Building the steering filters

To construct the 3-D steering filter operator, I followed the methodology described in Appendix  for cascading two 2-D steering filter operators to form my 3-D steering filter operator. I used the 13 reflectors picked in the last section. To calculate the dip field I began by calculating the slope in the (x,z) and (y,z) planes. I mapped these two dip fields into $(x,y,\tau)$ model space. I then interpolated the field to the entire model space.

Once I had the dips in both the (x,z) and (y,z) planes I constructed two filter banks which encompassed the range of dips in each direction. It was then a simple matter of creating a mapping operator that mapped the dip at a given model point to a specific filter in the bank. To see the effect of this new complex operator I filled the model with random noise and then applied A_3dA_3d' (Figure 10). As you can see, the 3-D steering filter does a good job in spreading energy along reflector directions.

 

random-3d
Figure 10 The result of putting random numbers into a model then applying A_3dA_3d'.