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
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.