Similarly to the case of 3-D plane-wave destruction, where the regularization operator is constructed from two orthogonal two-dimensional filters, 3-D differential offset continuation amounts to applying two differential filters, operating on the in-line and cross-line projections of the offset and midpoint coordinates. The corresponding system of differential equations has the form

(132) |

The result of a 3-D data regularization test is shown in Figure . The input data cube corresponds to the one in Figure . I used neighboring offsets in the in-line and cross-line directions and the differential 3-D offset continuation to reconstruct the empty traces. Although the reconstruction appears less accurate than the plane-wave regularization result of Figure , it successfully fulfills the following goals:

- The input traces are well hidden in the interpolation result. It is impossible to distinguish between input and interpolated traces.
- The main structural features are restored without using any assumptions about structural continuity in the midpoint domain. Only the physical offset continuity is used.

Figure 37

In the next section, I return to the 2-D case to consider an important problem of shot gather interpolation.

12/28/2000