Geoscience Reference
In-Depth Information
P
O
O
d
Velocity v
S
θ
Fig. 3.27
Zero-offset reflection ray-path for a dipping layer.
shift reflectors by large distances laterally. Consider the very simple case shown in
fig. 3.27
, where a single dipping reflector is overlain by constant-velocity overburden.
An identifiable point S on the reflector (perhaps a small fault) will be imaged on the
stack section below the point O where the zero-offset ray intersects the surface; OS is
perpendicular to the reflector. The migration process has to shift the image laterally to
the true location below P, over a distance
d
. Then
d
=
OS sin
θ
and if the two-way travel time for the zero-offset ray is
t
, then
=
v
t
2
d
sin
θ.
Of course, we do not directly observe the true dip in depth, but rather the dip on the
(unmigrated) time section, the rate of change of
t
with
d
, which is given by
2 sin
θ
v
.
Call this quantity
q
. Then
2
t
4
d
=
v
t
2
·
q
2
=
v
·
q
.
The error
δ
in
d
due to an error
δv
in
v
is then given by
qt
4
δ
=
2
vδv
·
,
or
d
=
2
δv
v
.
For example, suppose the overburden velocity is 3000 m/s. For an event at 2 s two-way
time with a dip of 15
◦
, the lateral shift would be 3000sin 15
◦
, or 776 m. A 2% error in
