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This book analyzes some problems encountered in imaging beneath under-compacted sediments and offshore mobile shales by employing a modelling approach. In the first analysis of the problem, ray tracing was used for illumination studies while finite-difference modelling was employed for complex propagation. By employing the random character concept, the author describe surfaces resulting from the interaction of under- compacted and over-pressured shale mass with adjacent sediments. 3-D models having rugous interface with well controlled statistical parameters were realized for different rugousity scales. Seismic wavefield scattering from the randomly rough interface is then studied. The influence of the rugous surface height on the scattered wavefield was also analyzed and calibrated. This book will be of interest to Seismic interpreters, Geophysicists and Engineers who wish to gain indepth knowledge on how wave scattering affects seismic image quality.