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Important for :
Conversion from traveltime to depth
Check of results by modelling
Imaging of the data (migration)
Classification and Filtering of Signal and Noise
Predictions of the Lithology
Aid for geological Interpretation
• Depend on medium properties
• Can be written as function of physical quantities
that describe stress/strain relations
• Measurements of velocities
• Definitions of velocities (interval, rms, average
etc.)
• Dix formula: relation between rms and interval
velocities
• Anisotropy
Depend on
• Matrix and structure of the stone
• Lithology
• Porosity
• Porefilling interstitial fluid
• Temperature
• Degree of compaction
• ………
Seismic Velocity depending on rock properties
(Sheriff und Geldard, 1995)
Physical quantities to describe stressstrain properties of isotropic medium
• Bulk modulus
k
volume stress/strain
• Shear modulus
m
shear stress/strain
• Poissons ratio
s
transverse/longitudinal strain\
• Young’s modulus
E
longitudinal stress/strain
Bulk modulus:
k = compressibility
P
1
k= =
κ DV / V
∆L
F/A
=
∆L/L
Shear modulus:
τ
µ=
tanθ
t is the shear stress
The shear modulus m is zero for fluids and gaseous media
-
Poisson’s ratio varies from 0 to ½.
Poisson’s ratio has the value ½ for fluids
=
+
L+
9kµ
E=
3k + µ
Seismic Velocities in a homogeneous medium
Can be espressed as function of different combinations of
K, s, E, m, r, l
Often used expressions
are:
k = Bulk modulus
s = Poisson ratio
4µ
k+
λ + 2µ
3
vp =
=
ρ
ρ
µ
vs =
ρ
E = Young’s modulus
m = Shear modulus
r = mass density
l = Lame’s lambda constant
2
λ=k- µ
3
Ratio Vp and Vs depends on Poisson ratio:
-s
-s
Vs
=
Vp
where
=
+
Measurements of velocities
• Laboratory measurements using probes
• Borehole measurements
• Refraction/Reflection seismics
• Analysis of reflection hyperbolas
P-wave velocities vp for different material in (km/s)
Unconsolidated Material
Sand (dry)
Sand (water saturated)
Clay
Glacial till (water saturated)
Permafrost
0.2 - 1.0
1.5 - 2.0
1.0 - 2.5
1.5 - 2.5
3.5 - 4.0
Sedimentary rocks
Sandstone
Tertiary sandstone
Pennant sandstone (Carboniferous)
Cambrian quartzite
Limestones
Cretaceous chalk
Jurassic oolites and bioclastic limestones
Carboniferous limestone
Dolomites
Salt
Anhydrite
Gypsum
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
Kearey and Brooks, 1991
P-wave velocities vp for different material in (km/s)
Igneous / Metamorphic rocks
Granite
Gabbro
Ultramafic rocks
Serpentinite
5.5 - 6.0
6.5 - 7.0
7.5 - 8.5
5.5 - 6,5
Pore fluids
Air
Water
Ice
Petroleum
0.3
1.4 - 1.5
3.4
1.3 - 1.4
Other materials
Steel
Iron
Aluminium
Concrete
6.1
5.8
6.6
3.6
Kearey and Brooks, 1991
Interval-Velocity
Instantaneous Velocity
VI =
zm - zn zm - zn
=
tm - tn
τm
dz
Vinst =
dt
n
n
å z åv τ
i
Average-Velocity
Vav =
=
i =1
n
åτ
i =1
i i
i
i =1
n
åτ
i =1
i
tm : measured reflected ray traveltime
tm : one-way reflected ray traveltime only through mth layer
Several horizontal layers
V1, t1
t1
t2
v2 , t2
Measured
traveltimes
v3 , t3
n
RMS-velocity (root-mean-square)
v2 =
rms
t3
åv τ
2
i i
i =1
n
åτ
i =1
i
Dix’ Formula
Conversion from v rms in vint (interval velocities)
é (VRMS , n )2 tn - (VRMS , n - 1)2 tn - 1 ù
V int = ê
ú
n - tn - 1
t
ë
û
VRMS , n - 1
tn - 1
tn
VRMS , n
n-1
V int
n
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)
Fast
Slow
Anisotropy(seismic): Variation of seismic velocity depending
on the direction in which it is measured.
• Calculate the reflection coefficient for a
wave that travels up and reflects at the freesurface of the see
• rair=10-3 kg/m3, rwater=1.025kg/m3
• Vair=0.3 m/s, vwater= 1.4 m/s)
R =
v 2 r2 – v1 r
v2 r 2 + v 1 r
=
-0.99958 = -1