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The two-dimensional problem of hydrodynamic interaction of the horizontal circular cylinders with a free-surface is investigated both analytically and numerically. The fully nonlinear initial boundary-value problem is described and a numerical solution for it is presented. The free motion of a cylinder rising towards, or moving away from the free-surface or moving horizontally is studied. The numerical calculations are compared with a simple analytic theory in which we take the low- and high-frequency limit of the added mass, and the constant added mass of the submerged cylinder in the coefficients of the equation of motion. Further numerical calculations of an initially displaced, spring-loaded cylinder undergoing slow motions are compared with a simple analytic theory in which we also take the low-frequency limit of the added mass of the submerged cylinder. The aim is to provide a useful approximate method for simulation of various offshore operations. Fully nonlinear calculations of the free-surface deformations of the initially calm water caused by forced constant velocity motion of a totally submerged circular cylinder are compared with small-time asymptotics due to Tyvand & Miloh (1995). Their analytic results, which are taken to third order5 when gravity terms first appear in the expansion, are in excellent agreement with the numerical calculations for small times, beyond which only the numerical method will give accurate results, valid until the free-surface breaks. The breaking of the surface as a result of vertical downward motion is further investigated with the aim of establishing when and how this happens, since the phenomena causes the breakdown of the numerical calculations. The free motion of a cylinder entering a free-surface, initially half-submerged in calm water and having specific gravity of 1.2 is also investigated. This motion is pursued beyond the complete submergence stage, giving rise to interesting free-surface deformations and body dynamics. This study is complemented by a further investigation involving impulsively started and forced constant motion of a cylinder entering a free-surface at various angles and Froude numbers, and is also taken beyond the complete engulfment stage. Hydrodynamic forces on the cylinder obtained for various angles at the same Froude number are compared. Also, the hydrodynamic forces for the motion in the same direction at various Froude numbers are compared.

Post-Stack inversion of reflection data in seismic exploration can be used to obtain detailed information about lithology variations in the zone of interest. Generalized Linear Inversion (GLI) has previously been applied as a useful tool to achieve this. The purpose of my investigation is to apply GLI to data from the Coal Measures. It is known that in the Coal Measures the most strongly reflecting horizons are the coal seams, which are the exploration targets. In the seismic bandwidth they are thin beds, which causes particular problems associated with vertical resolution for the inversion. The method is applied to a seismic line from the Belvoir Coalfield supplied by British Coal. In order to get better relative amplitudes and to keep the same bandwidth down the whole section, the data were carefully reprocessed using the ProMAX software. Wireline log data from two boreholes intersected by the seismic line were edited to generate acoustic impedance logs as functions of time. Software was developed to implement GLI, and tested on synthetic data before applying it to the reprocessed data. The initial guesses for earth and wavelet models at the boreholes were obtained after systematic studies to determine the best strategy. The construction of the initial guess for the boundary locations elsewhere on the section is very critical for the success of the search for the global minimum. A combination of structural interpretation and the inversion results obtained from the previous trace was found to do the best job. I have tried to invert separately for the boundary locations, acoustic impedances and the wavelet, with the wavelet parameterized in the frequency domain. I found that, provided that the wavelet extracted at a borehole is a good estimate with low error energy, the most successful strategy is just to invert for the boundary locations, keeping the acoustic impedances and the extracted wavelet fixed. If the extracted wavelet is not a good estimate, then parameterizing the wavelet in the frequency domain and optimizing those parameters at the borehole is a useful approach. None of the implemented inversion strategies produced a perfect result. Discrepancies were due to the difficulty in obtaining true relative amplitude values on the processed section. The inversion results and systematic studies on the field dataset indicate that the assumptions of the convolutional model are not satisfied by the processed section.

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