velocity Analysis in Post stack processing will help to enhance seismic section quality

1. Important for :
Conversion from traveltime to depth
Check of results by modeling
Imaging of the data (migration)
Classification and Filtering of Signal and Noise
Predictions of the Lithology
Aid for geological Interpretation
Seismic Velocities

2. Seismic velocities
 Can be written as function of physical quantities
that describe stress/strain relations
 Depend on medium properties
 Measurements of velocities
 Definitions of velocities (interval, rms, average
etc.)
 Dix formula: relation between rms and interval
velocities
 Anisotropy

3. Physical quantities to describe stress-strain
properties of isotropic medium
 Bulk modulus k volume
stress/strain
 Shear modulus  shear
stress/strain
 Poissons ratio  transverse/longitudinal
strain
 Young’s modulus E longitudinal stress/strain

4. Bulk modulus
V
V
P
k
/
κ
1



Bulk modulus:
 = compressibility

5. Shear modulus
tanθ
τ
μ 
Shear modulus:
The shear modulusis zero for fluids and gaseous media
ΔL/L
F/A

ΔL
is the shear stress

6. Poissons ratio
Poisson’s ratio varies from 0 to ½.
Poisson’s ratio has the value ½ for fluids
μ)
2(3k
2μ
3k
σ



-

7. Young’s modulus
L+
μ
3k
9kμ
E



8. 
= Shear modulus
ρ
2μ
λ
ρ
3
4μ
k
p




v
ρ
μ

s
v

= Lame’s lambda constant μ
3
2
k
λ 

Seismic Velocities in a homogeneous medium
k = Bulk modulus
 = mass density
Can be expressed as function of different combinations of
K, , E, , , 
Often used expressions
are:
E = Young’s modulus
 = Poisson ratio

9. Ratio Vp and Vs depends on Poisson ratio:





1
5
.
0
p
s
V
V
μ)
2(3k
2μ
3k
σ



where

10. Seismic velocity
Depend on
 Matrix and structure of the stone
 Lithology
 Porosity
 Porefilling interstitial fluid
 Temperature
 Degree of compaction
 ………

11. Seismic Velocity depending on rock properties
(Sheriff und Geldard, 1995)

13. Measurements of velocities
 Laboratory measurements using probes
 Borehole measurements
 Refraction seismics
 Analysis of reflection hyperbolas
 Vertical seismic profiling

14. Kearey and Brooks, 1991
Unconsolidated Material
Sand (dry)
Sand (water saturated)
Clay
Glacial till (water saturated)
Permafrost
Sedimentary rocks
Sandstone
Tertiary sandstone
Pennant sandstone (Carboniferous)
Cambrian quartzite
Limestones
Cretaceous chalk
Jurassic oolites and bioclastic limestones
Carboniferous limestone
Dolomites
Salt
Anhydrite
Gypsum
0.2 - 1.0
1.5 - 2.0
1.0 - 2.5
1.5 - 2.5
3.5 - 4.0
2.0 - 6.0
2.0 - 2.5
4.0 - 4.5
5.5 - 6.0
2.0 - 6.0
2.0 - 2.5
3.0 - 4.0
5.0 - 5.5
2.5-6.5
4.5 - 5.0
4.5 - 6.5
2.0 - 3.5
P-wave velocities vp for different material in (km/s)

15. Igneous / Metamorphic rocks
Granite
Gabbro
Ultramafic rocks
Serpentinite
Pore fluids
Air
Water
Ice
Petroleum
Other materials
Steel
Iron
Aluminium
Concrete
5.5 - 6.0
6.5 - 7.0
7.5 - 8.5
5.5 - 6,5
0.3
1.4 - 1.5
3.4
1.3 - 1.4
6.1
5.8
6.6
3.6
P-wave velocities vp for different material in (km/s)
Kearey and Brooks, 1991

18. Interval-Velocity
Instantaneous Velocity
Average-Velocity
m
n
m
n
m
n
m
I
τ
z
z
t
t
z
z
V





t
z
d
d
Vinst 









 n
i
i
n
i
i
n
i
i
n
i
i
av
v
z
V
1
1
i
1
1
τ
τ
τ
Velocities
tm : measured reflected ray traveltime
m : one-way reflected ray traveltime only through mth
layer

19. V1, 1
v2 , 2
v3 , 3
RMS-velocity (root-mean-square)
Several horizontal layers




 n
i
i
n
i
i
i
rms
v
v
1
1
2
2
τ
τ
t1
t2 t3
Measured
traveltimes

20. Conversion from vrms in vint (interval velocities)
Dix’ Formula
n
RMS
V ,
n-1
n
int
V
   












1
1
2
1
,
2
,
int
n
n
n
n
RMS
n
n
RMS
t
t
t
V
t
V
V
1
, 
n
RMS
V
n
t
1

n
t
Vrms is approximated by the stacking velocity that is obtained by
NMO correction of a CMP measurement.
(when maximum offset is small compared with reflector depth)

21. Fast
Anisotropy
Slow
Anisotropy(seismic): Variation of seismic velocity depending
on the direction in which it is measured.