Extracting the Green’s function of attenuating heterogeneous acoustic media from uncorrelated waves

Snieder, Roel

doi:10.1121/1.2713673

Cited by 144 publications

(132 citation statements)

References 49 publications

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“…(4) (Snieder 2007;Tsai 2011;Nakahara 2012). This difference is exemplary for the dependence of the coherency on the source distribution in case of a dissipative medium, which has been pointed out in detail by Tsai (2011).…”

Section: At T E N Uat I O N O F T H E a M B I E N T S E I S M I C F Imentioning

confidence: 99%

On the estimation of attenuation from the ambient seismic field: inferences from distributions of isotropic point scatterers

Weemstra¹,

Snieder

Boschi

2015

Geophys. J. Int.

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S U M M A R YCross-correlation of ambient seismic noise recorded by two seismic stations may result in an estimate of the Green's function between those two receivers. Several authors have recently attempted to measure attenuation based on these interferometric, receiver-receiver surface waves. By now, however, it is well established that the loss of coherence of the crosscorrelation as a function of space depends strongly on the excitation of the medium. In fact, in a homogeneous dissipative medium, uniform excitation is required to correctly recover attenuation. Applied to fundamental-mode ambient seismic surface waves, this implies that the cross-correlation will decay at the local attenuation rate only if noise sources are distributed uniformly on the Earth's surface. In this study we show that this constraint can be relaxed in case the observed loss of coherence is due to multiple scattering instead of dissipation of energy. We describe the scattering medium as an effective medium whose phase velocity and rate of attenuation are a function of the scatterer density and the average strength of the scatterers. We find that the decay of the cross-correlation in the effective medium coincides with the local attenuation of the effective medium in case the scattering medium is illuminated uniformly from all angles. Consequently, uniform excitation is not a necessary condition for the correct retrieval of scattering attenuation. We exemplify the implications of this finding for studies using the spectrally whitened cross-correlation to infer subsurface attenuation.Key words: Surface waves and free oscillations; Seismic attenuation; Theoretical seismology; Wave scattering and diffraction. I N T RO D U C T I O NIt is now generally accepted that the cross-correlation of recordings made by two receivers is related to (and can in practice be treated as an approximation of) the Green's function at one of these receivers position if there were an impulsive source at the other. The first successful application to the solid Earth is due to Campillo & Paul (2003) who used earthquake coda to obtain empirical Green's functions. Shapiro & Campillo (2004) showed that broad-band Rayleigh waves emerge by simple cross-correlation of continuous recordings of ambient seismic noise. The latter finding holds in media other than the Earth: for example, helioseismology (Duvall et al. 1993), underwater acoustics (Roux & Fink 2003), ultrasonics (Weaver & Lobkis 2001, 2002, engineering (Snieder & Şafak 2006;Kohler et al. 2007) and infrasound (Haney 2009 the Earth's ambient seismic field use ambient seismic surface wave energy: ocean gravity waves, the main source of ambient seismic noise on Earth, excite surface waves much more effectively than other seismic phases. The process of generating new responses by cross-correlation of ambient seismic signal is often referred to as 'passive seismic interferometry'.Recently, several researchers have focused on estimating attenuation based on interferometric measurements of surface waves (Prieto e...

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Section: At T E N Uat I O N O F T H E a M B I E N T S E I S M I C F Imentioning

confidence: 99%

On the estimation of attenuation from the ambient seismic field: inferences from distributions of isotropic point scatterers

Weemstra¹,

Snieder

Boschi

2015

Geophys. J. Int.

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“…Although we formulated theory only for acoustic and elastic wave propagation (see Supplementary Methods), this can be extended into forms appropriate for diffusive, attenuating, electro=magnetic or electro-kinetic energy propagation [11][12][13][14] . It is applied here to earthquake sources, but we could equally construct virtual sensors from fractures occurring in stressed solid material in a laboratory, or from impulsive pressure sources in liquid or gas, provided energy from such sources is recorded using an appropriately placed array of receivers.…”

Section: To Illustrate This New Methods Simply We Use Real Station Rementioning

confidence: 99%

“…Given a suitable receiver geometry, interferometry obviates the need for actual earthquake sources for imaging the Earth 2,6-10 . Variations of interferometric theory work in attenuative media, for diffusive, electromagnetic and electro-kinetic energy propagation [11][12][13][14] , when using active rather than passive sources of elastic or electromagnetic energy [15][16][17][18][19][20][21] and can be used to create novel methods for wavefield simulation [22][23][24] .…”

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confidence: 99%

Virtual seismometers in the subsurface of the Earth from seismic interferometry

et al. 2009

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“…18 It is well known that in acoustics, the cross-correlation of observed waves due to the excited random sources can yield the extraction of the Green's function. 19,20 For example, Snieder obtained the Green's function from the diffusive and the acoustic waves due to sources described by the Dirac delta functions. 20,21 This method is also utilized when the sources are placed inside a domain or on its surface.…”

Section: Introductionmentioning

confidence: 99%

“…19,20 For example, Snieder obtained the Green's function from the diffusive and the acoustic waves due to sources described by the Dirac delta functions. 20,21 This method is also utilized when the sources are placed inside a domain or on its surface. 20 Obtaining the Green's function by the correlation of the waves resulting from the randomly distributed sources has attracted much intention.…”

Section: Introductionmentioning

confidence: 99%

Spectral power density of the random excitation for the photoacoustic wave equation

Erkol

Ünlü

2014

AIP Advances

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The superposition of the Green's function and its time reversal can be extracted from the photoacoustic point sources applying the representation theorems of the convolution and correlation type. It is shown that photoacoustic pressure waves at locations of random point sources can be calculated with the solution of the photoacoustic wave equation and utilization of the continuity and the discontinuity conditions of the pressure waves in the frequency domain although the pressure waves cannot be measured at these locations directly. Therefore, with the calculated pressure waves at the positions of the sources, the spectral power density can be obtained for any system consisting of two random point sources. The methodology presented here can also be generalized to any finite number of point like sources. The physical application of this study includes the utilization of the cross-correlation of photoacoustic waves to extract functional information associated with the flow dynamics inside the tissue.

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Extracting the Green’s function of attenuating heterogeneous acoustic media from uncorrelated waves

Cited by 144 publications

References 49 publications

On the estimation of attenuation from the ambient seismic field: inferences from distributions of isotropic point scatterers

On the estimation of attenuation from the ambient seismic field: inferences from distributions of isotropic point scatterers

Virtual seismometers in the subsurface of the Earth from seismic interferometry

Spectral power density of the random excitation for the photoacoustic wave equation

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