Seismic method - Geophysics for the Mineral Exploration Geoscientist - page 376

correction for values of T 0 , varying from zero to the max-
imum time of interest, assuming the subsurface has a
constant velocity, for example using Eq. (6.19) .
Figure 6.21c shows the NMO-corrected CMP gathers for
six different correction velocities, the velocity used being
least for the gather on the left, increasing to the right.
These velocities have been speci cally chosen relative to
the V rms of each of the three re ections (V a , V b and V c in
Fig. 6.21a ) . With real data, the correction would be applied
using velocities in a range expected for the survey area,
creating perhaps 20 corrected gathers. Some real examples
are presented by Gibson ( 2011 ). Consider first the appear-
ance of the shallowest (least time) reflection in each of the
corrected gathers. With the correction velocity less than V a
it curves upward with increasing offset. Recall that the
purpose is to flatten the arrival, so in this case its NMO
has been over-corrected because the velocity used is too
low. This re

correction, the traces are stretched in time, more so with
increasing offset. This distorts (stretches) the arrivals and
when it exceeds a speci ed limit the data are muted (set to
zero) to avoid introducing noise into the stacked trace. The
summation of the muted and NMO-corrected traces pro-
duces the final stacked trace ( Fig. 6.21g ). Notice how the
amplitudes of the primary re ections are enhanced and
that they occur at their zero-offset times (T 0 ).
Stacking makes the assumption that the arrivals being
analysed are reflections from planar horizontal interfaces.
Dipping interfaces produce different travel time curves and
the estimated velocities will be incorrect, although they will
still allow the data to be effectively stacked if dips are not
too steep and so the travel time curves not too altered.
Varying dip directions may cause problems (see Pre-stack
time migration and dip-moveout processing in Section
6.5.2.5 ) . Also, if the interfaces dip, the re ection point is

flattened when the velocity equals V a .
As progressively higher velocities are used, two are found
(V b and V c ) that flatten the second and third re ections.
For a velocity greater than V c , all the re ections are under-
corrected because the velocity used is too high.
The velocity that attens a re ected arrival is the correct
velocity for removing the arrival

ection is no longer at the source - detector midpoint and is different

for each source detector pair in the CMP gather. For

moderate dips the displacements of the re ection points
are not large and are not a major problem because the
seismic waves are actually re ected from a (Fresnel) zone,
not a point (see Section 6.7.1.1 ). In general, stacking is a
very robust procedure and is still very effective even when
the geological environment is more complex than is
assumed in the way that it is implemented.

-

s NMO, and the attened
arrival will have an arrival time equal to T 0 . The velocity
that

'

'

s
stacking velocity (V stack ). It has a complicated relationship
with the true velocity of the subsurface; it depends upon
factors such as the heterogeneity of the geology and the
algorithm used to determine when a reflector is optimally
flattened (Al-Chalabi, 1974 ) . Figure 6.21d shows T 0 of each
flattened reflector plotted against the stacking velocity that
flattened it. Interpolating between three data points allows
V stack to be estimated for any value of T 0 , creating a
stacking velocity versus re

attens the re ector is known as the re ector

Stacking 3D data
The stacking of 3D seismic reflection data is, in principle,
the same as for 2D data. In sorting the 3D data to form
CMP gathers, variable source detector azimuth is a poten-

tial problem if the reflector is dipping, which must be
accounted for prior to NMO-correction and stacking.
Otherwise, stacking proceeds in a similar way to 2D data,
although the fold of the stack is generally smaller for 3D
surveys.

-

ection time function. Using
Eq. (6.19) , a travel time curve can be obtained for each
value of T 0 ( Fig. 6.21e ) . Note that moveout of re

ections
from deeper interfaces is less and the NMO correction is
less sensitive to the assumed velocity. This facilitates
stacking, but means that the stacking velocity versus re ec-
tion time function is less constrained for larger times, i.e.
velocity information from greater depths is less reliable.
Figure 6.21e shows that the travel time curves of the
re ections converge with increasing offset; compare

Display of stacked data
The stacked seismic data are displayed in a similar way to a
shot gather ( Fig. 6.13 ), i.e. the time scale is common but
the amplitude of each trace is individually scaled and the
relative positions of the traces are controlled by their
relative locations ( Fig. 6.20d ) . For stacked data the relative
positions of the traces is based on the locations of their
common midpoint. Note that the data are always displayed
with re ection time (TWT) increasing downwards, so as to
mimic a depth section. The coloured traces in the figure
identify the normal-incidence stacked traces produced

Δ T Near

Δ

and T Far . The NMO correction of the CMP gather will

flatten all these curves, i.e. they will be parallel, and in so
doing the primary reflections are flattened in preparation
for summation, as shown in Fig. 6.21f . During NMO