[S-SS09] Seismic wave propagation: Theory and Application

[SSS09-P08] Applying the shortest path method to anisotropic media in order to calculate ray paths

*Shoji Sekiguchi¹ (1.National Research Institute for Earth Science and Disaster Resilience)

Keywords:shortest path method, anisotropy, ray tracing

Calculating ray paths in anisotropic media in travel-time tomography is carried out in only a few studies. It is meaningful to apply the shortest path method to anisotropic media in order to calculating ray paths. Applying the shortest path method is easy, because nodes distributed in the media and ray paths between nodes are given and only the travel-time along the path need to be evaluated. However, it should be noted that it is important that ray (group) velocity in a given ray path direction can be easily evaluated in order to save calculation time. Generally, in ray tracing algorithms of anisotropic media, determinant of elastic parameter tensor in a given phase slowness direction is solved at first. The obtained phase slowness, etc. are substituted into the ray tracing equation. From the ray tracing equation, ray path and travel-time are calculated. Ray (group) velocity and its direction are also evaluated, but not input parameters. Here, in advance, we calculate ray (group) velocity in various phase slowness direction at each node by solving the determinant numerically, smooth them by Spline function and save them as linear function of two parameters: group velocity directions (colatitude, longitude). Using them when needed, we can easily obtain the ray (group) velocity of a given ray direction. The phase slowness is not needed anymore, but it is used in travel-time tomography. In such a case, three vector components of the phase slowness are saved as linear functions of the two parameters: group velocity directions. Next, to confirm that our way of the calculation is correct, we calculate ray (group) velocity in homogeneous transversely isotropic media, and compare our results with analytic solutions. We use elastic parameters of PREM at depth of 24.4km (at the top of LID layer). Our results are almost same as the analytic ones, which shows our calculation works fine. Anisotropic media produce two S phases (qS1 and qS2), but, only one travel-time as an S phase is picked in most observed data processing. To adjust to the actually available data, we assume the picked S data correspond to the first S arrivals, and adopt the faster group velocity of two S phases at each node to calculate the travel-time of the first S arrival.