presents a simple algorithm based on the Kirchoff
integral to perform the wavefield transformation from one datum
(U(x,z=z1 ,t)) to another (U(x,z=z2 ,t))
Each individual trace Uj (t) comprising U(x,z=z2 ,t) is calculated by
performing the sum:
where Qi(t-ti) is a filtered input trace recorded at location i
and delayed by traveltime ti.
is the input trace interval, is the angle between
the normal to the surface at z=z2 and the line ri connecting Uj and
Ui. The geometry of the transformation is illustrated in Figure .
A complete derivation of this equation is presented in Berryhill
Figure 1 Geometry for the continuation of a wavefield between an irregular
topography and a planar datum (after Berryhill, 1984)
My proposed method may be summerized in three steps:
- Extrapolate the data upwards to a flat datum (by using
equation ( 1)). This should unravel the distortions
caused by the irregular acquisition topography.
- Perform velocity analysis at the flat datum. This determines the
near-surface velocity structure.
- Either perform the processing and imaging or extrapolate
downward to some flat datum below the acquisition topography.
Stanford Exploration Project