Sensitivity Study of the Critical Angle in Elastic Orthorhombic Media

The critical angle plays a crucial role in data processing for refraction seismology. In the context of three-dimensional data, the critical angle exhibits azimuthal dependence, particularly in the presence of an anisotropic model. In this paper, we propose a method to determine the critical angle (phase angle) and analyse the sensitivity of the critical angle to the model parameters and the available azimuthal range for both transversely isotropic medium with a vertical symmetry axis and orthorhombic models. For more complex orthorhombic models, the critical angle can be computed while considering changes in azimuth. In a numerical example, we apply sensitivity analysis to examine the existence of the critical angle and determine its corresponding values to variations in model parameters and the azimuthal range. Additionally, we conduct computations of the critical angle for the simplified acoustic and elliptical orthorhombic models. This analysis can be extended to encompass all model parameters for different wave modes (pure and converted waves), and they provide generalized predictions for the available range of data in seismic data processing applications.