important for : conversion from traveltime to depth check of · pdf filedepend on •...
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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• ………
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
tanθτµ �Shear modulus:
The shear modulus ��is zero for fluids and gaseous media
∆L/LF/A
�
∆L
��is the shear stress
��= Shear modulus
ρ2µλ
ρ3
4µkp
��
�
�v
ρµ
�sv
��= Lame’s lambda constant µ32kλ ��
Seismic Velocities in a homogeneous medium
k = Bulk modulus
� = mass density
Can be espressed as function of different combinations ofK, �, E, �, �, �
Often used expressionsare:
E = Young’s modulus� = Poisson ratio
Measurements of velocities
• Laboratory measurements using probes
• Borehole measurements
• Refraction/Reflection seismics
• Analysis of reflection hyperbolas
Kearey and Brooks, 1991
0.2 - 1.01.5 - 2.01.0 - 2.51.5 - 2.53.5 - 4.0
2.0 - 6.02.0 - 2.54.0 - 4.55.5 - 6.02.0 - 6.02.0 - 2.53.0 - 4.0 5.0 - 5.5 2.5-6.54.5 - 5.0 4.5 - 6.52.0 - 3.5
Unconsolidated MaterialSand (dry)Sand (water saturated)ClayGlacial till (water saturated)Permafrost
Sedimentary rocksSandstoneTertiary sandstonePennant sandstone (Carboniferous)Cambrian quartziteLimestones Cretaceous chalkJurassic oolites and bioclastic limestonesCarboniferous limestoneDolomites SaltAnhydrite Gypsum
P-wave velocities vp for different material in (km/s)
5.5 - 6.0 6.5 - 7.0 7.5 - 8.5 5.5 - 6,5
0.3 1.4 - 1.53.41.3 - 1.4
6.15.86.63.6
Igneous / Metamorphic rocksGraniteGabbroUltramafic rocksSerpentinite
Pore fluidsAirWaterIcePetroleum
Other materialsSteel Iron AluminiumConcrete
P-wave velocities vp for different material in (km/s)
Kearey and Brooks, 1991
Interval-Velocity
Instantaneous Velocity
Average-Velocity
m
nm
nm
nmI
τzz
ttzzV �
�
�
�
�
tz
ddVinst �
�
�
�
�
�
�
�
�
�� n
ii
n
ii
n
ii
n
ii
av
vzV
1
1i
1
1
τ
τ
τ
tm : measured reflected ray traveltime�m : one-way reflected ray traveltime only through mth layer
V1, �1
v2 , �2
v3 , �3
RMS-velocity (root-mean-square)
Several horizontal layers
�
�
�
�
� n
ii
n
iii
rms
vv
1
1
2
2
τ
τ
t1
t2 t3
Measured traveltimes
Conversion from vrms in vint (interval velocities)
Dix’ Formula
nRMSV ,
n-1
nintV
� � � ���
���
�
�
��
�
��
1
12
1,2
,int
nn
nnRMSnnRMS
tttVtVV
1, �nRMSV
nt
1�nt
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.