Next: Constructing an ``isotropic'' Laplacian
Up: Fomel & Claerbout: Implicit
Previous: REFERENCES
Given the filter D_{2} (k), defined in formula (10), we can
construct an accurate approximation to the second derivative operator
k^{2} by considering a filter ratio (another Padétype
approximation) of the form
 
(25) 
where is an adjustable constant Claerbout (1985).
The actual Padé coefficient is . As pointed out by
Francis Muir, the value of gives an exact fit at the Nyquist frequency . Fitting the
derivative operator in the L_{1} norm yields the value of . All these approximations are shown in Figure
10.
sixth
Figure 10 The secondderivative operator
in the wavenumber domain and its approximations.

 
B
Next: Constructing an ``isotropic'' Laplacian
Up: Fomel & Claerbout: Implicit
Previous: REFERENCES
Stanford Exploration Project
10/9/1997