Effective Elastic Properties of Rocks with Gaussian Distribution of Vertical Fractures

Vertical fractures commonly develop across diverse strikes and exhibit intricate monoclinic anisotropy in subsurface rocks. The accurate determination of the elastic and anisotropic properties associated with the fracture strike distribution in multi-fractured media is of paramount importance for understanding subsurface reservoir characterization and optimizing development strategies. Based on the anisotropic effective medium theory, a rock physics model has been developed to comprehensively describe the elastic and anisotropic properties of multi - fractured rocks, taking into account specific fracture strike distribution features. To capture the complexity of non - parallel fracture sets, the model integrates the Bond transform matrix and Gaussian function, enabling a more realistic representation of the fracture strike distribution. Numerical analysis demonstrated that key parameters related to the fracture strike distribution, namely the average fracture strike, the standard deviation of fracture strike, and the integral interval of fracture strike, are critical in precisely characterizing the variations in the elastic and anisotropic properties of monoclinic multi - fractured media. Quantitative analysis reveals that the statistical distribution of multiple fractures has a profound impact on the pattern of anisotropy variation. When the integral interval of fracture strike decreases, fractures tend to align in a more directional manner. In such cases, the fractured media can be approximated as conventional fractured media with simpler anisotropic symmetry, such as orthorhombic, horizontal transverse isotropy, or vertical transverse isotropy. Conversely, an increase in the standard deviation of fracture strike indicates a transition towards a more random distribution of fractures, where the medium begins to exhibit properties similar to the background medium. It is important to note that even when the background medium has weak anisotropy, its influence on wave velocity and associated anisotropy cannot be neglected, and must be carefully considered in theoretical modeling frameworks. In summary, the proposed approach offers a novel and effective means of characterizing fracture distribution patterns. By providing a more in - depth understanding of the subsurface fracture network in complex fractured reservoirs, this method improves the accuracy of reservoir characterization, and ultimately contribute to more efficient hydrocarbon exploration and production operations.