Anisotropic seismic tomography with the reversible jump Markov chain Monte Carlo

The established isotropic tomographic models show the features of subduction zones in terms of seismic velocity anomalies, but they are generally subjected to the generation of artifacts due to the lack of anisotropy in forward modelling. There is evidence for the significant influence of seismic anisotropy in the mid-upper mantle, especially for boundary layers like subducting slabs. As consequence, in isotropic models artifacts may be misinterpreted as compositional or thermal heterogeneities. In this thesis project the application of a trans-dimensional Metropolis-Hastings method is investigated in the context of anisotropic seismic tomography. This choice arises as a response to the important limitations introduced by traditional inversion methods which use iterative procedures of optimization of a function object of the inversion. On the basis of a first implementation of the Bayesian sampling algorithm, the code is tested with some cartesian two-dimensional models, and then extended to polar coordinates and dimensions typical of subduction zones, the main focus proposed for this method. Synthetic experiments with increasing complexity are realized to test the performance of the method and the precautions for multiple contexts, taking into account also the possibility to apply seismic ray-tracing iteratively. The code developed is tested mainly for 2D inversions, future extensions will allow the anisotropic inversion of seismological data to provide more realistic imaging of real subduction zones, less subjected to generation of artifacts.

Parallelization of the algorithm WHAM with NVIDIA CUDA.

The aim of my thesis is to parallelize the Weighting Histogram Analysis Method (WHAM), which is a popular algorithm used to calculate the Free Energy of a molucular system in Molecular Dynamics simulations. WHAM works in post processing in cooperation with another algorithm called Umbrella Sampling. Umbrella Sampling has the purpose to add a biasing in the potential energy of the system in order to force the system to sample a specific region in the configurational space. Several N independent simulations are performed in order to sample all the region of interest. Subsequently, the WHAM algorithm is used to estimate the original system energy starting from the N atomic trajectories. The parallelization of WHAM has been performed through CUDA, a language that allows to work in GPUs of NVIDIA graphic cards, which have a parallel achitecture. The parallel implementation may sensibly speed up the WHAM execution compared to previous serial CPU imlementations. However, the WHAM CPU code presents some temporal criticalities to very high numbers of interactions. The algorithm has been written in C++ and executed in UNIX systems provided with NVIDIA graphic cards. The results were satisfying obtaining an increase of performances when the model was executed on graphics cards with compute capability greater. Nonetheless, the GPUs used to test the algorithm is quite old and not designated for scientific calculations. It is likely that a further performance increase will be obtained if the algorithm would be executed in clusters of GPU at high level of computational efficiency. The thesis is organized in the following way: I will first describe the mathematical formulation of Umbrella Sampling and WHAM algorithm with their apllications in the study of ionic channels and in Molecular Docking (Chapter 1); then, I will present the CUDA architectures used to implement the model (Chapter 2); and finally, the results obtained on model systems will be presented (Chapter 3).