Finite-difference migration in v(x,z)

For the finite-difference migration, I tested the 45-degree equation in $(\omega,x,z)$.The velocity model used has a constant gradient from the left upper side to the right lower side, which is shown in Figure (a). Using this velocity model, a syncline reflector was modeled by the finite-difference method using the 45-degree equation and is shown in Figure (b). The migration result obtained by the conjugate of the forward modeling is shown in Figure (c). The reflector has clearly imaged except for background artifacts which seem to be caused by the boundary reflection. Figure (d) shows that we can suppress these artifacts by using the least-squares imaging method.

 

Wxz45miginv
Figure 8 Least-squares finite-difference imaging in $(\omega,x,z)$: (a) The velocity model with a syncline reflector shown in Figure (a), (b) 45-degree finite-difference modeling, (c) The image obtained by the 45-degree finite-difference migration for (b), (d) The image obtained by the least-squares finite-difference imaging for (b) (after 10 iterations).