Linearized Rays , Amplitude and Inversion

In this paper, ray theoretical amplitudes and travel times are calculated in slightly perturbed velocity models using perturbation analysis. Also, test inversions using travel time and amplitude are computed. The perturbation method is tested using a 3-D velocity model for NORSAR having velocity variations up to 8.0 percent. The perturbed amplitudes are found to be in excellent agreement with the calculated ray amplitudes. Velocity inversions based on travel time and amplitude are next investigated. Perturbation analysis using linearized ray equations is efficiently used to compute amplitude derivatives with respect to model parameters. The trial linearized inversions use smaller velocity variations of 1.7 percent to avoid possible effects due to ray shift, even though the perturbation analysis is valid for larger variations. The trial 2-D inversion results show that linearized amplitude inversions are complementary and not redundant to travel time inversions, even in smoothly varying models.