##### Sammendrag

Natural fractures are widely distributed in the upper crust. Fracture research is quite important in many fields. To understand the seismic signatures in fractured rocks, several classic effective models for fractured rocks are proposed by geophysicists. For instance, a transverse isotropic medium with a horizontal symmetry axis (HTI) is commonly used for describing an isotropic background containing a set of parallel vertical fractures. The horizontally layered formation with orthogonal vertical fractures can be equivalent to a long-wavelength effective orthorhombic (ORT) medium. If the vertical fractures are not mutually orthogonal in the VTI background, the effective medium becomes a monoclinic medium with a horizontal symmetry plane.

In this thesis, I propose a long-wavelength monoclinic model involving two sets of nonorthogonal vertical fracture clusters embedded into a VTI background. I exploit three approaches to construct the effective monoclinic model. The first method is based on linear slip theory. The second one focuses on upscaling two different VFTI (vertically fractured VTI) media into an effective monoclinic model. The third approach is similar to the second method, but it includes one additional VTI medium for the effective monoclinic medium. For simplicity, I utilize The Gaussian function to describe the distribution of the vertical fracture clusters.

To compare the anisotropy discrimination between these approaches, the monoclinic anisotropy parameters and the NMO velocity ellipses for the P-, S1, and S2-waves are displayed by numerical examples. The fracture distribution parameters and fracture compliances are modified in the model to show the influence on the monoclinic anisotropy parameters and the NMO velocity ellipses. Finally, the NMO velocity ellipses with different upscaling ratios are computed and plotted for method 2 and method 3.

The results show that the fracture distribution parameters have a significant influence on the NMO velocity ellipses in the phase and group domains. In the group domain, the effects on azimuth anisotropy are a little larger compared to the phase domain. If the preferred azimuth angles are changed, the rotations of the NMO velocity ellipses for the S1-, and S2-waves are obvious, while the rotations for the P-waves are relatively smaller. The angular standard deviation can influence the NMO velocity ellipses and monoclinic anisotropy parameters, while the change is very small when the angular standard deviation is larger than 5. The influence of integration intervals of the vertical fracture clusters on the NMO velocity ellipses for S-waves is stronger than the P-wave.

The NMO velocities for the P-, S1-, and S2-waves in method 2 are consistently larger than in method 1. The upscaling ratio α is another essential parameter in terms of upscaling theory, which can influence the azimuth anisotropy of the effective media seriously. The monoclinic anisotropy parameters for P-, S1-, and S2-waves change quasi-linearly with the upscaling ratio α.