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 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

VVPk/κ

1�

��Bulk modulus:

� = compressibility

tanθτµ �Shear modulus:

The shear modulus ��is zero for fluids and gaseous media

∆L/LF/A

�

∆L

��is the shear stress

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

�

��

-

L+

µ3k9kµE�

�

��= 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

Ratio Vp and Vs depends on Poisson ratio:

�

�

�

�

�

p

s

VV

�

��

where

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.

• Calculate the reflection coefficient for a wave that travels up and reflects at the free-surface of the see

� �air=10-3 kg/m3, �water=1.025kg/m3

• Vair=0.3 m/s, vwater= 1.4 m/s)

Rv2�2 v1�–v2�2 v1�+= = -0.99958 = -1