Introduction to Seismic Migration

One-way traveltime

V=1 m/s

Homogeneous dipping planar reflector

One-way traveltime

V=1 m/s

Homogeneous dipping planar reflector

One-way traveltime

V=1 m/s

Homogeneous dipping planar reflector

Homogeneous dipping planar reflector

One-way traveltime

V=1 m/s

Stacked position= reflection position

Migrated position=true their subsurface location

Dipping reflections

More complex structure

DefinitionProcess which moves dipping reflections to their

true subsurface position and collapes diffractions

Process which reconstructs seismic image from stack section so that reflections and difractions are plotted at their true location

Stacked section

Migrated

sectionMigrationOperationVelocity

Objectives

• Moves dipping reflections to their true dip (up dip) and subsurface location

• Collapes diffraction• Un-tie bow-tie

Seismic Velocity

Seismic Velocity

• Instantaneous•Represents actual velocity•Similar to the well log velocity

• Interval•Instantaneous velocity over a defined interval

• Root mean square (RMS)•Used during NMO and diffraction modeling

• Average•Total distance with a total traveltime

dt

dzVins

2

1

2

1

2

2,12,1

2

2,12,1

1

1

T

T

insins

T

T

insins

dttVT

TV

dttVT

TV

Tt

t

insrms dttVT

tV0

22 1

Tt

t

insave dttVT

TV0

)(1

)(

RMS and Average Velocity

n

ii

n

ii

nrms

t

tVV

1

1

2int

2,

n

ii

n

ii

nave

t

tVV

1

1int

,

RMS velocity Average velocity

How to derive velocity

Pre-stack seismic gather stacking velocityVelocity analysis

RMS velocity

)cos(dipVV stackrms

Interval velocity

Dix equation

Dix Equation(Dix,1955)

Assumption• Horizontal planar reflectors• Small offset

2/1

1

122

int

)1()()(

nn

nrmsnrms

tt

tnVtnVnV Vint

Vrms(n-1)

Vrms(n)

TWT

tn-1

tn

CDP

Exercise-1

Compute RMS and average velocities at reflector B,C and D!

Z=1000 m

Z=2000 m

B

Vab=2000 m/s

Vcd=6000 m/s

Vbc=4000 m/s

C

D

A

Z=3000 m

Solution-1

Depth Vint DTi V_ave V_rms

1000 2000 0.5 2000.0 2000.0

2000 4000 0.25 2666.7 2828.4

3000 6000 0.167 3272.7 3618.1

V_aveV_rms

V_int

Velocity [m/s]

TWT

[s]

Exercise-2

Semicircle superposition

Impulse response migration

Diffraction summation

Kirchhoff Migration

Huygens’s secondary source

Huygens traveltime curve

Kirchhoff Summation

xin

RMS

out PtrV

xP *)(

cos

2

•Obliquity• Spherical spreading•Wavelet shaping factor

)/,0,( vrtzxP in

)0,2/,( 0 tvzxPout

220 zxxr

Kirchhoff time and depth

Kirchhoff migration parameters

• Velocity• Aperture• Maximum dip

Migration velocitiesOvermigrated Undermigrated

ZO

Desired migration

2500 m/s

5 %

10 %

20 %

Test for velocity

Test for velocity

Migration velocities

Tests for maximum dip to migrate

a. ZO sectionb. Desired migrationc. 4 ms/traced. 24 ms/trace

c

d

Tests for maximum dip

Undermigration

Migration strategy (Yilmaz)

2D versus 3D migrationPost- versus post- migrationTime versus depth migration

Case Migration Case Migrationdipping event time migration strong lateral

velocity variations associated with complex overburden structure

depth migrationconflicting dips with different stacking velocities

prestack migration

3D behavior of fault planes and salt flanks

3D migration

complex nonhyperbolic moveout

prestack migration

3D structure 3D migration

ZO versus stack /CMP stack section

1. Complex structure nonhyperbolic moveout

2. Conflicting dips

Pre-stack migration

Migration algorithm

• Integral solution to the scalar wave equation• Finite-difference solution• Frequency-wavenumber implementation: Stolt,

phase-shift/Gazdag1. Handle steep dips with sufficient accuracy2. Handle lateral and vertical velocity variations3. Be implemented, efficiently

Kirchhoff depth migration