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This study focuses on imaging local changes in heterogeneous media. The method employed is demonstrated and validated using numerical experiments of acoustic wave propagation in a multiple scattering medium. Changes are simulated by adding new scatterers of different sizes at various positions in the medium, and the induced decorrelation of the diffuse (coda) waveforms is measured for different pairs of sensors. The spatial and temporal dependences of the decorrelation are modeled through a diffuse sensitivity kernel, based on the intensity transport in the medium. The inverse problem is then solved with a linear least square algorithm, which leads to a map of scattering cross section density of the changes. [ABSTRACT FROM AUTHOR]

This paper investigates the scattering of scalar and elastic waves in two-phase materials and single-mineral-cubic, hexagonal, orthorhombic-polycrystalline aggregates with randomly oriented grains. Based on the Dyson equation for the mean field, explicit expressions for the imaginary part of Green's function in the frequency-wavenumber domain (ω, p), also known as the spectral function, are derived. This approach allows the identification of propagating modes with their relative contribution, and the computation of both attenuation and phase velocity for each mode. The results should be valid from the Rayleigh (low-frequency) to the geometrical optics (high-frequency) regime. Comparisons with other approaches are presented for both scalar and elastic waves. [ABSTRACT FROM AUTHOR]

This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation-the resolvent formula-Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the off-shell T-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell T-matrix are recovered in the usual far-field and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The T-matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed. [ABSTRACT FROM AUTHOR]

The spectral decomposition of the elastic wave operator in a layered isotropic half-space is derived by means of standard functional analysis methods. Particular attention is paid to the coupled P-SV waves. The problem is formulated directly in terms of displacements which leads to a 2×2 Sturm–Liouville system. The resolvent kernel (Green’s function) is expressed in terms of simple plane-wave solutions. Application of Stone’s formula leads naturally to eigenfunction expansions in terms of generalized eigenvectors with oscillatory behavior at infinity. The generalized eigenfunction expansion is employed to define a diffuse field as a white noise process in modal space. By means of a Wigner transform, we calculate vertical to horizontal kinetic energy ratios in layered media, as a function of depth and frequency. Several illustrative examples are considered including energy ratios near a free surface, in the presence of a soft layer. Numerical comparisons between the generalized eigenfunction summation and a classical locked-mode approximation demonstrate the validity of the approach. The impact of the local velocity structure on the energy partitioning of a diffuse field is illustrated. [ABSTRACT FROM AUTHOR]

A correction to the article ''Velocity and attenuation of scalar and elastic waves in random media: A spectral function approach'' in January 10, 2018 online issue is presented which discusses an error in the analytical expressions of the real and imaginary parts of the mass operator for two-phase media.