REAL DATA EXAMPLE

As a real data test, an irregular CMP gather was used as input to the algorithm. This gather comes from a collection of profiles published in Ozdagan Yilmaz' book, Seismic Data Processing 1987. The input cmp gather and velocity spectrum estimated with the preconditioned inversion are displayed in Figure 5. As can be seen from the figure, the data are severely aliased, and it is difficult to identify many events. The remodeled output is displayed in Figure 6. The data are definitely less aliased. Some artifacts have appeared, mostly above the mute zone. A close look at the input reveals plane waves above the first breaks, which are like hyperbolas with negative zero-offset travel times, and which are thus probably difficult to model with the velocity space transform. Simply muting the input above the first breaks likely removes most of the artifacts.

 

realin
Figure 5 An aliased CMP gather used as input to the preconditioned inversion (left), and its estimated velocity spectrum (right).

 

realout
Figure 6 The estimated velocity spectrum remodeled into a more finely sampled data space.