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A 3-D dip annihilation filter can
be approximated by cascading two perpendicular 2-D filters,
one oriented in the *x*-*z* plane and the other oriented in the *y*-*z* plane.
We can write this new filter as

| |
(2) |

where is our inverse
3-D steering filter operator, is an inverse
steering filter oriented in the x-direction, and
is an inverse y-direction
steering filter.
The construction of two 2-D filters allows for a large degree of freedom
in filter construction.
The method can deal with a range of spatial dips with little
variation in bandwidth response, Figure 1.
In addition we can vary the *range* over which the smoother operates,
both isotropically (Figure 2) and to some degree
anisotropically (Figure 3).

**angles
**

Figure 1 An example of filter behavior
at different dip angles. Note how the bandwidth response is approximately
the same in all panels.

**iso
**

Figure 2 By changing what the non-zero lag
coefficients sum to the area over which the filter acts can be drastically
altered.

**aniso
**

Figure 3 The cascading of two filters allows us
to create a filter that acts over different range in the x and y direction.

** Next:** Missing data example
** Up:** Methodology
** Previous:** 2-D steering filter
Stanford Exploration Project

9/5/2000