Raypath and traveltime computations for 2D transversely isotropic media with dipping symmetry axes

This paper presents a simple method to calculate the traveltimes and corresponding raypaths for the first-arrival (refraction), reflected, diffracted, and converted waves of the three modes (qP, qSV, qSH) in a 2D transversely isotropic medium, whose symmetry axis may have an arbitrary orientation in the xz-plane. This method is a direct extension of the 'shortest path' method to the anisotropic situation. In this extension, we employ analytic solutions for the group velocity of the three wave modes, and transform a 2D heterogeneous, transversely isotropic medium defined by five elastic moduli and the arbitrary orientation angle of the symmetry axis into the three group-velocity models, which correspond to the qP-, qSV- and qSH-waves. The three group velocities are functions of the spatial coordinates and the ray direction, as well as the orientation angle of the symmetry axis of the media. With these group-velocity models, the traveltimes of these waves and their corresponding raypaths are then simultaneously or individually calculated by a modified 'shortest path' method. We present some numerical experiments to show the accuracy, efficiency, and capability of the method. The results demonstrate that a rotated (dipping) symmetry axis may significantly change the kinematic properties of the three wave modes in a transversely isotropic medium.