Selection of five publications

My scientific carrier has been motivated by understanding and imaging both seismic sources and Earth structures. With a starting impulsion of Pr. R. Madariaga, I have been able to work on the difficult problem of seismic dynamic rupture as well as on the more computer-intensive problem of seismic imaging. The collaboration with Pr. A. Tarantola has been quite important for the second item.

Current efforts is concentrated on seismic imaging of structures while I may hope to go back to the rupture problem for imaging the evolution of rupture processes in the near future.

– Publication 1

Virieux, J. et R. Madariaga, 1982, Dynamic faulting studied by a finite difference metbod, Bull. Seismo. Soc. Am., 72, 345-369.

  • Summary in Engish: This work is devoted to the shear dynamic rupture on a plane either in 2D or in 3D. We illustrate numerical scaling laws based on constitutive parameters of the friction lax and on associated numerical parameters. Slip deficit related to a mechanical static load is estimated and may induce strong bias in the rupture history of an earthquake. We have shown that the FD technique is accurate enough for the spontaneous modelling of dynamic rupture. At that time, this demonstration for a 3D configuration has been a quite difficult task. More recent work has renewed this approach by considering non-planar conditions (Cruz-Atienza & Virieux (2004) or Ben Jemaa et al ( 2007, 2009) in 2D and Cruz-Atienza et al ( 2007) in 3D) using an extension of boundary conditions proposed by Madariaga et al (1998).

– Publication 2

Virieux, J., 1986, P-SV wave propagation in heterogeneous media: a velocity-stress finite-difference method, Geophysics, 51, 889-901.

  • Summary in English: This paper investigates properties of the numerical scheme for solving linear elastodynamic equations. This scheme is equivalent to the one developed by Yee (1966) in electromagnetism et turns out to be quite stable and relatively precise at an implicit boundary solid/liquid. We also show that the free surface requires a specific numerical implementation and that the number of grid points increases dramatically when accurate modelling is required. Specific properties of this “old” new scheme have pinpointed by this work which is the most cited one of my bibliography.

– Publication 3

Virieux, J. and V. Farra, 1991, Ray tracing in 3-D complex isotropic media: an analysis of the problem, Geophysics, 56, 2057-2069.

  • Summary in English: Although this difficult subject has a narrow audience, this paper tackles to important problem of ray tracing using hamiltonian formalism which helps doing the exact ray tracing as well as the paraxial one related to the approximation of Gauss in optics. We have developed a procedure for handling any arbitrary shape of interfaces through which we must estimation boundary conditions for paraxial rays, a difficult task. These perturbation techniques might be used for performing different tasks as amplitude estimation or two-points ray tracing problem.

– Publication 4

Auger, E., J. Virieux, A. Zollo, 2003, Locating and quantifying the seismic discontinuities in a complex medium through the migration and AVA analysis of reflected and converted waves: an application to the Mt Vesuvius volcano Geophys. J. Int.,152, 486–496.

  • Summary in English: Detection of significant zone with a quite low shear velocity beneath Mt Vesuvius is at the center of this article based on active seismic imaging techniques using amplitudes of converted phases. The impressive zone extends over 400 km2 at a depth of 10 km. Careful analysis of Amplitude versus Angle allows an study of variation of reflection coefficients which gives boundaries to velocity variations. This complexity of the structure under Mt Vesuvius could be extended toward the Campi Flegrei (Vanorio et al, 2005).

– Publication 5

Virieux, J. and S. Operto. An overview of full waveform inversion in exploration geophysics, Geophysics, 74(6), WCC127-WCC152, 2009.

* Summary in English: This article presents the state of the art in seismic full waveform inversion for the geophysical exploration. Therefore, by solving the Helmholtz equation in an heterogeneous media, thanks to non-reflecting boundaries, through a direct solver, we may consider the non-linear problem of fitting waveforms by perturbing velocity structure. Local techniques as gradient ou quasi-newton methods require thousands forward problems. The application of such techniques to real datasets is one original contribution of this paper over an extension of more that 100 km. We may penetrate down to a depth of 30 km which is the geodynamic target of the contact between two plates.