Previous publications have documented that the more specific aspects of global wave propagation can be dealt with by the SEM: Komatitsch & Vilotte (1998), Komatitsch & Tromp (1999) and Paolucci (2000b) incorporate effects due to anisotropy, and Komatitsch & Tromp (1999) implement attenuation.
In this article we combine all these ingredients to tackle the problem of global wave propagation.
In the Earth's mantle and inner core we solve the wave equation in terms of displacement, whereas in the liquid outer core we use a formulation based upon a scalar potential.
The three domains are matched at the inner core and core–mantle boundaries, honouring the continuity of traction and the normal component of velocity.
We implement the fluid–solid matching conditions using a simple and efficient domain decomposition technique.
In this article we demonstrate that the spectral-element method (SEM), introduced more than 15 years ago in computational fluid mechanics (Patera 1984; Maday & Patera 1989; Fischer & Rønquist 1994), can meet this challenge.
The method has been used to accurately model wave propagation on local and regional scales, both in 2-D (Priolo 1999).
Here we use a classical SEM based upon a conforming mesh that retains a diagonal mass matrix.
Chaljub (2000) and Capdeville (2002) incorporate the effects of self-gravitation, which we will consider in a subsequent article (Komatitsch & Tromp 2002), but they do not incorporate anisotropy or attenuation or the crust at short periods.
It is well-known, however, that finite-difference methods are inaccurate for surface waves because of numerical dispersion (e.g. Furthermore, the design of a grid for the globe poses geometrical difficulties because of the decrease in grid spacing with depth.