Ray tracing of multiple transmitted/reflected/converted waves in 2-D/3-D layered anisotropic TTI media and application to crosswell traveltime tomography

Abstract

To overcome the deficiency of some current grid-/cell-based ray tracing algorithms, which are only able to handle first arrivals or primary reflections (or conversions) in anisotropic media, we have extended the functionality of the multistage irregular shortest-path method to 2-D/3-D tilted transversely isotropic (TTI) media. The new approach is able to track multiple transmitted/reflected/converted arrivals composed of any kind of combinations of transmissions, reflections and mode conversions. The basic principle is that the seven parameters (five elastic parameters plus two polar angles defining the tilt of the symmetry axis) of the TTI media are sampled at primary nodes, and the group velocity values at secondary nodes are obtained by tri-linear interpolation of the primary nodes across each cell, from which the group velocities of the three wave modes (qP, qSV and qSH) are calculated. Finally, we conduct grid-/cell-based wave front expansion to trace multiple transmitted/reflected/converted arrivals from one region to the next. The results of calculations in uniform anisotropic media indicate that the numerical results agree with the analytical solutions except in directions of SV-wave triplications, at which only the lowest velocity value is selected at the singularity points by the multistage irregular shortest-path anisotropic ray tracing method. This verifies the accuracy of the methodology. Several simulation results show that the new method is able to efficiently and accurately approximate situations involving continuous velocity variations and undulating discontinuities, and that it is suitable for any combination of multiple transmitted/reflected/converted arrival tracking in TTI media of arbitrary strength and tilt. Crosshole synthetic traveltime tomographic tests have been performed, which highlight the importance of using such code when the medium is distinctly anisotropic.