Building the steering filters

To construct the 3-D steering filter operator I followed the methodology described in Clapp (2000), cascading two 2-D steering filter operators to form my 3-D steering filter operator. I used the five 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 ). As you can see the 3-D steering filter does a good job in spreading energy along reflector directions.

 

random-3d
Figure 5 The result of putting random numbers into the model then applying A_3dA_3d'.