyu Zhao ◽

Mrinal K. Sen

Keyword(s):

Plane Wave ◽

Least Squares ◽

Large Scale ◽

Green's Functions ◽

Green’S Functions ◽

Hessian Matrix ◽

Reverse Time ◽

Reverse Time Migration ◽

Image Domain ◽

Time Migration

We have developed a fast image-domain target-oriented least-squares reverse time migration (LSRTM) method based on applying the inverse or pseudoinverse of a target-oriented Hessian matrix to a migrated image. The image and the target-oriented Hessian matrix are constructed using plane-wave Green’s functions that are computed by solving the two-way wave equation. Because the number of required plane-wave Green’s functions is small, the proposed method is highly efficient. We exploit the sparsity of the Hessian matrix by computing only a couple of off-diagonal terms for the target-oriented Hessian, which further improves the computational efficiency. We examined the proposed LSRTM method using the 2D Marmousi model. We demonstrated that our method correctly recovers the reflectivity model, and the retrieved results have more balanced illumination and higher spatial resolution than traditional images. Because of the low cost of computing the target-oriented Hessian matrix, the proposed method has the potential to be applied to large-scale problems.

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