In this thesis I address the problem of determining fracture properties of subsurface rocks from geophysical surface seismic and vertical seismic profile (VSP) data. In the first part of this thesis I perform multi-attribute analysis, including frequency content, amplitude, travel time and angle of rotation studies on field VSP data from two different carbonate fields, both containing time-lapse surveys. I compare the findings to independent data available in the region and find that the interpreted fracture orientations from the attribute analyses correlate with independent fracture studies in the area, the principal axis of major faults, or the maximum horizontal stress of the area studied. Although I show the existence of these correlations, due to the limited knowledge of the rock properties, these correlations are only qualitative. A more robust inversion of fracture properties requires more knowledge of the physical properties of the medium and forward modelling of the seismic response. A rock physics theory would be required to model the elastic response of the fractured rock; hence a more quantitative fracture characterisation is necessary. In the second part of this thesis I address this need by developing and testing a method for fracture density inversion. Linearised approximations are commonly used in azimuthal amplitude versus offset (AVO) analysis. However, these approximations perform poorly at large angles of incidence where the effect of fractures is more significant. The method proposed here uses a model based approach that does not use these approximations but calculates the exact azimuthal AVO response based on prior knowledge of the elastic constants of the medium, assumed to be known, and a range of fracture densities. A rock physics theory is used for modelling the elastic constants of the fractured rock. I then create a linearized relationship for a specific model that separates the effect due to fracture density from the modelled AVOZ responses. This separation is key to the method, as it provides both a new set of orthogonal basis functions that can be used to express the AVOZ response of field data, and a set of coefficients that are related to fracture density. In general, the inversion is based on these coefficients. The coefficient or coefficients which present the highest correlation with fracture density must be determined on a case by case basis, as they will vary depending on the contrast between the elastic constants across the boundary of interest. I develop and test the method on synthetic surface seismic data and then apply it to seismic data acquired from a laboratory-scale physical geological model. Due to the prior knowledge of the rock properties and structure of the physical geological model, I am able to corroborate that the inverted fracture density from the seismic data matches that of the physical model within the error. I compare the inversion for two different levels of uncertainty in the velocities and densities of the modelled reflection coefficients and show that the inversion results are more precise and accurate when there is less uncertainty in the rock properties of the modelled reflection coefficients. In both the synthetic and physical geological model studies I find that the inversion is optimal for a certain range of offsets/angles of incidence. This means that the optimal range for inversion must be found on a case by case basis, as it depends on the behaviour of the data. Finally, as the inversion relies on the input modelled azimuthal AVO curves, a careful choice of the input rock properties is essential for the inversion process. The inverted fracture density values will only be valid if the rock properties of the field data fall within the range of the modelled ones. This is a limitation of the method, as adequate knowledge of the rock properties is not always available.

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