Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium.

@article{Margerin2011GeneralizedOT,
  title={Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium.},
  author={Ludovic Margerin and Haruo Sato},
  journal={The Journal of the Acoustical Society of America},
  year={2011},
  volume={130 6},
  pages={
          3674-90
        }
}
  • L. Margerin, H. Sato
  • Published 8 March 2011
  • Mathematics
  • The Journal of the Acoustical Society of America
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… 

Figures from this paper

Mean-field T-matrix approach to elastic wave scattering by small and point-like objects
The T-matrix of a small inclusion embedded in a homogeneous matrix is calculated for vector elastic waves. The theory relies on an approximation of the local stress and momentum inside the inclusion
Green's function retrieval from the CCF of random waves and energy conservation for an obstacle of arbitrary shape: noise source distribution on a large surrounding shell
SUMMARY For imaging the earth structure, the cross-correlation function (CCF) of random waves as ambient noise or coda waves has been widely used for the estimation of the Green’s function. We
Far-field scattering model for wave propagation in random media.
TLDR
The perturbed wave number in the developed model does not depend explicitly on the crystallite elastic properties even for arbitrary crystallographic symmetry; it depends on two nondimensional scattering elastic parameters and the macroscopic ultrasonic velocity which provides an advantage for potential schemes for inversion from attenuation to material microstructure.
Extended optical theorem in isotropic solids and its application to the elastic radiation force
In this article, we derive the extended optical theorem for the elastic-wave scattering by a spherical inclusion (with and without absorption) in a solid matrix. This theorem expresses the extinction
Generalized Optical Theorem and Point Sources
A simple derivation of the general form of the optical theorem (GOT) is given for the case of a conservative scatterer in a homogeneous lossless medium, suitable for describing point sources and an
Diffusion approximation with polarization and resonance effects for the modelling of seismic waves in strongly scattering small-scale media
SUMMARY This paper presents an analytical study of the multiple scattering of seismic waves by a collection of randomly distributed point scatterers. The theory assumes that the energy envelopes are
Boundary effect on multiple scattering of elastic waves in a half-space
The scattering of elastic waves is studied in the vicinity of a vacuum-medium boundary. The Green’s function for a half-space is re-derived within the mixed 2D-Fourier representation, which is
Nonlinear scattering based imaging in elastic media: Theory, theorems, and imaging conditions
With the more widespread introduction of multicomponent recording devices in land and marine ocean-bottom seismic acquisition, elastic imaging may become mainstream in coming years. We have derived
Absence of Geometrical Regime for Impedance‐Type Elastic Scatterers
In wave physics, the geometrical limit is defined as a propagation regime where the scattering 5 cross-section (cid:27) of an object becomes independent of its internal structure and tends to twice
A unified optical theorem for scalar and vectorial wave fields.
TLDR
A unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves that holds for scattering by anisotropic elastic and piezoelectric scatterer as well as bianisotropic (non-reciprocal) EM scatterers.
...
...

References

SHOWING 1-10 OF 59 REFERENCES
Recovering the Green's function from field-field correlations in an open scattering medium.
The possibility of recovering the Green’s function from the field-field correlations of coda waves in an open multiple scattering medium is investigated. The argument is based on fundamental
Retrieval of the Green’s Function from Cross Correlation: The Canonical Elastic Problem
In realistic materials, multiple scattering takes place and average field intensities or energy densities follow diffusive processes. Multiple P to S energy conversions by the random inhomogeneities
Retrieval of Green's function and generalized optical theorem for the scattering of complete dyadic fields.
TLDR
The presented derivation shows the Newton-Marchenko equation holdsif the condition of equipartition is not satisfied and the generalized optical theorem for the dyadic fields is derived based on the elastic dynamic interferometric equation.
Field Fluctuations, Imaging with Backscattered Waves, a Generalized Energy Theorem, and the Optical Theorem
TLDR
For general linear systems, it is shown that the imaginary component of the Green's function at the source accounts for the loss of generalized energy by dissipation and/or propagation of the fields away from the source.
Cancellation of spurious arrivals in Green's function extraction and the generalized optical theorem.
TLDR
It is shown that for an arbitrary small scatterer, the cross terms of scattered waves give an unphysical wave with an arrival time that is independent of the source position, and an alternative derivation of the generalized optical theorem is constituted.
Retrieval of Green's function having coda from the cross‐correlation function in a scattering medium illuminated by surrounding noise sources on the basis of the first order Born approximation
SUMMARY The peak lag time of the cross-correlation function (CCF) of random noise at two receivers give the wave propagation velocity. This idea has been widely used for the velocity tomography
Retrieval of Green's function having coda waves from the cross-correlation function in a scattering medium illuminated by a randomly homogeneous distribution of noise sources on the basis of the first-order Born approximation
SUMMARY The retrieval of Green's function of scalar waves for a given medium is possible from the cross-correlation function (CCF) of noises in the equi-partition state. For making such a state,
Scattering of Elastic Waves by a Spherical Inclusion
Abstract : A complete and exact solution for the problem of an incident P wave scattered by an elastic spherical inclusion is presented and described. The solution can be obtained from either
Scattering of elastic waves by a spherical inclusion–II. Limitations of asymptotic solutions
SUMMARY Starting with the exact solution for the scattering of a plane P wave by a homogeneous spherical inclusion, various types of approximate solutions are developed and discussed. The standard
...
...