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Fractures exert a strong influence on fluid flow in subsurface reservoirs, and hence an adequate understanding of fracture properties could provide useful information on how they may be managed optimally to produce oil and gas or to be used as repositories for carbon dioxide (CO2) to mitigate climate change. Since fractures are commonly aligned by the stress field, seismic anisotropy is a key tool in investigating their properties. Velocity anisotropy is now a well-established technique for determining properties such as fracture orientation and density, but in recent years, attention has focused on quantifying azimuthal variations in Pwave attenuation to provide additional information, especially on the fracture size. However, the practical application of this attribute in geophysical exploration is still limited due to the uncertainty associated with its measurement and the difficulty in its interpretation in terms of rock properties. There is still a lack of proper understanding of the physical processes involved in the mechanisms of attenuation anisotropy. In this thesis, I use the seismic modelling approach to study the effects of attenuation anisotropy in fractured porous media using P-waves with the main aim of improving the understanding of these effects and exploring the physical basis of using attenuation anisotropy as a potential tool for the characterization of fractured reservoirs. Fractures with length on the order of the seismic wavelength in reservoir rocks cause scattering of seismic waves which exhibits characteristic azimuthal variations. I study these scattering effects using complementary seismic physical (scale-model laboratory experiments) and numerical (finite difference) modelling approaches. The results of both approaches are consistent in delineating fracture properties from seismic data. The scattered energy is quantified through estimates of the attenuation factor (the inverse of the seismic quality factor Q) and shown to be anisotropic, with elliptical (cos2θ) variations with respect to the survey azimuth angle θ. The minor axis of the Q ellipse corresponds to the fracture normal. In this direction, i.e. across the material grain, the attenuation is a maximum. The major axis corresponds to the fracture strike direction (parallel to the material grain) where minimum attenuation occurs. Empirically, the magnitude of P-wave attenuation anisotropy is greater in fluid-saturated rocks than in dry rocks. I study the influence of fluid saturation on P-wave attenuation through synthetic modelling and compare the attenuation signature to that of dry fractured rocks. The results of the analysis show that the relaxation time strongly controls the frequency range over which attenuation occurs. The magnitude of the induced attenuation increases with polar angle and also away from the fracture strike direction. The attenuation exhibits elliptical variations with azimuth which are also well fitted with a cos2θ function. The magnitude of the attenuation anisotropy is higher in the case of the fluid-saturated rocks. All of these properties of the numerical model are in agreement with the results of empirical experiments in the laboratory. The same crack density can result from many small cracks, from a few large cracks, or from an equal number of cracks of various sizes with varying thicknesses in the same volume of background material. This makes it difficult to distinguish between the anisotropy caused by micro-cracks and that caused by macro-cracks. I study the effects of fracture thickness or aperture on P-wave scattering attenuation through seismic physical modelling, and find that the induced attenuation has a direct relationship with the fracture thickness or aperture. This result indicates the potential of using P-wave attenuation to get information which might be useful in examining the effects of voids in the rocks, and also provides a basis for further future theoretical development to distinguish the effects caused by thin micro cracks and large open fractures. Finally, I study the effects of two types of fluid saturation (brine and CO2 in the supercritical state) on P-wave attenuation through synthetic modelling, with particular attention to varying CO2 saturation using the CO2 properties at the Sleipner gas Field in the North Sea. The presence of CO2 causes more attenuation in the numerical model output than when the rock is saturated with only brine. The induced attenuation increases with decreasing percentage of CO2 saturation and has a maximum magnitude at 10 % CO2 saturation. Further work is needed to quantify the additional effect of fractures on these results.