To calculate raypath traveltime in anisotropic media, ray tracing has been shown as an efficient approach. The algorithm of Ray Tracing is to apply network theory and shortest paths in networks, so called shortest path ray tracing. By extending Sena’s (1991) anisotropic traveltime equation to TTI media and compared with anisotropic waveform modeling in terms of picked first arrivals, shortest path ray tracing can be proved as effective approach for calculating traveltime data in 2D/3D TTI media. The calculated first arrivals from ray tracing can be used in traveltime tomography with anisotropic parameter estimations.
In multilayered homogeneous anisotropic media, each layer consists of constant anisotropic parameter ε and δ, tilt angle φ of symmetry axis, and axial velocity along symmetry axis. A ray path is a sequence of nodes and connections succeeding each other. The traveltime along a path from one node to another is defined as the sum of the weights of the connections of the path. The final path is the path with smallest possible traveltime.
To extend the approach to 3D model, there are two different assumptions on the tilt angle of the anisotropic symmetry axis (Figure 2-7). The first one assumes that each model layer has a constant orientation of the symmetry axis, which is described by the tilt angle φ and azimuth angle Φ. However, geological interpretations indicate that it is rare that the symmetry axis in 3D deformable plane is expressed by only two angles.