Ray tomography based on azimuthal anomalies

A method of estimating the lateral velocity variations in the 2D case using the data on deviations of wave paths from straight lines (or great circle paths in the spherical case) is proposed. The method is designed for interpretation of azimuthal anomalies of surface waves which contain information on lateral variations of phase velocities supplementary to that obtained from travel-time data in traditional surface wave tomography. In the particular 2D case, when the starting velocity is constant (c ₀) and velocity perturbations δc(x,y) are sufficiently smooth, a relationship between azimuthal anomaly δα and velocity perturbations δc(x,y) can be obtained by approximate integration of the ray tracing system, which leads to the following functional: $$\delta \alpha = \int_0^L {\frac{{s(\nabla m,n_0 )}}{L}} ds,$$ wherem(x,y)=δc(x,y)/c ₀,L is the length of the ray,n ₀ is a unit vector perpendicular to the ray in the starting model, integration being performed from the source to the receiver. This formula is valid for both plane and spherical cases. Numerical testing proves that for a velocity perturbation which does not exceed 10%, this approximation is fairly good. Lateral variations of surface wave velocities satisfy these assumptions. Therefore this functional may be used in surface wave tomography. For the determination ofm(x,y) from a set ofδα _k corresponding to different wave paths, the solution is represented as a series in basis functions, which are constructed using the criterion of smoothness of the solution proposed byTarantola andNersessian (1984) for time-delay tomography problems. Numerical testing demonstrates the efficiency of the tomography method. The method is applied to the reconstruction of lateral variations of Rayleigh wave phase velocities in the Carpathian-Balkan region. The variations of phase velocities obtained from data on azimuthal anomalies are found to be correlated with group-velocity variations obtained from travel-time data.