Traveltimes and conversion-point positions for P-SV converted wave propagation in a transversely isotropic medium: numerical calculations and physical model studies

This study uses ultrasonic physical modelling to test the accuracies of numerical calculations of traveltimes and conversion-point (CP) positions for P-SV wave propagation in a horizontal transversely isotropic (TI) medium. Study results show that the traveltimes and CP positions for P-SV wave propagation on the isotropic plane of a TI medium computed using Fermat's minimum-time principle are the same as those of using the isotropic non-hyperbolic moveout equation and the isotropic CP equation. However, for P-SV wave propagation on the symmetry-axis plane of a TI medium, the arrival times and CP positions of SV-waves are difficult to determine by any ray methods when the propagation directions of SV-waves are within the cuspoidal SV-wave group velocities zone. But the first arrival times and the propagation of the dominant energy of P-SV waves can still be analysed by ray methods. Based on the calculation of Fermat's minimum-time principle, if the source-receiver offset is greater than a critical distance, the reflection angles of the converted SV-waves are fixed at a specific angle with a local maximum SV-wave group velocity of the neighbourhood area. This is because the converted SV-waves prefer to propagate along the cuspoidal directions with larger amplitude and higher velocity. Verified by the physical modelling, the Fermat's minimum-time principle used to calculate traveltimes of P-SV waves is better than the anisotropic non-hyperbolic moveout equation. The physical modelling for the CP position experiment can give a clearer visualisation of the variations of CP positions in the profile, and the feasibility of using Fermat's minimum-time principle to determine CP positions is also better than that of the anisotropic CP equations. Therefore, in the seismic data processing, Fermat's minimum-time method is recommended to accurately determine the arrival times and CP positions of P-SV wave propagation in TI media.