Field Fluctuations, Imaging with Backscattered Waves, a Generalized Energy Theorem, and the Optical Theorem

Snieder, Roel; Sánchez‐Sesma, Francisco J.; Wapenaar, Kees

doi:10.1137/08072913x

Cited by 35 publications

(17 citation statements)

References 52 publications

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“…In particular, it represents the rate of energy injected by the unit harmonic load at that point in the vertical direction (see e.g. Perton et al 2009; Snieder et al 2009). Since Im[ G zz ( x , x ,ω)] equals Im[ G zz ( y , y ,ω)] for x ≠ y in any horizontally layered medium excited with a diffusive wavefield, we can use both quantities to normalize the imaginary part of the Green's function between the locations x and y as Finally, using the last equation together with , it is possible to write a compact expression for the normalized cross‐correlation in the frequency domain in terms of the coherence function This result is essentially the same as that obtained in the pioneering work by Aki (1957) for the spatial autocorrelation coefficient, and can be used to obtain the phase velocity for a given frequency and distance.…”

Section: Methodsmentioning

confidence: 99%

Shallow structure of Deception Island, Antarctica, from correlations of ambient seismic noise on a set of dense seismic arrays

Luzón¹,

Almendros²,

García‐Jerez³

2011

Geophysical Journal International

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S U M M A R YWe investigated the shallow velocity structure of Deception Island volcano, Antarctica, using correlations of ambient seismic noise. We selected long records of noise obtained by eight seismic arrays deployed along the inner coast of Deception during the period 2003-2005. Using these data, we calculated average dispersion curves and estimated local 1-D velocity models for the array sites. The combination of these profiles allowed us to obtain a comprehensive model of the shallow velocity structure of the island. The volcano is composed of relatively soft layers of pyroclastic deposits and sediments extending to a depth of about 400 m, with different degrees of compaction. Two layers with thicknesses of about 100 and 300 m and S-wave velocities of around 0.2-0.8 and 0.7-1.1 km s −1 , respectively, can be differentiated. The deeper structure is highly variable in terms of wave velocities and layer depths. Although the resolving capabilities are reduced for these layers, the larger S-wave velocities in the range 1.3-2.8 km s −1 indicate that they can be associated with pre-caldera structures and products. There are substantial differences between the different models, which can be spatially related to heterogeneities in the volcano structure. The lowest S-wave velocities may be related to the alterations produced by hydrothermal activity near the surface. On the contrary, the largest velocities occur near the caldera border, revealing the presence of compact materials at shallow depths. Sharp lateral variations can also be observed in the northwest of the bay, which points to the presence of NW-SE faults and/or strong velocity gradients.

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Section: Methodsmentioning

confidence: 99%

Shallow structure of Deception Island, Antarctica, from correlations of ambient seismic noise on a set of dense seismic arrays

Luzón¹,

Almendros²,

García‐Jerez³

2011

Geophysical Journal International

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“…According to (35), G s (x B , x A , −t) is proportional to the time-reversed scattering matrix, advanced by t sct . According to (36), M 2 (x B , x A , t) is proportional to the time-reversed scattering matrix, delayed by t art .…”

Section: Figure 2 More Detailed Analysis Of the Dominating Contributmentioning

confidence: 99%

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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“…(6) is equal to 2iIm(G(r A , r A )), with Im denoting the imaginary part. Since the imaginary part of the Green's function satisfies a homogeneous equation, it is finite at the source, 16,17 and the right hand side of Eq. (6) therefore is finite.…”

Section: àIxtmentioning

confidence: 99%

Extracting the Green’s function from measurements of the energy flux

Snieder

Douma

Vasconcelos

2012

The Journal of the Acoustical Society of America

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Existing methods for Green’s function extraction give the Green’s function from the correlation of field fluctuations recorded at those points. In this work it is shown that the Green’s function for acoustic waves can be retrieved from measurements of the integrated energy flux through a closed surface taken from three experiments where two time-harmonic sources first operate separately, and then simultaneously. This makes it possible to infer the Green’s function in acoustics from measurements of the energy flux through an arbitrary closed surface surrounding both sources. The theory is also applicable to quantum mechanics where the Green’s function can be retrieved from measurement of the flux of scattered particles through a closed surface.

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Field Fluctuations, Imaging with Backscattered Waves, a Generalized Energy Theorem, and the Optical Theorem

Cited by 35 publications

References 52 publications

Shallow structure of Deception Island, Antarctica, from correlations of ambient seismic noise on a set of dense seismic arrays

Shallow structure of Deception Island, Antarctica, from correlations of ambient seismic noise on a set of dense seismic arrays

On the Retrieval of the Directional Scattering Matrix from Directional Noise

Extracting the Green’s function from measurements of the energy flux

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