Annual Report 2000 - WIT

84
Residual Fresnel Zone (m)
2000
1500
1000
500
__ Exact
--- 2nd Order
... Difference
xx Migration
0
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Source-Receiver Offset (m)
Figure 7: Fresnel zone as a function of offset. Shown are the exact (solid line) and
paraxial (dashed line) sizes of the Fresnel zone, their difference (dotted line) and the
estimated resolution region (crosses) after Kirchhoff depth migration.
is reached only with perfect, that is, noise-free, correctly sampled, unbiased, data.
Any additional distortion due to the wave propagation in an inhomogeneous reflector
overburden, such as transmission losses, focusing and defocusing, caustics, etc., as
well as acquisition effects such as irregular source and receiver spacing, source and
receiver coupling, uncalibrated traces, etc., will not only affect the recovery of the best
possible amplitudes but will also degrade the seismic resolution.
SUMMARY
In this paper, we have discussed horizontal resolution of true-amplitude Kirchhoff
depth migration in dependence on the source-receiver offset. We have seen that the
region around the reflection point affected by the reflected wavefield after migration is
closely related to the difference between the time-domain Fresnel zone and its paraxial
approximation. Since this difference increases with offset as the paraxial approximation
is getting worse, so does the resolution power of seismic migration. A possible
explanation of this behaviour is that Kirchhoff migration is an algorithm that is based