Forward Modeling

 Forward modeling is done by ray tracing in the initial velocity model. An imaginary shot (focus point) is positioned in the subsurface and rays are traced towards receivers at the surface. In this way modeled focusing operators are obtained. The differences between the traveltimes of these operators and the real focusing operators are used to optimize the velocities in the model and the locations of the focus points. Moreover, the traced rays are needed to define the relation between the traveltime data and the model parameters (matrix $\mathbf{A}$, in the next subsection).