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Seismic waves in heterogeneous media

Tuesday 24 January 2012 by Jean

Computational Seismology

Lectures on « Seismic waves in heterogeneous media »
In the framework of the Ecole Doctorale “Terre-Univers-Environnement”

by Jean Virieux

  • Invited professor at the University of Naples – Federico II Professor at the University Joseph Fourier – Grenoble I


by Romain Brossier

  • Assistant professor at the University Joseph Fourier - Grenoble I

- In collaboration with Stéphane Operto (CNRS) and Gilles Lambaré (ENSMP/CGG-VERITAS)

Lecture A: Waves in heterogeneous media

In the introduction, we shall present strategies for ground motion estimations through attenuation laws; numerical simulations and mixed simulations using Empirical Green Functions. We shall insist on the multi-scale structure of the Earth and the practical issue of the description using either blocky structures or grid structures. The elastodynamic equations will be presented in visco-elastic media. Finally asymptotic wave formulation will be given and finite frequency effects will be appreciated.

Lecture B: Ray tracing methods (practical issues) (computer training)

The numerical integration of ordinary differential equations related to ray equations will be presented with a Runge-Kutta integration scheme. Computer codes will be developed by students in a 2D smooth medium. Solving the eikonal equation using ENO (essentially non oscillating) approaches will be illustrated and practices of related softwares will enlight features of this technique related to first-arrival travel time estimations. Solving the paraxial equations will be addressed as well and computer codes will be developed by students in a 2D smooth medium. Finally, two-point ray tracing problems will be presented using different approaches.

Lecture C: Finite Difference numerical methods

We shall introduce finite difference discretisation of the derivatives as well as the medium properties. The different time integration will be discussed as well as the frequency formulation with linear algebra issues. For complex geometries, the natural forward extension in finite volume formulation will be discussed. Links with finite element methods will be briefly discussed. Designing a 1D finite difference code in time will be performed by students using non parsimonious and parsimonious formulations. Implementation of boundary conditions will be discussed and technically formulated. Source excitation will be considered as point sources or planar waves. Designing a 1D finite difference code in frequency will be performed as well by students. Comparison with the time domain will be discussed.

Lecture D: Full Waveform Inversion)

Tentative content concerning an introduction to full waveform inversion

Reference Computer Codes have been designed by following people: (a list will be provided at the end of the course)

Each lecture is about 3 hours.

titre documents joints

15 March 2011
info document : PowerPoint
6.1 Mb

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