The faster growth curves in the speed of GPUs relative to CPUs in recent years and its rapidly gained popularity have spawned a new area of development in computational technology. There is much potential in utilizing GPUs for solving evolutionary partial differential equations . We are concerned with modeling tsunami waves, where computational time is of extreme importance. We have employed the NVIDIA board 8600M GT on a MacPro to test the efficacy of the GPU on the set of shallow-water equations. We have compared the relative speeds between CPU and GPU on a single processor for two types of spatial discretization based on second-order finite-differences and radial basis functions, which is a more novel method based on a gridless and a multi-scale, adaptive framework. For the NVIDIA 8600M GT we found a speed up by a factor of 8 in favor of GPU for the finite-difference method and a factor of 7 for the RBF scheme. WThe timesteps employed for the RBF method are larger than those used in finite-differences, because of the much fewer number of nodal points needed by RBF. This ratio, favoring the RBFs over the finite-difference points, increases with the number of grid points. Thus, in modeling wave-propagation over the same physical time transpired , RBF acting in concert with GPU would be the fastest way to go.

The Irregular seismic velocity structure is a defining characteristic of the D" layer in the deep lower mantle above the core-mantle boundary (CMB) The occurence of the postperovskite phase transition with an extremely steep Clapeyron slope of 13 MPa/K would mean very rugged topography can be produced by thermal anomalies of a few hundred degrees close to the CMB. We have investigated the irregular structure that can be ascribed to this particular phase transition and have conducted mantle convection experiments in 2-D cylindrical geometry with models including the postperovskite phase transition. The models are based on composite rheology including both Newtonian diffusion creep and Non-newtonian dislocation creep to allow for an increased propensity for non-linear creep predicted for the postperovskite phase.

The convection results shows typical lens shaped postperovskite structures, which are relatively cold remnants of subducted lithosphere. The lenses are interrupted by hot perovskite plumes rising from the CMB. Viscous creep is dominantly non-Newtonian in the post-perovskite lenses and Newtonian in the hot perovskite regions.

We have computed predictions of seismic shear wave velocity structure of the bottom lower mantle from temperature snapshots of the convection results based on mineral physics. Then we imaged these spatially heterogeneous seismic velocity fields with curvelets, which clearly brings out the post-perovskite phase boundary on top and bottom of the lense like structures. However, our results show the importance of obtaining more accurate seismic wave derivatives with respect to both temperature and depth, as the wave interaction with the steep phase boundaries demand high accuracy of the control parameters associated with the elastic wave propagation. Using curvelets, we have picked up six scales of the wave interaction. The bottom phase boundary is well inside the CMB thermal boundary layer and produces a more pronounced transition in the seismic wave velocity than the top layer. This is shown quantitively by the much smaller scales picked up by the Paley-Littlewood decomposition of the curvelet coefficients. The results agree well with similar decomposition of the SCS wave interaction in actual seismic data within the D" layer underneath the Cocos plate. They would suggest that the realistic seismic results can be interpreted within the framework of a thermal convection model in which two major separation of scales are clearly unveiled by the curvelet decomposition.