## REFERENCES

Claerbout, J. F., 1992, Anti aliasing: SEP-73, 371-390.

Hale, D., 1991, A nonaliased integral method for dip moveout: Geophysics, 56, no. 6, 795-805.

Mathematica code to calculate weighting functions for bilinear interpolation.

```(* Bilinear approximating function within a cell bounded by x1,y1,x2,y2 *)
(* values at corners of cell are    *)
(*            (x1,y1) => f1	  *)
(*            (x1,y2) => f2       *)
(*            (x2,y1) => f3       *)
(*            (x2,y2) => f4       *)
bilin[ x_, t_ ] := f1 ( 1- (x-x1)/(x2-x1))(1-(t-t1)/(t2-t1) ) +                     f2 ( 1 - (x-x1)/(x2-x1)) (t-t1)/(t2-t1) +                     f3 (x-x1)/(x2-x1) (1-(t-t1)/(t2-t1) ) +                      f4  (x-x1)/(x2-x1) (t-t1)/(t2-t1)
(* A linear path across the cell *)
(* Starts at xx0,tx0, exits at xx1,tx1 *)
tau[ x_ ] := tx0 ( 1-(x-xx0)/(xx1-xx0)) + tx1 (x-xx0)/(xx1-xx0)
(* The bilinear function along the path *)
bilin[ x_ ] := bilin[ x, tau[ x ] ]
(* Integral along the path *)
res = Integrate [ bilin[x], {x, xx0, xx1 } ]

Print[""]
Print["Coeffficient in f1"]
cf1 = Simplify[ Coefficient[ Collect[ res, f1],f1]]
Print[""]
TeXForm[ cf1 ]

Print[""]
Print["Coeffficient in f2"]
cf2 = Simplify[ Coefficient[ Collect[ res, f2],f2]]
Print[""]
TeXForm[ cf2 ]

Print[""]
Print["Coeffficient in f3"]
cf3 = Simplify[ Coefficient[ Collect[ res, f3],f3]]
Print[""]
TeXForm[ cf3 ]

Print[""]
Print["Coeffficient in f4"]
cf4 = Simplify[ Coefficient[ Collect[ res, f4],f4]]
Print[""]
TeXForm[ cf4 ]
```