02defin

2.1

Velocity Definitions 1

Abnormal moveout velocity, Air wave velocity, Apparent velocity, Average interval velocity, Average velocity, Background velocity, Channel wave velocity, Compressional wave velocity, Conversion velocity, Converted wave velocity, Depth normalized interval velocity, Dilatational wave velocity, Direct wave velocity, Distortional wave velocity, Diving wave velocity, Dix interval velocity, Elevation velocity, Equivalent velocity, Formation velocity, Ground roll velocity, Group velocity, Head wave velocity, Horizontal velocity, H-wave velocity, Hydrodynamic wave velocity, Instantaneous velocity, Interval stacking velocity, Interval velocity, Longitudinal wave velocity, Long wave velocity, Love wave velocity, Marker velocity, Migration velocity, Moveout velocity, Normal moveout velocity, Optical stacking velocity, Particle velocity, Phase velocity, Primary velocity, Primary wave velocity, Pseudo velocity, Pseudo Rayleigh wave velocity, P-wave velocity, Rayleigh wave velocity, Refraction velocity, Replacement velocity, Root mean square velocity, Root mean square interval velocity, Sample velocity, Seam wave velocity, Secondary wave velocity, Seismic wave velocity, Sezawa M2 wave velocity, Shear wave velocity, SH wave velocity, Small aperture migration velocity, Sonic velocity, Stacking velocity, Stoneley wave velocity, Sub-weathering velocity, Surface SH wave velocity, Surface wave velocity, SV wave velocity, S-wave velocity, Transverse wave velocity, Trapped wave velocity, Tube wave velocity, Up-hole velocity, Vertical velocity, Water velocity, Wave velocity,Weathering velocity.

There are morethan 70 velocitydefinitions. Wewill consideronly a few.


Speed = length / time Velocity = speed in a given direction Slowness = 1 / velocity

2.2


Average Velocity VAThe ratio of a given distance along a certain path to the time required for a seismic wave to traverse the path. While it has meaning only with respect to a particular path, a vertical path is often implied, that is, it is given by a depth, z, divided by a one-way seismic traveltime, t, to that depth, usually assuming straight raypath travel.

VA = z / t


Measured by determining the travel time over an interval in the subsurface, usually along a vertical raypath. The value is the average velocity of the interval. It is the velocity most often used in models.

Average Interval Velocity VI

VIj = zj / tjlayer j

2.3


Average Velocity VAFor the following model calculate the average velocity to the second reflector.

VA = z / tThickness VI1500 m 2000 m/s

Thickness VI1000 m 4000 m/s

z


Average Velocity VASuppose we now change the model, we keep the two lithologies but instead of two massive units, we nowinterbed the lithologies with a geological wavelength d.

How do we find the average velocity?

VELOCITY

DE

PTH

2000 4000

d

2.4


The Average Velocity is found according to:

1 / VA = r1 / V1 + r2 / V2

Where r1 and r2 are the proportional thicknesses of the layers such that r1 + r2 = 1

Geologists will recognize this as Wylies time-average equation.

VA =

VELOCITY

DE

PTH

2000 4000

PR

OP

OR

TIO

N

0.6 PR

OP

OR

TION

0.4Average Velocity VA


This average velocity is only valid for predicting seismic travel times when the wavelength of the seismic wavelet, , is less than ~5 interbedded cycles, geological wavelength,d.

This form of average velocity is also known as the ray theoretical average velocity.

VELOCITY

DE

PTH

V1 V2

PR

OP

OR

TIO

N r 1 PR

OP

OR

TION

r2

Average Velocity VA

2.5


VELOCITY

DE

PTH

V1 V2

PR

OP

OR

TIO

N r 1 PR

OP

OR

TION

r2

When the seismic wavelength is much greater than the layering thickness the velocity needed to correctly model the travel time of a seismic wave through the finely layered section is: -

The effective medium velocity :

VBAC = 1/[r1/V12 + r2/V22]it comes from Backus (1962).

Backus Average Velocity VBAC


Backus Average Velocity VBACThis velocity is also known as the Effective Medium Velocity.

VBAC = 1/[r1/V12 + r2/V22]=

How does the value compare with the ray theoretical average velocity?

VELOCITY

DE

PTH

2000 4000

PR

OP

OR

TIO

N

0.6 PR

OP

OR

TION

0.4

2.6


Velo

city

0.1 1 10 100/d

Ray theoreticalaverage velocity

Effective mediumvelocity

5 12

See Marion et al, 1994, Velocity dispersion in stratified media, Geophysics.

Average Velocity VAThe average velocity of a seismic wavelet depends on its wavelength with respect to the bed thicknesses of the layers

2500 m/s

2390 m/s


Average Velocity VA

Log Seismic

2.7


Instantaneous Velocity Vi

Instantaneous velocity is the velocity of a wavefront in the direction of energy propagation.

Vi = f ( x, y, z, r, Vi)

The velocity log is a good representation of the instantaneous velocity in the direction of the borehole -often vertical, in which case we make the simplification

Vi = dz / dt


Pseudo Velocity(Apparent, Effective)

An estimate of average velocity calculated from seismic reflection time and measured well depth.

TIM

E

DEP

TH

2.8


Root Mean Square (RMS) Velocity VRMSRoot mean square velocity is not a measurable velocity, it is calculated for a given model according to the following formula:

where VIj is the average interval velocity in the jth layer, tj the one-way vertical traveltime in the jth layer, to is the vertical incidence reflection time to the base of the Nth layer.

N.B. RMS formulae work with either one or two-way time.

1

j

N

VIj , tj

to

tRMS

Ij j

VV=

2j

j N ==

1

tj

j N

=

=

1j


Vi = dz/dt

VI = (z2-z1)/(t2-t1)= z/t

VA = z3/t3

Pseudo velocity= zlog/tseismic

Summaryt

z

VA

VI

Vi

t1 t2 t3

z1

z2

z3

2.9


Velocity Curves

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

6000

8000

10000

12000

14000

16000

18000

20000

22000

Velocity ft/sec

Dep

th ft

Average Instantaneous Interval

Summary


SummaryAverage Velocity: VA = z/t

Ray theoretical average velocity:1 / VA = r1 / VI1 + r2 / VI2 with r1 + r2 =1

Backus average velocity:VBAC = 1/[r1/VI12 + r2/VI22] with r1 + r2 =1

Interval Velocity: VI = z / tInstantaneous Velocity: Vi = dz / dt

Pseudo velocity = zlog/tseismic

DefinitionsExercise 2.1

The supplied CD contains the dataset as the file Ex 2.1.xls so you may do the exercise in a spreadsheet.

The following table gives checkshot values to key formation boundaries from well A that we will make use of in exercises throughout this course. The results of this exercise will be useful in later exercises. Well A was drilled at SP 78394 on the seismic line that we will interpret later.

Calculate the interval velocities for each formation and the average velocities to the layer boundaries.

z ft t sec0 0.0000

108 0.0223734 0.1275

1283 0.21301672 0.26502424 0.37854852 0.60776608 0.75207927 0.82628243 0.8527

2.10

Definitions

2.11

Definitions

The wavelet in the seismic data at the depth of the indicated formation is 20 msec long and the average velocity is 8000 ft/sec.Based on the scale of interbedding and seismic wavelength should we use a ray theoretical average velocity or an effective medium velocity? (Velocity = wavelength x frequency)

If we acquired checkshots at the top and bottom of the formation A what interval velocity would you anticipate if the two lithologies involved have velocities of 16,000 ft/sec and 11,000 ft/sec and their thicknesses are in the proportions 0.59 to 0.41?

Exercise 2.2

140 90 40 sec/ft10

0 ft

Data courtesy of ARCO British Ltd

Formation A

2.12

Definitions

2.13

02defin

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