(8) |

Figure 7

The circular symmetry of the operator enables
it to be realized using McClellan filter.
Figure shows the ideal-extrapolator in 3-D for a certain
temporal frequency . The parameters used in generating
the extrapolator
are *dx*=*dz*=12.5 *m*, , and *v* = 1000. *m*/*s*.
A tapered 1-D extrapolator was designed by applying a
Gaussian taper to the ideal explicit wavefield extrapolation filter.
This leads to a stable extrapolation filter as described in Nautiyal *et* *al*, 1993.
The Gaussian taper is given by )
where is a parameter to
be chosen.
Figure
shows the amplitude spectrum for the ideal and
the tapered extrapolator . The extrapolation filter in two dimensions is
a symmetric filter with complex coefficients. Figure
shows the absolute
magnitude of the filter coefficients. Using the filter coefficients for
the tapered extrapolator, I generated the corresponding 3-D extrapolator
(Figure ) at
the frequency using the McClellan transformation. Compare this
3-D extrapolator with the ideal one shown in Figure .

explicit
The ideal 2-D wavefield extrapolator (continuous curve) and
the tapered extrapolator (dashed curve) in wavenumber domain.
Figure 8 |

migfil
The magnitude of the tapered extrapolator in space domain. The filter
coefficients are complex. It is a nineteen coefficient symmetric operator.
The spatial wavelet magnitude is shown for one side.
Figure 9 |

Figure 10

11/17/1997