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Some properties of the Green's function of simplified elastodynamic problems

  • Sanchez-Sesma, Francisco J. (Instituto de Ingenieria, Universidad Nacional Autonoma de Mexico) ;
  • Rodriguez-Castellanos, Alejandro (Instituto Mexicano del Petroleo, Eje Central Lazaro Cardenas) ;
  • Perez-Gavilan, Juan J. (Instituto de Ingenieria, Universidad Nacional Autonoma de Mexico) ;
  • Marengo-Mogollon, Humberto (Coordinacion de Proyectos Hidroelectricos, Comision Federal de Electricidad) ;
  • Perez-Rocha, Luis E. (Division de Sistemas Mecanicos, Instituto de Investigaciones Electricas) ;
  • Luzon, Francisco (Division de Sistemas Mecanicos, Instituto de Investigaciones Electricas)
  • Received : 2011.12.07
  • Accepted : 2012.04.10
  • Published : 2012.06.25
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Abstract

It is now widely accepted that the resulting displacement field within elastic, inhomogeneous, anisotropic solids subjected to equipartitioned, uniform illumination from uncorrelated sources, has intensities that follow diffusion-like equations. Typically, coda waves are invoked to illustrate this concept. These waves arrive later as a consequence of multiple scattering and appear at "the tail" (coda, in Latin) of seismograms and are usually considered an example of diffuse field. It has been demonstrated that the average correlations of motions within a diffuse field, in frequency domain, is proportional to the imaginary part of Green's function tensor. If only one station is available, the average autocorrelation is equal to the average squared amplitudes or the average power spectrum and this gives the Green's function at the source itself. Several works address this point from theoretical and experimental point of view. However, a complete and explicit analytical description is lacking. In this work we study analytically some properties of the Green's function, specifically the imaginary part of Green's function for 2D antiplane problems. This choice is guided by the fact that these scalar problems have a closed analytical solution (Kausel 2006). We assume the diffusiveness of the field and explore its analytical consequences.

Keywords

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