Solution.

The new coupled method of spectral elements and modal solution for wave
propagation in 3D global earth models (*Capdeville et al.*, 2000; 2001;
*Chaljub et al.*, 2001) is well adapted to
assess the study of Seismic attenuation in the crust and the D''
structure by forward modeling approach. To perform these studies,
numerical developments, such as the possibility to have a layer of
spectral elements between two modal solutions, are required and have
been performed this year.

We also plan to study the 3D structure of the D" layer, the region of the Earth just above the Core Mantle Boundary (CMB), by performing seismic wave propagation simulations in realistic 3D D" models and comparing results with observed waveforms of seismic waves sensitive to this region of the earth (e.g. Sdiffracted). We hope to obtain new constraints on the character of 3D structure in D".

The coupled method for wave propagation in global Earth models is based upon the coupling between the spectral element method and a modal solution method. The Earth is decomposed, depending on the problem addressed, in two or three spherical shells, one shell with 3D lateral heterogeneities and one or two shells with only spherically symmetric heterogeneities (see Figure 26.1).

A description of the method with illustrations can be found on
`http://seismo.berkeley.edu/yann`

- The implementation of the code on the IBM SP of the NERSC.
- Technical and practical developments and optimizations of the code.
- The development of the "sandwich" coupling. Six month ago, the only configuration allowed was a spectral element outer shell coupled with a modal solution inner sphere. To study the D" at high frequency, a sandwich of spectral elements between two modal solutions is required. This implies to develop the coupling of an outer shell modal solution with a spectral element inner sphere, which has been performed with success this year.

Thanks to Dimitri Komatitsch who gave us his attenuation code for the spectral element method. The computation were made using the computational resources of the NERSC, especially the IBM SP, under repo mp342 starting project.

Chaljub, E. Capdeville, Y. Vilotte, J.P. and Y Maday,
Solving elastodynamics in a solid heterogeneous 3D-sphere: a parallel spectral element approximation on non-conforming grids,
In preparation for *Journal for numerical methods in engineering*, 2001

Capdeville Y., E. Chaljub, J.P. Vilotte and J.P. Montagner,
Coupling Spectral Elements and Modal Solution: a New Efficient Tool for Numerical Wave Propagation in Laterally
Heterogeneous Earth Models,
*Geophys. J. Int.*, submitted, 2001

Capdeville, Y.,
Méthode couplée éléments spectraux - solution modale pour la propagation d'ondes dans la Terre à l'échelle globale, Université Paris 7,
*PhD thesis*, 2000.

Questions or comments? Send e-mail: www@seismo.berkeley.edu

© 2001, The Regents of the University of California.