scholarly journals Green's function retrieval from reflection data, in absence of a receiver at the virtual source position

2014 ◽  
Vol 135 (5) ◽  
pp. 2847-2861 ◽  
Author(s):  
Kees Wapenaar ◽  
Jan Thorbecke ◽  
Joost van der Neut ◽  
Filippo Broggini ◽  
Evert Slob ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Virtual Source ◽  
Source Position ◽  
Reflection Data

scholarly journals On the Marchenko equation for multicomponent single-sided reflection data

2014 ◽  
Vol 199 (3) ◽  
pp. 1367-1371 ◽  
Author(s):  
Kees Wapenaar ◽  
Evert Slob
Keyword(s):  
Green’S Function ◽  
Recent Work ◽  
Green's Function ◽  
Scattered Field ◽  
Iterative Solution ◽  
Virtual Source ◽  
Function Representation ◽  
Reflection Data ◽  
Marchenko Equation ◽  
Multicomponent Data

Abstract Recent work on the Marchenko equation has shown that the scalar 3-D Green's function for a virtual source in the subsurface can be retrieved from the single-sided reflection response at the surface and an estimate of the direct arrival. Here, we discuss the first steps towards extending this result to multicomponent data. After introducing a unified multicomponent 3-D Green's function representation, we analyse its 1-D version for elastodynamic waves in more detail. It follows that the main additional requirement is that the multicomponent direct arrival, needed to initiate the iterative solution of the Marchenko equation, includes the forward-scattered field. Under this and other conditions, the multicomponent Green's function can be retrieved from single-sided reflection data, and this is demonstrated with a 1-D numerical example.

scholarly journals Tutorial on seismic interferometry: Part 2 — Underlying theory and new advances

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A211-75A227 ◽  
Author(s):  
Kees Wapenaar ◽  
Evert Slob ◽  
Roel Snieder ◽  
Andrew Curtis
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Seismic Interferometry ◽  
Virtual Source ◽  
Bending Waves ◽  
Complex Source ◽  
Recent Developments ◽  
Diffusion Phenomena ◽  
Quantum Mechanical Scattering ◽  
Moving Media

In the 1990s, the method of time-reversed acoustics was developed. This method exploits the fact that the acoustic wave equation for a lossless medium is invariant for time reversal. When ultrasonic responses recorded by piezoelectric transducers are reversed in time and fed simultaneously as source signals to the transducers, they focus at the position of the original source, even when the medium is very complex. In seismic interferometry the time-reversed responses are not physically sent into the earth, but they are convolved with other measured responses. The effect is essentially the same: The time-reversed signals focus and create a virtual source which radiates waves into the medium that are subsequently recorded by receivers. A mathematical derivation, based on reciprocity theory, formalizes this principle: The crosscorrelation of responses at two receivers, integrated over differ-ent sources, gives the Green’s function emitted by a virtual source at the position of one of the receivers and observed by the other receiver. This Green’s function representation for seismic interferometry is based on the assumption that the medium is lossless and nonmoving. Recent developments, circumventing these assumptions, include interferometric representations for attenuating and/or moving media, as well as unified representations for waves and diffusion phenomena, bending waves, quantum mechanical scattering, potential fields, elastodynamic, electromagnetic, poroelastic, and electroseismic waves. Significant improvements in the quality of the retrieved Green’s functions have been obtained with interferometry by deconvolution. A trace-by-trace deconvolution process compensates for complex source functions and the attenuation of the medium. Interferometry by multidimensional deconvolution also compensates for the effects of one-sided and/or irregular illumination.

scholarly journals Data-driven wavefield focusing and imaging with multidimensional deconvolution: Numerical examples for reflection data with internal multiples

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA107-WA115 ◽  
Author(s):  
Filippo Broggini ◽  
Roel Snieder ◽  
Kees Wapenaar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Imaging Techniques ◽  
Velocity Model ◽  
Single Scattering ◽  
Data Driven ◽  
Multiple Reflections ◽  
Prestack Migration ◽  
Reflection Data ◽  
Internal Multiples

Standard imaging techniques rely on the single scattering assumption. This requires that the recorded data do not include internal multiples, i.e., waves that have bounced multiple times between reflectors before reaching the receivers at the acquisition surface. When multiple reflections are present in the data, standard imaging algorithms incorrectly image them as ghost reflectors. These artifacts can mislead interpreters in locating potential hydrocarbon reservoirs. Recently, we introduced a new approach for retrieving the Green’s function recorded at the acquisition surface due to a virtual source located at depth. We refer to this approach as data-driven wavefield focusing. Additionally, after applying source-receiver reciprocity, this approach allowed us to decompose the Green’s function at a virtual receiver at depth in its downgoing and upgoing components. These wavefields were then used to create a ghost-free image of the medium with either crosscorrelation or multidimensional deconvolution, presenting an advantage over standard prestack migration. We tested the robustness of our approach when an erroneous background velocity model is used to estimate the first-arriving waves, which are a required input for the data-driven wavefield focusing process. We tested the new method with a numerical example based on a modification of the Amoco model.

On the fundamentals of the virtual source method

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. A13-A17 ◽  
Author(s):  
Valeri Korneev ◽  
Andrey Bakulin
Keyword(s):  
Green’S Function ◽  
Direct Measurement ◽  
Green's Function ◽  
Velocity Model ◽  
Practical Approach ◽  
Virtual Source ◽  
Processing Stage ◽  
Source Method ◽  
Complex Part ◽  
Seismic Images

The virtual source method (VSM) has been proposed as a practical approach to reduce distortions of seismic images caused by shallow, heterogeneous overburden. VSM is demanding at the acquisition stage because it requires placing downhole geophones below the most complex part of the heterogeneous overburden. Where such acquisition is possible, however, it pays off later at the processing stage because it does not require knowledge of the velocity model above the downhole receivers. This paper demonstrates that VSM can be viewed as an application of the Kirchhoff-Helmholtz integral (KHI) with an experimentally measured Green’s function. Direct measurement of the Green’s function ensures the effectiveness of the method in highly heterogeneous subsurface conditions.

scholarly journals Monitoring of induced distributed double-couple sources using Marchenko-based virtual receivers

Solid Earth ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1301-1319 ◽  
Author(s):  
Joeri Brackenhoff ◽  
Jan Thorbecke ◽  
Kees Wapenaar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Synthetic Data ◽  
Real Data ◽  
Point Sources ◽  
Reflection Data ◽  
Double Couple ◽  
Source Mechanisms ◽  
Source Signal ◽  
Time Part

Abstract. 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 using the Marchenko method. By applying homogeneous Green’s function retrieval, these virtual receivers are then used to monitor the responses from subsurface sources. We consider monopole point sources with a symmetric source signal, for which the full wave field without artifacts in the subsurface can be obtained. Responses from more complex source mechanisms, such as double-couple sources, can also be used and provide results with comparable quality to the monopole responses. If the source signal is not symmetric in time, our technique based on homogeneous Green’s function retrieval provides an incomplete signal, with additional artifacts. The duration of these artifacts is limited and they are only present when the source of the signal is located above the virtual receiver. For sources along a fault rupture, this limitation is also present and more severe due to the source activating over a longer period of time. Part of the correct signal is still retrieved, as is the source location of the signal. These artifacts do not occur in another method that creates virtual sources as well as receivers from reflection data at the surface. This second method can be used to forecast responses to possible future induced seismicity sources (monopoles, double-couple sources and fault ruptures). This method is applied to field data, and similar results to the ones on synthetic data are achieved, which shows the potential for application on real data signals.

scholarly journals Reflection images from ambient seismic noise

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. A63-A67 ◽  
Author(s):  
Deyan Draganov ◽  
Xander Campman ◽  
Jan Thorbecke ◽  
Arie Verdel ◽  
Kees Wapenaar
Keyword(s):  
Surface Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Seismic Noise ◽  
Seismic Exploration ◽  
Ambient Seismic Noise ◽  
Reflection Data ◽  
Parallel Lines ◽  
Reflection Image ◽  
Sirte Basin

One application of seismic interferometry is to retrieve the impulse response (Green’s function) from crosscorrelation of ambient seismic noise. Various researchers show results for retrieving the surface-wave part of the Green’s function. However, reflection retrieval has proven more challenging. We crosscorrelate ambient seismic noise, recorded along eight parallel lines in the Sirte basin east of Ajdabeya, Libya, to obtain shot gathers that contain reflections. We take advantage of geophone groups to suppress part of the undesired surface-wave noise and apply frequency-wavenumber filtering before crosscorrelation to suppress surface waves further. After comparing the retrieved results with data from an active seismic exploration survey along the same lines, we use the retrieved reflection data to obtain a migrated reflection image of the subsurface.

scholarly journals Marchenko imaging

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA39-WA57 ◽  
Author(s):  
Kees Wapenaar ◽  
Jan Thorbecke ◽  
Joost van der Neut ◽  
Filippo Broggini ◽  
Evert Slob ◽  
...  
Keyword(s):  
Green’S Function ◽  
Inverse Scattering ◽  
Green's Function ◽  
Seismic Interferometry ◽  
Virtual Source ◽  
Target Zone ◽  
Scattering Problems ◽  
Inverse Scattering Problems ◽  
Marchenko Equation ◽  
Internal Multiples

Traditionally, the Marchenko equation forms a basis for 1D inverse scattering problems. A 3D extension of the Marchenko equation enables the retrieval of the Green’s response to a virtual source in the subsurface from reflection measurements at the earth’s surface. This constitutes an important step beyond seismic interferometry. Whereas seismic interferometry requires a receiver at the position of the virtual source, for the Marchenko scheme it suffices to have sources and receivers at the surface only. The underlying assumptions are that the medium is lossless and that an estimate of the direct arrivals of the Green’s function is available. The Green’s function retrieved with the 3D Marchenko scheme contains accurate internal multiples of the inhomogeneous subsurface. Using source-receiver reciprocity, the retrieved Green’s function can be interpreted as the response to sources at the surface, observed by a virtual receiver in the subsurface. By decomposing the 3D Marchenko equation, the response at the virtual receiver can be decomposed into a downgoing field and an upgoing field. By deconvolving the retrieved upgoing field with the downgoing field, a reflection response is obtained, with virtual sources and virtual receivers in the subsurface. This redatumed reflection response is free of spurious events related to internal multiples in the overburden. The redatumed reflection response forms the basis for obtaining an image of a target zone. An important feature is that spurious reflections in the target zone are suppressed, without the need to resolve first the reflection properties of the overburden.

scholarly journals Monitoring induced distributed double-couple sources using Marchenko-based virtual receivers

2019 ◽  
Author(s):  
Joeri Brackenhoff ◽  
Jan Thorbecke ◽  
Kees Wapenaar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Synthetic Data ◽  
Real Data ◽  
Point Sources ◽  
Reflection Data ◽  
Double Couple ◽  
Source Mechanisms ◽  
Source Signal ◽  
Time Part

Abstract. 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 using the Marchenko method. By applying homogeneous Green’s function retrieval, these virtual receivers are then used to monitor the responses from subsurface sources. We consider monopole point sources with a symmetric source signal, where the full wavefield without artefacts in the subsurface can be obtained. Responses from more complex source mechanisms, such as double-couple sources, can also be used and provide results with comparable quality as the monopole responses. If the source signal is not symmetric in time, our technique that is based on homogeneous Green’s function retrieval provides an incomplete signal, with additional artefacts. The duration of these artefacts is limited and they are only present when the source of the signal is located above the virtual receiver. For sources along a fault rupture, this limitation is also present and more severe due to the source activating over a longer period of time. Part of the correct signal is still retrieved, as well as the source location of the signal. These aretefacts do not occur in another method which creates virtual sources as well as receivers from reflection data at the surface. This second method can be used to forecast responses to possible future induced seismicity sources (monopoles, double-couple sources and fault ruptures). This method is applied to field data, where similar results to synthetic data are achieved, which shows the potential for the application on real data signals.

Retrieving reflections by source-receiver wavefield interferometry

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. SA1-SA8 ◽  
Author(s):  
Oleg V. Poliannikov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Boundary Data ◽  
Ray Theory ◽  
Geometric Description ◽  
Virtual Source ◽  
Classical Correlation ◽  
Common Path ◽  
The Common ◽  
Stationary Sources

Source-receiver wavefield interferometry has been proposed recently as an extension of classical correlation-based interferometry. Under idealized assumptions, it allows the Green’s function between a source and a receiver to be reconstructed from boundary data that are collected using two closed contours of sources and receivers, respectively. An intuitive geometric description of this method, based on ray theory, can be used to design a method for reconstructing virtual-gather events that typically are lost when conventional interferometry is employed. In classical interferometry, events in the Green’s function between two receiver locations are reconstructed by automatically finding a ray that emanates from a stationary source, passes through the virtual source, reflects off the structure, and finally is recorded by the second receiver. The common path to both receivers is then canceled by a suitable crosscorrelation. If illumination of the structure is not ideal, such a ray may not exist and the reflection is not reconstructed. Source-receiver wave interferometry can be given a similar geometric description. The reflection off the structure can be constructed using not one but multiple rays produced simultaneously by two stationary sources. This new redatuming technique proves successful in geometries in which classical interferometry fails. Extensive numerical simulations support these theoretical conclusions.

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