Computation of Travel times and Station Correction Surfaces in Eurasia Using Three Dimensional Velocity Models

We have investigated the performance of a variety of travel time computation methods for application in highly heterogeneous three-dimensional (3-D) velocity structures, such as those found in Central Eurasia. Recent 3-D models of the crust and upper mantle beneath Central Eurasia (e.g., Villaseñor et al., 2000) contain sharp vertical and horizontal velocity contrasts and thin layers which complicate the accurate computation of travel times. Techniques based on ray-perturbation theory or the graph method (e.g., Pulliam and Snieder, 1996; Nolet and Moser, 1993) do not appear to work well when the velocity anomalies are large relative to the reference model. In these cases the reference ray can be very different from the minimum-time ray, and the methods fail to converge rapidly and in some cases do not converge at all to the global minimum. Ray shooting and finite-difference algorithms are more computationally expensive, but provide accurate results in the presence of large velocity contrasts. In the ray-shooting method, the model is parameterized in terms of smooth polynomials in all directions. Ray-shooting methods are normally implemented only in 2-' H J ýHUYHQê DQG 3ãHQþtN DQG GR QRW FRQVLGHU SURSDJDWLRQ SDWKV RII WKH VDJLWWDO SODQH 7KH ILQLWH GLIIHUHQFH PHWKRG FRPSXWHV travel times for first-arriving phases for the entire model (e.g., Podvin and Lecomte, 1991). Rays are obtained afterward by back-tracing from any point inside the model (receiver) to the source. This method is 3-D and the model is parameterized in terms of constant-velocity cubic cells. The accuracy of the travel times is determined by the cell size. Computer memory effectively limits the minimum cell size for a given region but this constraint can be overcome by computing travel times in 2-D. Ray shooting and finite difference methods produce similar travel times, but differences can locally be greater than 1 s largely due to the differences in model parameterization between the two methods. We report estimates of uncertainties in travel times and station correction surfaces between these two methods and also discuss the effect of computing travel times in 2-D rather than in 3-D. For IMS stations in Central Eurasia we present travel time correction surfaces relative to the 1-D model ak135 predicted by the 3-D velocity model of Villaseñor et al. (2000). At epicentral distances less than about 10 degrees, the character of the correction surfaces is dominated by the difference in crustal thickness between the 3-D model and ak135. Beyond 5-10 degrees, velocity variations in the uppermost mantle become increasingly important.