Spatial Interpolation of Steep Dips
, by Dave Hale
A common misconception is that, to avoid spatial aliasing, we must spatially
sample our seismic data at a wavenumber (spatial frequency) twice the highest
wavenumber contained in our data. Since high wavenumbers correspond to steeply
dippping events, we tend to think that steep dips imply spatial aliasing. This
paper attacks this misconception by showing (1) that the range, not the absoulte
magnitude, of dips present in our data determines whether or not the data is
spatially aliased; and (2) that this range of dips need only be restricted locally,
that the range may change from sample to sample without danger of aliasing.
Aliasing implies an inablity to accureatedly reconstruct a continous wavefield
from the discrete data obtained by sampling; i.e., it implies an inability to
interpolate correctly. Actually, correct interpolation requires only knowledge
of the limited range of dips present at any given sample and of how that range
changes form sample to sample. This knowledge is often obtainable with seismic
data, and an example is provided to illustrate and interpolation method based
on this knowledge.
STANFORD