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Retrieval of elastic green’s tensor near a Cylindrical Inhomogeneity from Vector Correlations

Communications in Computational Physics 2008年第1期3卷 250-270页

作者： Juan AP´erez-Ruiz Francisco Luzon Francisco J.sanchez-sesma Grupo de Geof´ısica Aplicada Departamento de F´ısica AplicadaUniversidad de Almer´ıaCa˜nada de San Urbano s/n04120-Almer´ıaSpain Departamento de sismolog´ıa Instituto de IngenieriaUniversidad Nacional Aut´onoma de M´exicoCd.UniversitariaCircuito Escolar s/nCoyoac´an 04510M´exico D.F.Mexico.

Multiple scattering of elastic waves in realistic media makes that averagefield intensities or energy densities follow diffusive processes. In such regime the successiveP to s energy conversions by distributed random inhomogeneities give rise toequipartition which means that in the phase space the available elastic energy is distributedin averagewith equal amounts among the possible states of P and s waves. Insuch diffusive regime the P to s energy ratio equilibrates in an universal way independentof the particular details of the scattering. It has been demonstrated that averagingthe cross correlations at any two points of an elastic medium subjected to diffuse elasticwavefields leads to the emergence of the green function, which is the wave fieldthat would be observed at one position if an impulsive load is applied at the other. Inthis work we study the problem of the retrieval of the 2D tensor elastodynamic greenfunction in an infinite elastic space containing a circular cylinder inclusion. We illuminateisotropically the elastic spacewith plane waves. We assume the spectra for both Pand s waves uniform but such that the energy ratio Es/EP=(a/b)2, which is the onepredicted by equipartition theory in two-dimensions. We then show that the Fouriertransform of azimuthal average of the cross-correlation of motion between two pointswithin an elastic medium is proportional to the imaginary part of the exact green tensorfunction between these points. The numerical results presented here point out thepossibility of detection and imaging of diffractors and resonant diffractors by crosscorrelation even in presence of attenuation exists.

关键词： Multiple scattering elastic waves elastic green’s tensor

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