Application of Bayesian recursive estimation for seismic signal processing

Bayesian recursive estimation (BRE) requires that the posterior density function be estimated so that conditional mean estimates of desired parameters or states can be obtained. BRE has been referred to as a complete solution to the estimation problem since the posterior density function embodies all available statistical information (i.e., prior, likelihood and evidence). Until recent advances in BRE, most applications required that the system and measurement equations be linear, and that the process and measurement noise be Gaussian and white. A Kalman filter, KF, (closed form solution to the BRE) could be applied to systems that met these conditions. Previous applications of the KF to solve seismic signal processing problems (e.g., deconvolution) have had very limited success and acceptability in the geophysics signal processing community due to the restrictive nature of the KF. The recently new BRE development of sequential Monte Carlo (SMC) techniques for numerically solving non-stationary and non-linear problems has generated considerable interest and active research within the last decade. This thesis focuses upon the implementation of SMC techniques (e.g., particle filtering) for solving seismic signal processing problems. All the associated filters of BRE (hidden Markov model filter, KF, particle filter, Rao-Blackwellised particle filter, and jump Markov systems) and a new and highly robust and unique model of the seismic source wavelet are implemented in two innovative algorithms for solving the important problems of passive seismic event detection and blind seismic deconvolution. A ground-breaking concept in blind seismic deconvolution referred to as principle phase decomposition (PPD) is outlined and evaluated in this thesis. The PPD technique estimates and separates overlapping source wavelets instead of estimating high bandwidth reflection coefficients. It is shown that one can then easily generate reflection coefficients from the separated source wavelets. In this thesis many advantages of the PPD are outlined. Simulated seismogram data with low signal-to-noise ratios is blindly deconvolved where non-stationary, mixed-phase, and zero-phase source wavelets are present. I believe that there are currently no existing blind seismic deconvolution techniques which could obtain comparable performance results of the PPD technique. The work in this thesis has resulted in three IEEE publications and one peer reviewed conference publication.Science, Faculty ofEarth, Ocean and Atmospheric Sciences, Department ofGraduat