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Retrieving the Green’s function in an open system by cross correlation: A comparison of approaches (L)

Wapenaar, C.P.A. (author), Fokkema, J. (author), Snieder, R. (author)

We compare two approaches for deriving the fact that the Green’s function in an arbitrary inhomogeneous open system can be obtained by cross correlating recordings of the wave field at two positions. One approach is based on physical arguments, exploiting the principle of time-reversal invariance of the acoustic wave equation. The other approach...

journal article 2005

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Spurious multiples in seismic interferometry of primaries

Snieder, R. (author), Wapenaar, C.P.A. (author), Larner, K. (author)

Seismic interferometry is a technique for estimating the Green's function that accounts for wave propagation between receivers by correlating the waves recorded at these receivers. We present a derivation of this principle based on the method of stationary phase. Although this derivation is intended to be educational, applicable to simple media...

journal article 2006

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Seismic interferometry-turning noise into signal

Curtis, A. (author), Gerstoft, P. (author), Sato, H. (author), Snieder, R. (author), Wapenaar, C.P.A. (author)

Turning noise into useful data—every geophysicist's dream? And now it seems possible. The field of seismic interferometry has at its foundation a shift in the way we think about the parts of the signal that are currently filtered out of most analyses—complicated seismic codas (the multiply scattered parts of seismic waveforms) and background...

journal article 2006

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Unified Green’s Function Retrieval by Cross Correlation

Wapenaar, C.P.A. (author), Slob, E.C. (author), Snieder, R. (author)

It has been shown by many authors that the cross correlation of two recordings of a diffuse wave field at different receivers yields the Green’s function between these receivers. Recently the theory has been extended for situations where time-reversal invariance does not hold (e.g., in attenuating media) and where source-receiver reciprocity...

journal article 2006

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Unified Green's function retrieval by cross-correlation: Connection with energy principles

Snieder, R. (author), Wapenaar, K. (author), Wegler, U. (author)

journal article 2007

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Retrieving electric resistivity data from self-potential measurements by cross-correlation

Slob, E.C. (author), Snieder, R. (author), Revil, A. (author)

We show that the two-point cross-correlation of self-potential field recordings is equal to the electric resistivity between the two points. This holds under the condition that spatially and temporally uncorrelated noise sources exist throughout the volume. These sources should have a known amplitude spectrum and their correlated strengths...

journal article 2010

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On seismic interferometry, the generalized optical theorem, and the scattering matrix of a point scatterer

Wapenaar, C.P.A. (author), Slob, E.C. (author), Snieder, R. (author)

We have analyzed the far-field approximation of the Green's function representation for seismic interferometry. By writing each of the Green's functions involved in the correlation process as a superposition of a direct wave and a scattered wave, the Green's function representation is rewritten as a superposition of four terms. When the...

journal article 2010

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Synthetic aperture controlled source electromagnetics

Fan, Y. (author), Snieder, R. (author), Slob, E. (author), Hunziker, J.W. (author), Singer, J. (author), Sheiman, J. (author), Rosenquist, M. (author)

Controlled?source electromagnetics (CSEM) has been used as a de?risking tool in the hydrocarbon exploration industry. Although there have been successful applications of CSEM, this technique is still not widely used in the industry because the limited types of hydrocarbon reservoirs CSEM can detect. In this paper, we apply the concept of...

journal article 2010

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Tutorial on seismic interferometry: Part 1 — Basic principles and applications

Wapenaar, C.P.A. (author), Draganov, D.S. (author), Snieder, R. (author), Campman, X. (author), Verdel, A. (author)

Seismic interferometry involves the crosscorrelation of responses at different receivers to obtain the Green's function between these receivers. For the simple situation of an impulsive plane wave propagating along the x-axis, the crosscorrelation of the responses at two receivers along the x-axis gives the Green's function of the direct wave...

journal article 2010

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

Wapenaar, C.P.A. (author), Slob, E.C. (author), Snieder, R. (author), Curtis, A. (author)

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...

journal article 2010

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Increasing the sensitivity of controlled-source electromagnetics with synthetic aperture

Fan, Y. (author), Snieder, R. (author), Slob, E.C. (author), Hunziker, J.W. (author), Singer, J. (author), Sheiman, J. (author), Rosenquist, M. (author)

Controlled-source electromagnetics (CSEM) has been used as a derisking tool in the hydrocarbon exploration industry. We apply the concept of synthetic aperture to the lowfrequency electromagnetic field in CSEM. Synthetic aperture sources have been used in radar imaging for many years. Using the synthetic aperture concept, big synthetic sources...

journal article 2012

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Synthesized 2D CSEM-interferometry Using Automatic Source Line Determination

Hunziker, J.W. (author), Slob, E.C. (author), Fan, Y. (author), Snieder, R. (author), Wapenaar, C.P.A. (author)

Interferometry by multidimensional deconvolution applied to Controlled-Source Electromagnetic data replaces the medium above the receivers by a homogeneous halfspace, suppresses the direct field and redatums the source positions to the receiver locations. In that sense, the airwave and any other interactions of the signal with the air-water...

conference paper 2012

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Creating Virtual Sources Inside an Unknown Medium from Reflection Data: A New Approach to Internal Multiple Elimination

Wapenaar, C.P.A. (author), Thorbecke, J.W. (author), Van der Neut, J.R. (author), Broggini, F. (author), Snieder, R. (author)

It has recently been shown that the response to a virtual source in the subsurface can be derived from reflection data at the surface and an estimate of the direct arrivals between the virtual source and the surface. Hence, unlike for seismic interferometry, no receivers are needed inside the medium. This new method recovers the complete...

conference paper 2012

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Focusing the wavefield inside an unknown 1D medium: Beyond seismic interferometry

Broggini, F. (author), Snieder, R. (author), Wapenaar, C.P.A. (author)

With seismic interferometry one can retrieve the response to a virtual source inside an unknown medium, if there is a receiver at the position of the virtual source. Using inverse scattering theory, we demonstrate that, for a 1D medium, the requirement of having an actual receiver inside the medium can be circumvented, going beyond seismic...

journal article 2012

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Three-Dimensional Single-Sided Marchenko Inverse Scattering, Data-Driven Focusing, Green’s Function Retrieval, and their Mutual Relations

Wapenaar, C.P.A. (author), Broggini, F. (author), Slob, E.C. (author), Snieder, R. (author)

The one-dimensional Marchenko equation forms the basis for inverse scattering problems in which the scattering object is accessible from one side only. Here we derive a three-dimensional (3D) Marchenko equation which relates the single-sided reflection response of a 3D inhomogeneous medium to a field inside the medium. We show that this equation...

journal article 2013

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Electromagnetic interferometry in wavenumber and space domains in a layered earth

Hunziker, J.W. (author), Slob, E.C. (author), Fan, Y. (author), Snieder, R. (author), Wapenaar, C.P.A. (author)

With interferometry applied to controlled-source electromagnetic data, the direct field and the airwave and all other effects related to the air-water interface can be suppressed in a data-driven way. Interferometry allows for retreival of the scattered field Green’s function of the subsurface or, in other words, the subsurface reflection...

journal article 2013

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Creating the green's response to a virtual source inside a medium using reflection data with internal multiples

Broggini, F. (author), Snieder, R. (author), Wapenaar, C.P.A. (author), Thorbecke, J.W. (author)

Seismic interferometry is a technique that allows one to reconstruct the full wavefield originating from a virtual source inside a medium, assuming a receiver is present at the virtual source location. We discuss a method that creates a virtual source inside a medium from reflection data measured at the surface, without needing a receiver inside...

conference paper 2013

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3D Marine CSEM Interferometry by Multidimensional Deconvolution in the Wavenumber Domain for a Sparse Receiver Grid

Hunziker, J.W. (author), Slob, E.C. (author), Fan, Y. (author), Snieder, R. (author), Wapenaar, C.P.A. (author)

We use interferometry by multidimensional deconvolution in combination with synthetic aperture sources in 3D to suppress the airwave and the direct field, and to decrease source uncertainty in marine Controlled-Source electromagnetics. We show with this numerical study that the method works for very large receiver spacing distances, even though...

conference paper 2013

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Data-driven green's function retrieval from reflection data: Theory and example

Wapenaar, C.P.A. (author), Slob, E.C. (author), Broggini, F. (author), Snieder, R. (author), Thorbecke, J.W. (author), Van der Neut, J.R. (author)

Recently we introduced a new approach for retrieving the Green's response to a virtual source in the subsurface from reflection data at the surface. Unlike in seismic interferometry, no receiver is needed at the position of the virtual source. Here we present the theory behind this new method. First we introduce the Green's function G and a so...

conference paper 2013

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Data-driven Green's function retrieval and imaging with multidimensional deconvolution: Numerical examples for reflection data with internal multiples

Broggini, F. (author), Snieder, R. (author), Wapenaar, C.P.A. (author)

Standard imaging techniques rely on the single scattering assumption. This requires that the recorded data do not include internal multiples, i.e. waves bouncing multiple times between layers before reaching the receivers at the acquisition surface. When multiple reflections are present in the data, standard imaging algorithms incorrectly image...

journal article 2013