scholarly journals Directional balancing for seismic and general wavefield interferometry

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. SA1-SA14 ◽  
Author(s):  
Andrew Curtis ◽  
David Halliday
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Acoustic Scattering ◽  
Data Driven ◽  
Seismic Interferometry ◽  
Noise Sources ◽  
Naturally Occurring ◽  
Passive Seismic ◽  
Incoming Energy ◽  
Solid Bodies

In passive seismic interferometry using naturally occurring, heterogeneous noise sources and in active-source seismic interferometry where sources can usually only be distributed densely on the exterior of solid bodies, bias can be introduced in Green’s function estimates when amplitudes of energy have directional variations. We have developed an algorithm to remove bias in Green’s function estimates constructed using seismic interferometry when amplitudes of energy used have uncontrollable directional variations. The new algorithm consists of two parts: (1) a method to measure and adjust the amplitudes of physical, incoming energy using an array of receivers and (2) a method to predict and remove nonphysical energy that remains (and can be accentuated) in interferometrically derived Green’s functions after applying the method in step 1. To accomplish step 2, we have created two data-driven methods to predict the nonphysical energy using direct computation or move-out-based methods, and a way to suppress such energy using (in this case) helical least-squares filters. Two-dimensional acoustic scattering examples confirm the algorithm’s effectiveness.

scholarly journals Seismic Interferometry from Correlated Noise Sources

2021 ◽  
Vol 13 (14) ◽  
pp. 2703
Author(s):  
Daniella Ayala-Garcia ◽  
Andrew Curtis ◽  
Michal Branicki
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Ambient Noise ◽  
Ocean Waves ◽  
Seismic Interferometry ◽  
Correlated Noise ◽  
Highway Traffic ◽  
Noise Sources ◽  
Estimation Errors ◽  
Band Limited

It is a well-established principle that cross-correlating seismic observations at different receiver locations can yield estimates of band-limited inter-receiver Green’s functions. This principle, known as Green’s function retrieval or seismic interferometry, is a powerful technique that can transform noise into signals which enable remote interrogation and imaging of the Earth’s subsurface. In practice it is often necessary and even desirable to rely on noise already present in the environment. Theory that underpins many applications of ambient noise interferometry assumes that the sources of noise are uncorrelated in time. However, many real-world noise sources such as trains, highway traffic and ocean waves are inherently correlated in space and time, in direct contradiction to the these theoretical foundations. Applying standard interferometric techniques to recordings from correlated energy sources makes the Green’s function liable to estimation errors that so far have not been fully accounted for theoretically nor in practice. We show that these errors are significant for common noise sources, always perturbing or entirely obscuring the phase one wishes to retrieve. Our analysis explains why stacking may reduce the phase errors, but also shows that in commonly encountered circumstances stacking will not remediate the problem. This analytical insight allowed us to develop a novel workflow that significantly mitigates effects arising from the use of correlated noise sources. Our methodology can be used in conjunction with already existing approaches, and improves results from both correlated and uncorrelated ambient noise. Hence, we expect it to be widely applicable in ambient noise studies.

scholarly journals Green’s function representations for seismic interferometry

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI33-SI46 ◽  
Author(s):  
Kees Wapenaar ◽  
Jacob Fokkema
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Layered Medium ◽  
Closed Surface ◽  
Reciprocity Theorem ◽  
Stationary Points ◽  
Seismic Interferometry ◽  
Noise Sources ◽  
Shaping Filter ◽  
Reversal Invariance

The term seismic interferometry refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations. The first version of this principle was derived by Claerbout (1968), who showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response. For an arbitrary 3D inhomogeneous lossless medium it follows from Rayleigh’s reciprocity theorem and the principle of time-reversal invariance that the acoustic Green’s function between any two points in the medium can be represented by an integral of crosscorrelations of wavefield observations at those two points. The integral is along sources on an arbitrarily shaped surface enclosing these points. No assumptions are made with respect to the diffusivity of the wavefield. The Rayleigh-Betti reciprocity theorem leads to a similar representation of the elastodynamic Green’s function. When a part of the enclosing surface is the earth’s free surface, the integral needs only to be evaluated over the remaining part of the closed surface. In practice, not all sources are equally important: The main contributions to the reconstructed Green’s function come from sources at stationary points. When the sources emit transient signals, a shaping filter can be applied to correct for the differences in source wavelets. When the sources are uncorrelated noise sources, the representation simplifies to a direct crosscorrelation of wavefield observations at two points, similar as in methods that retrieve Green’s functions from diffuse wavefields in disordered media or in finite media with an irregular bounding surface.

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.

scholarly journals Acoustic scattering from a one-dimensional array; Tail-end asymptotics for efficient evaluation of the quasi-periodic Green’s function

Wave Motion ◽  
2019 ◽  
Vol 89 ◽  
pp. 232-244
Author(s):  
Georgia M. Lynott ◽  
Victoria Andrew ◽  
I. David Abrahams ◽  
Michael J. Simon ◽  
William J. Parnell ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Acoustic Scattering ◽  
One Dimensional ◽  
Dimensional Array

On estimating the impulse response between receivers in a controlled ultrasonic experiment

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI79-SI84 ◽  
Author(s):  
K. van Wijk
Keyword(s):  
Data Processing ◽  
Laboratory Experiment ◽  
Green’S Function ◽  
Detailed Analysis ◽  
Elastic Medium ◽  
Impulse Response ◽  
Green's Function ◽  
Geophysical Data ◽  
Seismic Interferometry ◽  
Band Limited

A controlled ultrasonic laboratory experiment provides a detailed analysis of retrieving a band-limited estimate of the Green's function between receivers in an elastic medium. Instead of producing a formal derivation, this paper appeals to a series of intuitive operations, common to geophysical data processing, to understand the practicality of seismic interferometry. Whereas the retrieval of the full Green's function is based on the crosscorrelation of receivers in the presence of equipartitioned signal, an estimate of the impulse response is recovered successfully with 40 sources in a line covering six wavelengths at the surface.

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