Global optimization with application to geophysics

The thesis presents an improved global optimization scheme for applications in geophysical optimization problems with large model dimension. The importance of regularization in the geophysical inversion problems is discussed with particular emphasis on enforcement of edge preserving regularization.;In the first part, I am dealing with an optimization problem where the cost function surface is unknown. I have introduced a new method based on simulated annealing optimization to estimate the phase of the embedded wavelet in the seismic data.;The second part of the thesis deals with optimization schemes in the context of different regularization constraints. A new global optimization technique based on model space preconditioning is developed to enforce blockyness in the estimated model. The model space preconditioning is achieved by means of nonlinear edge preserving operators such that the global optimization algorithm, rather than relying completely on the random perturbations, samples a favorably biased model space. The new approach is studied on optimization of one dimensional earth elastic parameters from amplitude variation with offset (AVO) seismic data. The results, with and without applications of model preconditioning operators, are compared. A linearized inversion scheme is also presented for the estimation of elastic parameters from AVO data. The thesis shows a comparison of results when the linearized inversion has failed and global optimization has succeeded in estimating the elastic parameters from AVO data. The results are further validated by a careful comparison of well log data with the estimated elastic parameters from AVO data.;Last part of the thesis deals with the application of model preconditioning based global optimization in optimizing over a two dimensional model space. Classical global optimization schemes have very slow convergence when the model dimension is large. Model preconditioning based global optimization has paved the way for optimization involving large model space. I have successfully applied the scheme to optimize for the interval velocity and density over a two dimensional grid via waveform inversion.