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Computation of Green's Function of 3-D Radiative Transport Equations for Non-isotropic Scattering of P and Unpolarized S Waves

Abstract : In this work, I propose to model the propagation of high-frequency seismic waves in the heterogeneous Earth by means of a coupled system of radiative transfer equations for P and S waves. The model describes the propagation of both coherent and diffuse waves in a statistically isotropic heterogeneous medium and takes into account key phenomena such as scattering conversions between propagation modes, scattering anisotropy and absorption. The main limitation of the approach lies in the neglect of the shear wave polarization information. The canonical case of a medium with uniform scattering and absorption properties is studied in details. Using an adjoint formalism, Green's functions (isotropic point source solutions) of the transport equation are shown to obey a reciprocity relation relating the P energy density radiated by an S source to the S energy density radiated by a P source. A spectral method of calculation of the Green's function is presented. Application of Fourier, Hankel and Legendre transforms to time, space and angular variables, respectively, turns the equation of transport into a numerically tractable penta-diagonal linear system of equations. The implementation of the spectral method is discussed in details and validated through one-to-one comparisons with Monte Carlo simulations. Numerical experiments in different propagation regimes illustrate that the ratio between the correlation length of heterogeneities and the incident wavelength plays a key role in the rate of stabilization of the P-to- S energy ratio in the coda. The results suggest that the rapid stabilization of energy ratios observed in the seismic coda is a signature of the broadband nature of crustal heterogeneities. The impact of the texture of the medium on both pulse broadening and generation of converted S wave arrivals by explosion sources is illustrated. The numerical study indicates that smooth media enhance the visibility of ballistic-like S arrivals from P sources.
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Submitted on : Tuesday, May 24, 2022 - 12:04:34 PM
Last modification on : Monday, July 4, 2022 - 9:16:56 AM

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Ludovic Margerin. Computation of Green's Function of 3-D Radiative Transport Equations for Non-isotropic Scattering of P and Unpolarized S Waves. Pure and Applied Geophysics, 2017, 174, pp.4057-4075. ⟨10.1007/s00024-017-1621-z⟩. ⟨insu-03676807⟩

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