|Wave-equation migration velocity analysis by residual moveout fitting|
I plan to solve the optimization problem defined in 4 by a gradient-based optimization algorithm. Therefore, the development of an algorithm for efficiently computing the gradient of the objective function with respect to slowness is an essential step to make the method practical. In this section I outline the methodology to compute the gradient, and I leave some of the details to Appendix A.
The gradient is computed
using the chain rule.
The first term of the chain is the derivative of the objective function
in equation 4 with respect the moveout parameters.
The second term is the derivatives
of the moveout parameters with respect to slowness
that are computed from the objective function 5.