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Seismic amplitude variation versus offset (AVO) inversion is widely used technology in reservoir geophysics, for estimating the elastic parameters of the Earth subsurface media. Following the ray-impedance concept, I conducted the AVO inversion in the ray-parameter domain. The pre-stack seismic gathers are constructed in the ray-parameter domain, by using a bending ray-tracing method. One of my research objectives is to estimate three elastic parameters from the single P-wave data with limited angle/offsets. The conventional single P-wave AVO inversion has difficulty in estimating three elastic parameters simultaneously, especially for the bulk density. I attempted to constrain the non-linear AVO inversion results with the geological interpreted horizons, assuming each stratified layer is homogeneous. This geological operator transforms the sample-based models into the layer-based models and hence produces geologically meaningful inversion results. I also applied the first-order spatial derivative as the Tikhonov regularisation operator to control the lateral continuity. I demonstrated that, using the proposed geological layer constraints and the spatial regularisation operator, reliable inversion results with high lateral continuity can be obtained. I employed a subspace inversion method, in which three elastic parameters are separated into different subspaces in order to invert for the three elastic parameters simultaneously: P-wave impedance, S-wave impedance and the density. I parameterised each model of single elastic parameter by a Fourier series in which the Fourier coefficients of different wavenumber components are grouped into different subspaces. In order to further handle different sensitivities associated to different groups of coefficients, the Hessian matrix is also modified by applying a range of damping factors to different coefficients within each subspace. This inversion scheme is referred to as multi-damped subspace method. I applied the ray-parameter domain, multi-damped subspace method to two field datasets. One of field datasets is from the Tarim basin where deposited an Ordovician carbonate reservoir, and the other is from Ordos basin where deposited a coal bearing gas reservoir. The multi-damped inversion results show a high resolution and a good lateral continuity of the elastic parameters. For the first field dataset, the inversion results clearly delineate the top of the carbonate reservoir by a sharp increase in all the P-wave impedance, S-wave impedance and the density. For the second field dataset, the Possion’s ratio is calculated from the inverted elastic parameters and is used as the gas indicator. The low Possion’s ratio area matches the gas production zones explored in the wells. The horizon slices of the three elastic parameters, the P-wave impedance, S-wave impedance and the density as well as the Possion’s ratio are studied to exploit the potential gas reservoir targets in the whole area. Based on field data application, the inverted elastic parameters are reliably used for reservoir characterisation. The main conclusions I have drawn from this PhD studies are: (1) The ray-parameter domain seismic elastic inversion can exhibit superior features for reservoir characterisation, following the ray-impedance theory. (2) The AVO inversion constrained by the geological horizons enables the inversion results to satisfy the geological background. Further applied Tikhonov regularisation operator is able to control the lateral continuity. (3) The multi-damped subspace AVO inversion has shown potential in estimating P-wave impedance, S-wave impedance and the density simultaneously using P-wave seismic data with the limited offset range.