Seismic Velocities

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Seismic Velocities
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
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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

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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
• Youngs modulus E longitudinal stress/strain

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Bulk modulus
Bulk modulus
k compressibility
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Shear modulus
Shear modulus
t is the shear stress
The shear modulus m is zero for fluids and
gaseous media
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Poissons ratio
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Poissons ratio varies from 0 to ½. Poissons
ratio has the value ½ for fluids
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Youngs modulus
L
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Seismic Velocities in a homogeneous medium
Can be expressed as function of different
combinations of K, ?, E, ?, ?, ? Often used
expressions are
k Bulk modulus
? Poisson ratio
E Youngs modulus
m
Shear modulus
? mass density
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Ratio Vp and Vs depends on Poisson ratio
where
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Seismic velocity

• Depend on
• Matrix and structure of the stone
• Lithology
• Porosity
• Porefilling interstitial fluid
• Temperature
• Degree of compaction

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Seismic Velocity depending on rock properties
(Sheriff und Geldard, 1995)
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Measurements of velocities

• Laboratory measurements using probes
• Borehole measurements
• Refraction seismics
• Analysis of reflection hyperbolas
• Vertical seismic profiling

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P-wave velocities vp for different material in
(km/s)
Kearey and Brooks, 1991
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P-wave velocities vp for different material in
(km/s)
Kearey and Brooks, 1991
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Velocities
Interval-Velocity
Instantaneous Velocity
Average-Velocity
tm measured reflected ray traveltime tm
one-way reflected ray traveltime only through mth
layer
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Several horizontal layers
t1
V1, ?1
t2
t3
v2 , t2
Measured traveltimes
v3 , t3
RMS-velocity (root-mean-square)
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Dix Formula
Conversion from v
in vint (interval velocities)
rms
n-1
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)
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Anisotropy
Fast
Slow
Anisotropy(seismic) Variation of seismic
velocity depending on the direction in which it
is measured.