Retrieval of Elastic Green's Tensor Near a Cylindrical Inhomogeneity from Vector Correlations (Communications in Computational Physics, 2008)
Multiple scattering of elastic waves in realistic media makes that averagefield intensities or energy densities follow diffusive processes. In such regime the successive P to S energy conversions by distributed random inhomogeneities give rise toequipartition which means that in the phase space the available elastic energy is distributed in average with 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 independent of 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 elastic wavefields 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 illuminate isotropically the elastic space with plane waves. We assume the spectra for both P and S waves uniform but such that the energy ratio ES/EP =(α/β)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 tensor function 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.