A number of numerical examples are given in DGS. Here we show just one, the application of conjugate gradient and multi-grid methods to the residual statics problem. (For a description of the general approach see ``Combining the multigrid and gradient methods to solve the seismic inversion problem'' Saleck et. al in the Proceedings of the 63nd SEG meeting, Washington, D.C., 688-691.)
Figure 4 shows a stacked section acquired over a permafrost zone without statics corrections. The black bar on the right shows the time window of data used to compute the statics corrections. Figure 5 shows the result of applying the COOOL non-quadratic version of conjugate gradient to optimize the stacking power in succesively wider frequency bands. It is clear that the continuity of the reflections was restored, and the resolution and signal-to-noise ratio improved.
Figure 4: A stacked section acquired over a
permafrost zone without statics corrections. The black bar
on the right shows the time window of data used to
compute the statics corrections.
Figure 5: Using the COOOL library
we searched for optimum surface-consistent statics by optimizing the
stacking power in succesively wider frequency bands. The result is shown
here. It is clear that the continuity of the reflections was
restored and the resolution and signal-to-noise ratio improved.
