Migration

DP START Oslo
2004
 At the end of this Session, you will be able to:
• Define the term ‘migration’ and describe why we need to migrate seismic data.
• Define the term ‘diffraction energy’.
• Describe how the application of migration can affect dipping events and diffraction energy.
• To introduce the importance of the velocity field in the process of migration.
• Define the terms ‘under migration’ and ‘over migration’ in relation to a migration velocity
field.
• Describe at least 3 ways in which a stacking velocity field may be manipulated to improve
its suitability for the post-stack migration.
• Describe at least 2 reasons why scaling of stacking velocity fields may be required prior to
their use in migration.
• Define the term ‘migration smile’.

DP START Oslo
2004
 The Routemap

 What is, and why perform, migration ?

 What types of migration are there ?

 What does the choice of migration type depend on ?

 What velocities do we use for migration ?

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 What is Migration and why do we need to
Migrate seismic data ?

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 What is Migration ?

 Migration is a process which attempts to correct the

distortions of the geological structure inherent in the
seismic section

 Migration re-distributes energy in the seismic section

to better image the true geological structures

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2004
 Why Migrate ?
 Rearrange seismic data so that reflection events
may be displayed at their true position in both space
and time.
 laterally in up-dip direction
 upward in time

 Collapse diffractions back to their point of origin

 Improve lateral resolution - collapse Fresnel zone

 To obtain more accurate velocity information (when performed

pre-stack)

 For more accurate ‘depth’ section

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2004
 Apparent Dip

Wrong
Correct

Wrong Correct

A zero offset stack section gives a false picture of dipping reflectors as events A”
and B” are plotted at trace positions A’ and B’ respectively.
The apparent dip of an event on a zero offset stack section
is less than the true dip of the event.
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2004
 Recap

Depth section Time section

SR SR SR SR
x x
after migration

how the event appears

before migration

true subsurface position

of the event
depth time

This is a constant velocity case

> Migration moves events updip

> Migration steepens events
> Migration shortens events
DP START Oslo
2004
 Diffractions
When wave energy strikes discontinuities in the subsurface, diffraction occurs
and the seismic waves are bent around the discontinuity.

This happens at layer pinchouts, faults etc.

The termination point of the

pinchout acts like a point source
and seismic energy is reflected
layer pinch-out out in all directions.

How the diffraction

appears on a seismic
cross-section.
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 Data Example

Diffractions

Diffracted energy appears

very similar to that reflected
from an anticline.

Diffracted energy IS useful

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 Velocity Errors

Diffractions not collapsed Turned into a smile

Undermigrated Overmigrated

Velocities too low Velocities too high

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Important Structural Features
Anticline
1 2 3 4 5 6 7
x

Geology

1 2 3 4 5 6 7
x

Stacked - (structure
appears too broad)

T
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 Anticline - Data Example

STACK

Geology MIGRATION

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 Important Structural Features
Syncline
• Left, below, shows true zero-offset ray paths for coincident sources and receivers at surface points A
through G to a synclinal reflector. The curvature of the reflecting horizon is such that there are multiple
perpendicular ray paths from surface positions B through F. On the right is shown how a syncline will
appear on a stacked section

Distance Distance
A B C D E F G A B C D E F G

Depth

Time

Geology

DP START Oslo Stack

2004
 Syncline - Data Example

STACK
(showing
“bow-tie”
effect)

Geology MIGRATION

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Important Structural Features
Fault

Geology

dif
fra
cti
Stack

on
di
ffr
ac
tio
n

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Fault - Stacked Data Example

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 Importance of Velocity
A local high- Anticline appears wider on the stacked section. The
apparent width depends on the dips on each flank - the steeper
the dips the wider the structure on the stacked section.

stacked section migrated section

Anticline

If our velocities are incorrect, the final migrated structure may be

narrower or wider than the true structure - this could lead to the
wrong estimate of any oil or gas reserves under this “high”.
DP START Oslo
2004
 Importance of Velocity
A local depression - Syncline appears narrower on the stacked section
Syncline

stacked section
migrated section

If the velocities are too high, the syncline will be wider than it should
be after migration. Velocities that are too low will “under migrate”
the structure, leaving it too narrow.
DP START Oslo
2004
 Importance of velocity

A perfectly horizontal event with a fault plane.

If the velocity field is incorrect, the fault plane will not “move”
to the correct place and the diffraction curves from the “corners”
of the structure will not focus correctly

DP START Oslo
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 Migration Velocity Field

Modifications must be made to the stacking velocity field so that it can be

used for Migration.

Smoothing

Time migration algorithms cannot handle strong lateral velocity variations

Filtering in time / horizon

consistent manner

Stacking velocity field Smoothed velocity field

DP START Oslo
2004
 Migration Velocity Field
Scaling

Trial migrations are conducted using varying percentages of the stacking velocity
field

80% of stacking 100% of stacking 120% of stacking

velocities velocities velocities

Conversion to interval velocities

Stacking velocities must be converted to interval velocities to be of use to

most migration algorithms. These conversions are done internally.
DP START Oslo
2004
 A strange structure
If we had an inverted perfectly parabolic event in the ground, with its centre
on our CDP, we would see only one point on our stacked section

Parabolic smile

A glitch or a spike

(stacked section) (migrated section)

If we have a single “point” of energy in our stacked section that

does not correspond to a “real event” (e.g a spike), this will
migrate into a parabolic “smile” on our migrated section.
DP START Oslo
2004
 Recap

Why do we need to migrate seismic data ?

• re-arrange events to true subsurface positions

• dipping events will shorten, steepen and move updip

• diffraction energy will be collapsed

• amount of under and over migration will depend on

the velocity

DP START Oslo
2004
 At the end of this Session, you will be able to:

• Define the ‘imaging principle’ and describe how it is related to the concept of ‘exploding
reflectors’.
• Define the principle of ‘downward continuation’ and describe how it is used in the
migration process.
• Define the term ‘migration algorithm’.
• Define the 3 main categories of migration technique namely, ‘Finite-Difference’ ,
‘Integral’ and ‘Transform’ methods
• Name at least 4 algorithms based on these techniques.
• Define the terms ‘pre-stack migration’ and ‘post-stack migration’.
• Define the terms ‘ time migration’ and ‘depth migration’.

DP START Oslo
2004
Types of Migration

•Principles

•Techniques / Algorithms

•Time or Depth?

•Pre-Stack or Post Stack?

•2D or 3D?

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2004
 Important Principles
Exploding Reflectors
Each point on a reflector can be considered as a secondary source of energy.
If we could measure the shape of the wave front at t=0 (i.e. at the reflector surface),
since no propagation has occurred at this time then the wave front shape must be the
same as the reflector shape that generated the wave front. This is the IMAGING principle.

surface

Point Reflector
(exploding reflector)

Based on Huygen’s Principle

DP START Oslo
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Important Principles
Downward Continuation

The imaging is achieved by extrapolating the wave-field

back in depth, from the surface to the exploding reflector
where, t =0

Downward continuation is performed at regular depth

or time intervals until all reflectors are ‘imaged’.

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2004
Migration Techniques

Most modern migration techniques are based on

the scalar wave equation, which ‘relates the spatial
and time dependence of a disturbance which can
propagate as a wave’*. * R.E.Sheriff

In rectangular co-ordinates x, y and z

 2  2  2 1
   
x 2
y 2
z 2
V 2

Where  represents wave displacement (pressure, rotation etc)

and V the velocity of the wave
DP START Oslo
2004
 Migration Techniques
Three main categories
(most of these use the principle of downward continuation
and exploding reflector model)

•Finite-Difference Methods- based on differential

solutions to the scalar wave equation

•Integral Methods- integral solution to the scalar wave

equation. Based on summing the seismic amplitudes along
a diffraction hyperbola whose curvature is governed by the
medium velocity

•Transform Methods- involving co-ordinate transformation

into mainly F-K domain
DP START Oslo
2004
 Migration Techniques

•Finite-Difference Methods-
generally used when vertical velocity variations exist with gentle lateral
velocity variations and dips of the events are moderate.

•Integral Methods-. Used mainly when data exhibits high dips.

Lateral velocity variations can still be a problem. Kirchhoff migration is
an example. Uses RMS velocities instead of interval velocities.

•Transform Methods- usually implemented in F-K domain.

Examples are: Phase-shift and Stolt migrations. These are relatively
cheap to run.

DP START Oslo
2004
 Important Migration Algorithms
Name Method Comments
Downward continuation can only handle dips up to 60 degrees
Finite-Difference migrates in steps from receivers can handle minor lateral velocity variations
downwards can handle low S/N

Kirchhoff based on diffraction can handle dips up to 90 degrees

summation. Uses Huygen’s cannot handle strong lateral velocity variations
principle poor when low S/N

converts to frequency- can handle dips up to 90 degrees

F-K wave-number domain before generally poor at handling lateral velocity
(Stolt, Phase-Shift) migrating. Stolt can be used variations.
to perform residual migration poor when low S/N

F-X type of Finite-Difference can handle dips up to 90 degrees

(Omega-X) migration in the frequency can handle moderate velocity variations.
domain each frequency can be processed separately.
poor when low S/N
DP START Oslo
2004
 Time or Depth Migration?

DP START Oslo
2004
 Time or Depth Migration ?
Ideally we want a depth section from a stacked section. The best
way to achieve this is to do Depth Migration. However, time migration is
considered adequate for most surveys. Depth Migration is too time
consuming and expensive to be widely used

• interpreters prefer to evaluate the velocity of migrated section by

comparing with un-migrated data. More common is to migrate with
varying percentages and then compare the results.

• Stacking velocities are accurate for stacking and may not be true
velocities. Much work is required to build a velocity model for
depth migration.
However,
•when lateral variations in velocity are severe, Depth Migration is
needed as the ray-path bending takes place due to strong velocity contrasts.
In such cases, Time Migration is not adequate.
DP START Oslo
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Time or Depth Migration

Model

DP START Oslo
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Time or Depth Migration ?

DP START Oslo
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Time or Depth Migration ?

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 Time or Depth Migration ?

Model

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 Pre-stack or post-stack migration?

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 Pre Stack Migration

Pre-Stack Migration is performed on unstacked data

It can be performed in both Time and Depth domains

Ability to correct for ray path distortions and uncommon

reflection points in areas of complex structure and dip

Better quality Migrated stack result

Retention of AVO and phase change information

Lower S/N ratio

Cost

DP START Oslo
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Pre-stack or Post-stack Migration ?
Post-stack depth migration Pre-stack depth migration

DP START Oslo
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 At the end of this Session, you will be able to:

• Describe the important factors that influence the choice of migration type for a particular
dataset.
• Describe and compare the advantages and disadvantages of the following migration
methods: pre-stack, post-stack, time, depth, 2D and 3D.

DP START Oslo
2004
 Problems with Post Stack Time Migration

Time migration followed by depth conversion (as shown earlier)

will not produce accurate imaging in the presence of steep
dips and severe lateral velocity variations
R
E
A
S
O
N

Poor quality imaging from time migration

R
E
A
S
O
N

Time migration equations describe wavefield

propogation through a horizontally layered medium

DP START Oslo
2004 SOLUTION ?
 Dip-Moveout Correction (DMO)
The CMP stack is an approximation to the zero-offset
case - based on NMO correction -
2 2 2 2
t X = t 0 + X / V

But for dipping layers, correction should be -

2 2 2 2 2
t X = t 0 + X cos / V
2 2 2 2 2
2 2
Or t X = t 0 + X / V - X sin / V

NMO term DMO term

DP START Oslo
2004
 DMO - A Pre-Stack Partial Migration

DMO + Post Stack Migration = Full Pre Stack Migration

does both
corrects for reflector repositions reflection points
dispersal to true subsurface location

DMO allows post-stack time migration to become equivalent

to pre-stack time migration.

DP START Oslo
2004
 Migration of 3D Data

2D Migration 3D Migration
hyperboloid

hyperbola

uses energy from both

Only energy reflected in the plane in and out of the plane
of the section is correctly imaged of the section

3D Migration will have a higher resolution as it can move energy

from outside the plane back to its correct position

DP START Oslo
2004
 One pass versus Two pass

Migration of 3D data can be performed in one or two passes

One Pass Two Pass

3D stack data in 3D stack data in

migrate inlines and migrate in inline

xlines simultaneously direction

migrate in xline
3D migrated data direction

3D migrated data

DP START Oslo
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 One pass versus Two pass

Two Pass One Pass

overmigration

increase in accuracy and cost

When limited velocity variation

Two pass is a good match for One pass 3D migration

DP START Oslo
2004
 One pass versus Two pass

Two Pass One Pass

Simple to implement with variation in velocities more

existing algorithms accurately handled

efficient use of resources both time and depth migration

are possible
allows for use of two
different algorithms
increased resources
allows extra QC step

restricted to time migration

use of omega-x migration
algorithm - each frequency
tends to overmigrate for realistic can be processed separately
velocity models

DP START Oslo
2004
 Which Migration to use?

Time or Depth?

Pre-Stack or Post Stack?

2D or 3D?

Algorithm?

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 Which Migration To Use?

DP START Oslo
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 Which Migration To Use?

What does the choice of migration type depend on ?

 type of data
2D or 3D

 cost
pre or post stack, algorithm

 data characteristics
S/N ratio, maximum dip, lateral velocity variation, algorithm

 client objectives
zone of interest, resources, own ideas
DP START Oslo
2004
 Factors Affecting Migration
Some additional factors that affect migration quality

• Noise - mainly coherent noise

• Spatial Sampling - in the presence of steep dips, aliasing

can be a problem

• Migration Aperture - related to horizontal displacement

of the reflection point

• Amplitude Anomalies - spikes, noise bursts, truncated traces etc.

DP START Oslo
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 Example of aliasing

DP START Oslo
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 What velocities do we use for migration ?

 Post-stack time migration

stacking velocity field may be smoothed and scaled

 Pre-stack time migration

partial migration based on constant velocity (approx. 2000-3000m/s)
performed on common-offset gathers. The data is then
demigrated and velocities a re picked

 Depth migration
requires highly accurate velocity-depth model

DP START Oslo
2004
 Summary

DP START Oslo
2004
 At the end of this Session, you will be able to:
• Define the term ‘migration’ and describe why we need to migrate seismic data.
• Define the term ‘diffraction energy’.
• Describe how the application of migration can affect dipping events and diffraction energy.
• To introduce the importance of the velocity field in the process of migration.
• Define the terms ‘under migration’ and ‘over migration’ in relation to a migration velocity
field.
• Describe at least 3 ways in which a stacking velocity field may be manipulated to improve
its suitability for the post-stack migration.
• Describe at least 2 reasons why scaling of stacking velocity fields may be required prior to
their use in migration.
• Define the term ‘migration smile’.

DP START Oslo
2004
 At the end of this Session, you will be able to:

• Define the ‘imaging principle’ and describe how it is related to the concept of ‘exploding
reflectors’.
• Define the principle of ‘downward continuation’ and describe how it is used in the
migration process.
• Define the term ‘migration algorithm’.
• Define the 3 main categories of migration technique namely, ‘Finite-Difference’ ,
‘Integral’ and ‘Transform’ methods and
• Name at least 4 algorithms based on these techniques.

DP START Oslo
2004
 At the end of this Session, you will be able to:

• Define the terms ‘pre-stack migration’ and ‘post-stack migration’.

• Define the terms ‘ time migration’ and ‘depth migration’.
• Define the term ‘depth conversion’ and describe how it is different from depth migration.
• Describe the important factors that influence the choice of migration type for a particular
dataset.
• Describe and compare the advantages and disadvantages of the following migration
methods: pre-stack, post-stack, time, depth, 2D and 3D.

DP START Oslo
2004