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

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

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

Bulk modulus

VV

Pk

/κ

1

Bulk modulus:

= compressibility

Shear modulus

tanθ

τμ Shear modulus:

The shear modulusis zero for fluids and gaseous media

ΔL/L

F/A

ΔL

is the shear stress

Poissons ratio

Poisson’s ratio varies from 0 to ½. Poisson’s ratio has the value ½ for fluids

μ)2(3k

2μ3kσ

-

Young’s modulus

L+

μ3k

9kμE

= Shear modulus

ρ

2μλ

ρ3

4μk

p

v

ρ

μsv

= Lame’s lambda constant μ3

2kλ

Seismic Velocities in a homogeneous medium

k = Bulk modulus

= mass density

Can be expressed as function of different combinations ofK, , E, , ,

Often used expressionsare:

E = Young’s modulus

= Poisson ratio

Ratio Vp and Vs depends on Poisson ratio:

1

5.0

p

s

V

V

μ)2(3k

2μ3kσ

where

Seismic velocityDepend 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)

Measurements of velocities

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

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)

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

Interval-Velocity

Instantaneous Velocity

Average-Velocity

m

nm

nm

nmI

τ

zz

tt

zzV

t

z

d

dVinst

n

ii

n

ii

n

ii

n

ii

av

vzV

1

1i

1

1

τ

τ

τ

Velocities

tm : measured reflected ray traveltimem : 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 v rms in vint (interval velocities)

Dix’ Formula

nRMSV ,

n-1

n

intV

1

12

1,2

,int

nn

nnRMSnnRMS

tt

tVtVV

1, nRMSV

nt

1nt

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

Anisotropy

Slow

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