On unified dual fields and Einstein deconvolution

Loewenthal, Dan; Robinson, Enders A.

doi:10.1190/1.1444720

Cited by 25 publications

(4 citation statements)

References 16 publications

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“…When such measurements are available, it is possible to separate upgoing from downgoing waves at any receiver point by summing and subtracting u and a suitable component of ͑ i ͒ ‫1מ‬ ٌ u ͑e.g., Loewenthal and Robinson, 2000;Amundsen, 2001;Amundsen et al, 2001͒. Interferometry based on dual-sensor wavefield separation has a similar objective to that of direct-wave interferometry: It reconstructs upgoing waves propagating between r B and r A by the interference of upgoing waves recorded at r A with downgoing waves recorded at r B .…”

Section: Dual-field Separationmentioning

confidence: 99%

“…They then turned to correlation because it tends to be more stable. Loewenthal and Robinson ͑2000͒ show that the deconvolution of dual wavefields can be used to change the boundary conditions of the original experiment to generate only upgoing scattered waves at the receiver locations and to recover reflectivity. In a series of papers on free-surface multiple suppression, Amundsen and coworkers use inverse deconvolution operators designed to remove the free-surface boundary condition ͑e.g., Amundsen et al, 2001;Holvik and Amundsen, 2005͒.…”

Section: Introductionmentioning

confidence: 99%

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Interferometry by deconvolution: Part 1 — Theory for acoustic waves and numerical examples

2008

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Interferometry allows for synthesis of data recorded at any two receivers into waves that propagate between these receivers as if one of them behaves as a source. This is accomplished typically by crosscorrelations. Based on perturbation theory and representation theorems, we show that interferometry also can be done by deconvolutions for arbitrary media and multidimensional experiments. This is important for interferometry applications in which ͑1͒ excitation is a complicated source-time function and/or ͑2͒ when wavefield separation methods are used along with interferometry to retrieve specific arrivals. Unlike using crosscorrelations, this method yields only causal scattered waves that propagate between the receivers. We offer a physical interpretation of deconvolution interferometry based on scattering theory. Here we show that deconvolution interferometry in acoustic media imposes an extra boundary condition, which we refer to as the free-point or clamped-point boundary condition, depending on the measured field quantity. This boundary condition generates so-called free-point scattering interactions, which are described in detail. The extra boundary condition and its associated artifacts can be circumvented by separating the reference waves from scattered wavefields prior to interferometry. Three wavefield-separation methods that can be used in interferometry are direct-wave interferometry, dual-field interferometry, and shot-domain separation. Each has different objectives and requirements.

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Section: Dual-field Separationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interferometry by deconvolution: Part 1 — Theory for acoustic waves and numerical examples

2008

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“…In summary, up‐over‐down (Einstein) deconvolution removes the upper system and all of its ill effects. The lower system remains, all by itself (Loewenthal and Robinson ).…”

Section: Non‐free‐surface and Free‐surface Reflection Seismograms: Eimentioning

confidence: 99%

Inverse problem for Goupillaud‐layered earth model and dynamic deconvolution

Bardan

Robinson

2018

Geophysical Prospecting

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This paper presents, in a tutorial form, some analytical inversion techniques for the Goupillaud‐layered earth model. Finding the reflection coefficients from the reflection seismogram is the inverse problem for the model. For this reason we present a thorough description of the inverse problem for the Goupillaud model, two solutions to solve the inverse scattering problem using linear discrete equations and the solution obtained using the classic dynamic deconvolution method. The inversion is achieved using Robinson's polynomials Pk(z), Qk(z), Ak(z) and their reverse polynomials, as well as some properties of the model (the Lorentz transformation and the Einstein subtraction formula). The method of dynamic deconvolution, which makes the inversion of the model very simple computationally, is based on the physical structure of the reflection seismogram. We present the classic dynamic deconvolution algorithm for the non‐free‐surface Goupillaud model to show that the dynamic deconvolution method can provide efficient discrete procedures for the inversion. For this reason, though the inverse dynamic deconvolution procedures are old algorithms, they could be useful today for solving inverse scattering problems arising in exploration geophysics and various fields.

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“…In contrast, the the free-surface multiples contain down-going energy. Since we have both the hydrophone and vertical geophone recording, we use dualsensor summation (Jiao, et.al., 1998;Barr, et.al., 1996;Barr, 1997;Barr and Sanders, 1989;Barr, et.al., 1997;Dragoset and Barr, 1994;Paffenholz and Barr, 1995;Ball and Corrigan, 1996;Soubaras, 1996;Canales and Bell, 1996;Loewenthal, 1994;Loewenthal and Robinson, 2000;Robinson, et.al., 1999) to separate the up-going Figure 11. Cartoon showing the arrivals that causes the two reflection events D and E shown in Figure 7.…”

Section: Attenuation Of Free-surface Multiplesmentioning

confidence: 99%

Virtual source gathers and attenuation of free‐surface multiples using OBC data:implementation issues and a case study

Mehta

Snieder

Calvert

et al. 2006

SEG Technical Program Expanded Abstracts 2006

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Virtual source imaging is a technique based on extracting the Green's function that characterizes wave propagation between two receivers by cross-correlating the wave-fields recorded by these receivers. We focus on implementation issues in generating a virtual source gather from a multi-component OBC data recorded at the Mars field. The implementation issues include choice of the receiver that acts as the virtual source and the number of sources over which the cross-correlated data is stacked. The pre-stack correlated data (correlation gather) is a useful diagnostic for quality control and for assessing the source locations that give a stationary phase contribution. By stacking over specific source locations, we restrict the direction of the incoming energy and generate virtual source gathers containing arrivals within a specified horizontal slowness interval. We compare the virtual source gather generated by using a small number of sources to the virtual source gather generated by using a larger source aperture for stacking. Artifacts due to the traces at the edges of the source aperture can be suppressed by applying a taper before stacking the correlation gather. Another artifact observed in virtual source gathers is due to side-lobes of the auto-correlation of the source-time function. We show the use of dualsensor summation to separate the up-and the down-going energy in the raw data and using that to generate virtual source gathers containing only the upgoing energy, hence attenuating the free-surface multiples.

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On unified dual fields and Einstein deconvolution

Cited by 25 publications

References 16 publications

Interferometry by deconvolution: Part 1 — Theory for acoustic waves and numerical examples

Interferometry by deconvolution: Part 1 — Theory for acoustic waves and numerical examples

Inverse problem for Goupillaud‐layered earth model and dynamic deconvolution

Virtual source gathers and attenuation of free‐surface multiples using OBC data:implementation issues and a case study

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