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This study investigates the sensitivity of singularity points in the Vertical Fracture Transverse Isotropy (VFTI) model (a standard orthorhombic model) to changes in fracture weaknesses. The analysis highlights that the position of singularity points in the group velocity domain is sensitive to variations in fracture weaknesses, specifically in orthorhombic anisotropic media. For fractures aligned perpendicularly to symmetry planes, the anomalies in singularity points are almost insensitive to changes in certain fracture weakness parameters (δN), whereas others (δH and δV) lead to significant alterations. The corresponding group velocity ellipses, representing these anomalies, exhibit changes in shape and size, with the square of these ellipses quantifying the anomaly's extent. This sensitivity underscores the potential for using such anomalies as constraints in seismic data inversion to refine fracture parameter estimates. This approach enhances the precision of fracture characterization in subsurface modelling and improves the understanding of anisotropy in fractured reservoirs.