Filtering Random Layering Effects For Imaging and Velocity Estimation

This work was also published as a Rice University thesis/dissertation.Imaging compactly supported reflectors in highly heterogeneous media is a challenging problem due to the significant interaction of waves with the medium which causes considerable delay spread and loss of coherence. The imaging problem consists in finding the support of small reflectors using recorded echoes at an array of sensors. The thesis considers the case of randomly layered media, in which significant multiple scattering by the layered structures and quick loss of coherence is observed. These strong, backscattered echoes from the layers can overwhelm the weaker coherent signals due to the compactly supported reflectors. This signal-to-noise problem must be addressed to image effectively. Using techniques routinely used in exploration seismology, filters (layer annihilators) are designed to remove the primary reflections of the stronger layered features in the medium. However, it observed that these filters also remove the incoherent signal that is due to the fine, random layers. The main achievement of this thesis is the theoretical and numerical analysis of this phenomenon. Additionally, the applicability of the layer annihilators for velocity estimation is presented