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Analytical Solution for Wave Propagation in Stratified Poroelastic Medium. Part I: the 2D Case

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 Added by Julien Diaz
 Publication date 2008
  fields Physics
and research's language is English




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We are interested in the modeling of wave propagation in poroelastic media. We consider the biphasic Biots model in an infinite bilayered medium, with a plane interface. We adopt the Cagniard-De Hoops technique. This report is devoted to the calculation of analytical solutions in two dimensions. The solutions we present here have been used to validate numerical codes.



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We are interested in the modeling of wave propagation in poroelastic media. We consider the biphasic Biots model in an infinite bilayered medium with a plane interface. We adopt the Cagniard-De Hoops technique. This report is devoted to the calculation of analytical solution in three dimension.
We are interested in the modeling of wave propagation in an infinite bilayered acoustic/poroelastic media. We consider the biphasic Biots model in the poroelastic layer. The first part is devoted to the calculation of analytical solution in two dimensions, thanks to Cagniard de Hoop method. In this second part we consider the 3D case.
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We investigate the singularities of the trace of the half-wave group, $mathrm{Tr} , e^{-itsqrtDelta}$, on Euclidean surfaces with conical singularities $(X,g)$. We compute the leading-order singularity associated to periodic orbits with successive degenerate diffractions. This result extends the previous work of the third author cite{Hil} and the two-dimensional case of the work of the first author and Wunsch cite{ForWun} as well as the seminal result of Duistermaat and Guillemin cite{DuiGui} in the smooth setting. As an intermediate step, we identify the wave propagators on $X$ as singular Fourier integral operators associated to intersecting Lagrangian submanifolds, originally developed by Melrose and Uhlmann cite{MelUhl}.
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