I. Preprocessing for Towed Streamer, Ocean Bottom and Onshore Acquisition, for Horizontal or Non-Horizontal Acquisition Surface: Implications for Multiple Removal, Structural Determination and Amplitude Analysis; II. Inverse Scattering Series Internal Multiple Attenuation in an Absorptive Dispersive Earth, without Knowing, Needing or Estimating Elastic or Anelastic Subsurface Properties

The first part of this dissertation advances Green's theorem wave separation methods for separating the reference wave and reflection data and for deghosting. There are several contributions within this first topic area. Firstly, note that a depth-variable acquisition surface can frequently occur either with a feathered cable in water or with a complicated topography in onshore or ocean bottom acquisition. Under these circumstances, directly applying Green's theorem deghosting method cannot deghost the recorded data on the acquisition surface. This dissertation proposes a new approach which is able to effectively solve this problem. Secondly, Green's theorem wave separation is a mature application in marine towed streamer acquisition. This dissertation extends the deghosting method to ocean bottom data. Thirdly, the current filtering methods for onshore ground roll removal may often damage reflection data; this dissertation develops Green's theorem wave separation algorithm which can satisfactorily address this issue. In a further step, this dissertation proposes a simplified algorithm to achieve onshore wave separation with a reduced data requirement. These solutions can enhance the capability of Green's theorem wave separation method and provide an adequate satisfaction of prerequisites for the subsequent multiple removal, structural determination, and amplitude analysis. The second part of this dissertation investigates the performance of the inverse scattering series internal multiple attenuation method for an anelastic medium with absorption and dispersion. Both analytical and numerical tests demonstrate the attenuation method retains its effectiveness to predict the internal multiple with the right time and approximate amplitude, and without requiring any elastic or anelastic property. For an anelastic medium, the approximate amplitude predicted by the inverse scattering internal multiple attenuation algorithm is further from the exact amplitude than in the corresponding acoustic/elastic circumstance. When the anelastic property can be provided or estimated, a new algorithm is developed to improve the predicted amplitude.