Seismic tomography : Algorithms and applications

Abstract: A preferred algorithm for seismic tomography needs to have capabilities including computational efficiency, minimal computer memory requirements, easy regularization and nonuniqueness analysis. In this thesis, regularised recursive least squares for seismic tomography is developed. This algorithm is equivalent to full matrix inverse techniques but is preferable because the computational costs can be reduced by avoiding operations with zeros. Subjective choice of the a priori model covariance matrix based on ray density is conceptually similar to reparameterization of the model. The optimal weight, in a statistical sense of the minimum variance estimate, leads to a dynamic regularization. The main advantage of using RRLS is that it allows us to calculate the updated covariance matrix automatically. Because in RRLS storage for the updating covariance matrix is necessary, it is prefered for medium size seismic tomographic problems. The formulae derived for calculating the resolution and covariance matrices for the LSQR solver, which require only small changes in LSQR computer code, make LSQR become even more powerful in very large scale seismic tomography. Because with LSQR the inversion is usually carried out in a Krylov space the components of the solution are inevitably correlated to some extent. Therefore, it is necessary to examine the resolution matrix corresponding to increasing iteration number until an acceptable correlation level has been reached. Based on the Lanczos process, the algorithm for solving regularised tomographic problems in Krylov space was developed for facilitating the choice of the regularization parameter, which makes the regularization very practical in real applications. The two techniques considered for choosing the regularization level work well in our modeling. Because in real cases the errors in the observed data may not be known, the cross validation technique may be a good candidate for the choice of the regularization parameter. Finally, the regularized recursive least squares inversion method in combination with a finite difference travel time calculation technique was applied to the travel time data from the network in Costa Rica and the three-dimensional P and S wave velocity structure below Costa Rica were deduced. The tomographic images together with the resolution matrices provide interesting information regarding the geology and tectonics within this area. Comparing the results with that from the other methods shows that both the method and the results are reliable.