Conclusions

Modeling and migration of a data set with a Gaussian velocity anomaly shows that the main differences between the two-way vs. one-way modeled data are at far offsets. The one-way modeled data amplitudes decay with offset, because of the many approximations used (PSPI to handle variable horizontal velocities) and the absence of the Jacobian of the change of variable from $\omega$ to k_z.

An important fact derived from the numerical experiments is that the one-way modeled data migration vs. migration "Hessian impulse response" show differences. Those differences are attributed to the computed number of off-diagonal terms of the Hessian matrix. An added value of this comparison is that it corroborates the approximations used to compute the Hessian.

The results indicate that if the modeling and the inversion operators differ there is little chance to recover the correct AVA in poor illumination areas. Because, in areas of poor illumination, this problem will have a large null space. The proper strategy to recover the AVA in those areas is the use of regularization, where previous knowledge about the model can be introduced to reduce the model null space.