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

Wapenaar, Kees; Slob, Evert; Snieder, Roel

doi:10.1190/1.3374359

Cited by 43 publications

(34 citation statements)

References 35 publications

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“…For this situation the last term in (38) vanishes on account of the optical theorem (6) and the symmetry relation (5) for the scattering matrix [32,36,37]. This leaves…”

Section: Figure 2 More Detailed Analysis Of the Dominating Contributmentioning

confidence: 99%

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On the Retrieval of the Directional Scattering Matrix from Directional Noise

Wapenaar¹,

Thorbecke²

2013

SIAM J. Imaging Sci.

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Abstract. The crosscorrelation of ambient acoustic noise observed at two receivers yields the impulse response between these receivers, assuming that the noise field is diffuse. In practical situations the noise field exhibits directionality, which imprints the angle-dependent correlation function. For the situation of a directional scatterer in a directional noise field, the correlation function contains the product of the directional scattering matrix and the directional noise. This seemingly underdetermined problem can be resolved by exploiting a relation between the causal and acausal parts of the correlation function. For a given pair of receivers, the causal and acausal parts of the correlation function contain the same element of the scattering matrix (by reciprocity) but different elements of the directional noise field. This property can be used to estimate the directionality of the noise (apart from an undetermined scaling factor) and, subsequently, of the scattering matrix.

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“…For this situation the last term in (38) vanishes on account of the optical theorem (6) and the symmetry relation (5) for the scattering matrix [32,36,37]. This leaves…”

Section: Figure 2 More Detailed Analysis Of the Dominating Contributmentioning

confidence: 99%

“…where λ is the wavelength in the homogeneous embedding medium and a the effective size of the scatterer (i.e., the support of the inverse spatial Fourier transform of the scattering matrix f [32]). The scattering matrix obeys the reciprocity relation [31] …”

Section: Introductionmentioning

confidence: 99%

On the Retrieval of the Directional Scattering Matrix from Directional Noise

Wapenaar¹,

Thorbecke²

2013

SIAM J. Imaging Sci.

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“…On the other hand, Margerin and Sato (2011) demonstrated the effects of a multiple scattering process in the retrieval of the 3-D scalar-wave Green's function using Feynman diagrams. Some studies have also taken the higher-order perturbation of waves into consideration for the retrieval process (Sanchez-Sesma et al, 2006;Snieder et al, 2008;Wapenaar et al, 2010). A general theory of Green's function retrieval for linear partial differential equations was recently presented by Fleury et al (2010).…”

Section: Discussionmentioning

confidence: 99%

Retrieval of long-wave tsunami Green’s function from the cross-correlation of continuous ocean waves excited by far-field random noise sources on the basis of a first-order Born approximation

Saito

Kawahara

2012

Earth Planet Sp

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We investigate the theoretical background for the retrieval of the tsunami Green's function from the crosscorrelation of continuous ocean waves. Considering that a tsunami is a long-wavelength ocean wave described by 2-D linear long-wave equations, and that the sea-bottom topography acts as a set of point-like scatterers, we use a first-order Born approximation in deriving the tsunami Green's function having coda waves. The scattering pattern is non-isotropic and symmetrical with respect to the forward and backward directions. We indicate a retrieval process which shows that the derivative of the cross-correlation function of wavefields at two receivers with respect to the lag time gives the tsunami Green's function when point noise sources generating continuous ocean waves are distributed far from, and surrounding, the two receivers. Note that this relation between the cross-correlation and the Green's function is different from the case in which uncorrelated plane-wave incidence from all directions is assumed to be continuous ocean waves. The Green's function retrieved from continuous ocean waves will be used as a reference to examine the validity of the Green's function obtained by numerical simulations.

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“…In practice, the amplitude of the multiple scattering and the perturbation are small and the Born series does converge. Another way to look at the convergence of the scattering series is by analyzing the corresponding series of scattering matrices described by Wapenaar et al (2010). The scattering matrices approach is applicable here because we have set the amplitude of the Green's functions to be one; i.e., we have regularized them.…”

Section: Conventional Imaging (With Smooth Velocity)mentioning

confidence: 99%

Generalized internal multiple imaging

Zuberi

Alkhalifah

2014

GEOPHYSICS

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Internal multiples deteriorate the image when the imaging procedure assumes only single scattering, especially if the velocity model does not have sharp contrasts to reproduce such scattering in the Green's function through forward modeling. If properly imaged, internal multiples (internally scattered energy) can enhance the seismic image. Conventionally, to image internal multiples, accurate, sharp contrasts in the velocity model are required to construct a Green's function with all the scattered energy. As an alternative, we have developed a generalized internal multiple imaging procedure that images any order internal scattering using the background Green's function (from the surface to each image point), constructed from a smooth velocity model, usually used for conventional imaging. For the first-order internal multiples, the approach consisted of three steps, in which we first back propagated the recorded surface seismic data using the background Green's function, then crosscorrelated the back-propagated data with the recorded data, and finally crosscorrelated the result with the original background Green's function. This procedure images the contribution of the recorded first-order internal multiples, and it is almost free of the single-scattering recorded energy. The cost includes one additional crosscorrelation over the conventional single-scattering imaging application. We generalized this method to image internal multiples of any order separately. The resulting images can be added to the conventional single-scattering image, obtained, e.g., from Kirchhoff or reversetime migration, to enhance the image. Application to synthetic data with reflectors illuminated by multiple scattering (double scattering) demonstrated the effectiveness of the approach.

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

Cited by 43 publications

References 35 publications

On the Retrieval of the Directional Scattering Matrix from Directional Noise

On the Retrieval of the Directional Scattering Matrix from Directional Noise

Retrieval of long-wave tsunami Green’s function from the cross-correlation of continuous ocean waves excited by far-field random noise sources on the basis of a first-order Born approximation

Generalized internal multiple imaging

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