### Velocity_Analysis

```Velocity Analysis
Yilmaz, ch 3.1-3.3.2
Introduction to Seismic Imaging
ERTH 4470/5470
Figs 3-1 to 3-3
• Velocities of sediment and sedimentary and
volcanic rocks increase with depth.
• For sediment this is due to compaction of
pore space with increasing pressure.
• Increase in rock velocity is due to closure of
cracks with increasing pressure.
Normal Moveout (NMO) Correction
for Flat Layers
Normal Moveout Correction (NMO)
x
t
ec
dir
iva
arr
/v
=x
l td
to
t
l tr
rriva
ted a
c
le
f
re
tr
For single layer (Figs. 3-4, 3-6 and 3-8). NMO
depends on {x2/v2}, so we need to know v(z) in
order to flatten CMP gather before stacking. For
brute stack we assume a constant velocity (e.g.
water) for simplificity, while knowing that this will
not give a good image for deeper structures.
time
Shot
R
R
2
2 1/2
2(x /4 +h )
V
h
Z=h
x/2
Z
2
2
tr 
x
 h2
4
v
2h
v
2
x
4h 2 x 2
t r2  2  2  2  t o2
v
v
v
to 
plot of tr2 vs x2 is linear
  x 2 
t r  t o 1    
  vto  


1/ 2
using binomial expansion we get
2
4


 x 
 x 


t r  t o 1  1 2    18    
vt
vt


 o
 o


for x  2h ,
2
x
 1 and t NMO  t r  t o  x
2v 2 t o
vto
(This is the NMO correction)
•
For multiple layers, t2 = t2(0) + x2/vrms2,
so plots of t2 vs x2 will give a straight
line with slope of 1/vrms.
•
The root-mean square velocity (vrms) is
determined by eq. 3.4 in terms of the
interval velocity (vi) and travel time
(Δti) of each layer interval (i). (Figs. 3.9
to 3-11)
For “real” data, we expect moveout of reflectors to decrease with depth (=time)
as velocity increases with depth due to compaction
Various definitions of velocity (Box6.4)
2t
0
0.4
0.8
1.2
1.6
t
0.2
0.4
0.6
0.8
v
2
2.5
3
3.5
4
Vrms
0
1.6
4.1
7.7
12.6
2
2.263846
2.533114
2.806243
z
0
0.4
0.9
1.5
2.2
Vavg
2
2.25
2.5
2.75
•
•
Notice difference between vrms and vav
but it is small
Note also that vnmo = vrms only for the
(Fig. 3-22). For larger spread offsets,
the best fit to flatten the actual
moveout is not the same.
For continuous data (not individual picks) we need to
flatten arrivals (ie remove increase in t as function of x
and v) by stretching the time axis.
This results in non-linear expansion
of the time axis, which is greater for
larger x and smaller v.
This changes the frequency of the
arrivals. (Fig. 3-13 and Table 3-2).
When this effect becomes too large
(generally in the upper 1-2 sec
TWTT), we need to mute the result
(Fig. 3-12).
This can be done automatically for
stretching greater than a certain
amount, or by picking the front mutes
by hand as we did to remove the
refraction arrivals. (Fig. 3-14).
Methods for Velocity Analysis
Synthetic example with 4 layers showing CMP gather, velocity spectrum and t 2-x2 plots.
Spectrum is unnormalized, cross-correlation sum with a gated row plot.
Real example with 4 primary layers and
multiple secondary layers.
Spectrum is unnormalized, cross-correlation
sum with contour plot.
Use of constant-velocity gathers (CVG) for a single CMP gather at various velocities to help
detail exact nature of stacking velocities
Use of constant velocity stack (CVS) for range of gathers at different stacking
velocities. Helpful in sections of low signal-to-noise (e.g. at greater depths in the
section)
Limitations in accuracy and resolution
of velocity estimates
Synthetic examples of 4 layers
showing various plots of velocity
spectra.
Lack of long offsets reduce
resolution of lower (high velocity)
layers with smaller moveout
Lack of near-offsets reduce
resolution of shallow layers
Partial stacking (using
incomplete fold) can save
money (computer time) but
can result in reduced
resolution
Reduced resolution caused by decrease in signal-to-noise
Effect of dipping layer
Effect of dip is only significant when dip
angle is large (i.e. > 20o)
```