Anisotropy of fracture nodes using wavelet analysis

 Abstract:

Fracture networks play a critical role in controlling rock mechanics, fluid flow, and crustal deformation. However, many conventional analytical approaches do not adequately account for the spatial anisotropy of fracture nodes. This study introduces a wavelet-based angular variance method to quantify multiscale anisotropy in fracture network nodes, including I-, Y-, X-, and X + Y-nodes, as well as barycenters, using both synthetic and natural datasets.

Synthetic experiments demonstrate that isotropic fracture systems produce spatially random node distributions, whereas anisotropic systems generate distinct directional clustering, such as cross-shaped patterns aligned along NE–SW and NW–SE orientations. Application of the method to field data reveals strong correspondence between node anisotropy and underlying structural features. In the Jabal Akhdar dataset, X- and X + Y-nodes show pronounced elongation along an ENE–WSW direction, I-nodes exhibit weaker lobation in the same orientation, and barycenters remain largely isotropic. In contrast, the Getaberget dataset displays significant anisotropy across barycenters and multiple node types (Y, X, and X + Y), with dominant N–S to NNW trends consistent with NE–SW and NW–SE fracture sets.

These results demonstrate that wavelet-based node analysis is capable of detecting subtle, scale-dependent anisotropy in fracture systems. The proposed approach provides a sensitive, continuous, and scalable framework for quantifying fracture network organization, offering valuable insights for reservoir characterization, geothermal resource assessment, and the analysis of fracture-controlled fluid flow in geological systems.

 Keywords: Fracture network; Nodes; Spatial analysis; Point anisotropy; Wavelet analysis

 Acknowledgement

PG acknowledges the Indian Institute of Technology Roorkee and the Ministry of Human Resource Development (MHRD), Government of India, for support through a PhD fellowship. SB acknowledges financial support from the Department of Science and Technology (DST), Government of India (Project No: SRG/2021/001903), and from FIG (Grant No: FIG-100886-ESD), Indian Institute of Technology Roorkee, India.