migration velocity analysis

Migration Velocity AnalysisMigration Velocity Analysis

01

OutlineOutline

MotivationMotivationEstimate a more accurate velocity model for migrationEstimate a more accurate velocity model for migration

Tomographic migration velocity analysis Tomographic migration velocity analysis

02

TheoryTheory

Numerical ResultsNumerical Results

ConclusionsConclusions

Motivation

03

d = L m

mmig = LT d

Forward modeling

Kirchhoff Migration

Function of velocity: LT (s)

Inaccurate velocity model

mmig = LT d

Motivation

04

True velocity model

True velocity model

Kirchhoff Migration Image



Kirchhoff Migration Image

Goal of MVA:To get a more accurate velocity model

Structure error

Position error

OutlineOutline


Tomographic Migration Velocity AnalysisTomographic Migration Velocity Analysis

05

TheoryTheory



Theory

06

The fundamental principle underlying MVA is that the migration image of the same reflector should be the same for different source, when using the correct velocity, so pre-stack common image gather (CIG) provides the information of whether the migration velocity is correct and how far away it is from the true velocity.

Theory

07

Common Image Gather ( CIG)

different CSGs

CSG #1

CSG #2

CSG #3

Point scatterer

Theory

08

Common Image Gather ( CIG)

Prestack migration

s

KM of CSG #1

x

z

x0

x

z

KM of CSG #2

x0

x

z

KM of CSG #3

x0

CIG

Theory

09

Tomographic MVAxx0

z

xx0

z

s

z

CIG

Flat

xx0

z

Correct Velocity

x

z

2000 m/s

x0

Theory

10

Tomographic MVA

Curved

Incorrect Velocity

1500 m/s

x

z

x0

xx0

z

s

z

CIG

xx0

z z

xx0

Theory

11

Offset (km) 1

CIG

-1

CIG

Offset (km) 1-1

Tomographic MVA

Hyperbolic approximation

Zh2 = Z0

2 + A h2

picking depth,

Zh

Zh

Z0

zero-offset depth,Z0

Depth residual reference depth

Usually choose Z0 as Zref

ΔZ = Zh - Zref Zref

x0

h

offset, h

Theory

12

Tomographic MVA

Convert depth residual to time residual

x0xs xgFind the source-receiver pair by ray tracing to obey Snell’s lawθ1 θ2

x0xs xg

R reflector with reference depth Zref

R’ reflector with picked depth Zh t’ = LSR’ s + LRG st = LSR s + LRG s

Δt = t’ - t

Theory

13

For a small slowness perturbation

traveltime, raypath operator, background slowness.

t = L st L s

Δs

Δt = t’-t0 = LΔs = L(s’-s0)Parameterize the model as a grid of cells

traveltime residual for the raypath , slowness purturbation in grid cell

Δti = Σ Δsj Δlij

n

j=1Δti i Δsj

j

Update the slowness with a steepest descent method

Back project along the raypaths to get

Δti Δsj

sj(k+1) = sj

(k+1) – α Δsj(k+1)

Tomographic MVAUpdate the slowness

Theory

14

Misfit function

Iteration will stop when all curved events in CIG are flatten.

picked depth residual for offset in CIG of the iteration

Tomographic MVA

Fmisfit = Σ Σ (Δzij )2 i=1 j=1

m n(k) (k)

Δzij j i k(k)

15

Migration velocity model s0

TheoryTheory

Predict travel time by eikonal solver

Pre-stack KM , form CIGs

Pick the reference depth residual (usually zero-offset)

Find ray paths connecting the reflector to both S and R positions

Convert depth residual to travel time residual

Update velocity model by back projecting the traveltime residuals along the raypaths.

Work Flow:

Migration velocity model sk

Pick the depth residual automatically

Observed data

All events are flattened?

Y

MVA finished !

N

OutlineOutline



16

TheoryTheory



Numerical Results

17

2D Synthetic Model

KM image CIGTrue velocity model

H. Sun. 1999

Numerical Results

18

2D Synthetic Model

H. Sun. 1999

Homogeneous velocity model KM image CIG

Numerical Results

19

2D Synthetic Model

H. Sun. 1999

Final updated velocity model KM image CIG

Initial Migration VelocityInitial Migration Velocity

0000

1818

1.51.5

Horizontal Distance (km)Horizontal Distance (km)

Dep

th (

km)

Dep

th (

km) 2.12.1

1.51.5

(km

/s)

(km

/s)

KM Image with Initial VelocityKM Image with Initial Velocity0000

18 km18 km

1.51.5

Dep

th (

km)

Dep

th (

km)

00

1.51.5

Dep

th (

km)

Dep

th (

km)

KMVA Velocity Changes in the 1st IterationKMVA Velocity Changes in the 1st Iteration

5050

00

(m

/s)

(m /s

)

KM Image with Initial VelocityKM Image with Initial Velocity

KM Image with Updated VelocityKM Image with Updated Velocity

9 km9 km

12601260

De

pth

(m

)D

ep

th (

m)

2 km2 km

10701070

12601260

De

pth

(m

)D

ep

th (

m)

10701070

KMVA CIGs with Initial VelocityKMVA CIGs with Initial Velocity

00

1.51.5

Dep

th (

km)

Dep

th (

km)

KMVA CIGs with Updated VelocityKMVA CIGs with Updated Velocity

0000

18 km18 km

1.51.5

Dep

th (

km)

Dep

th (

km)

00

1.51.5

Dep

th (

km)

Dep

th (

km)

KMVA Velocity Changes in the 1st Iteration (CPU=6)KMVA Velocity Changes in the 1st Iteration (CPU=6)

5050

00

(m

/s)

(m /s

)

WMVA Velocity Changes in the 1st Iteration (CPU=1)WMVA Velocity Changes in the 1st Iteration (CPU=1)

5050

00

(m

/s)

(m /s

)

WM Image with Initial VelocityWM Image with Initial Velocity

WM Image with Updated VelocityWM Image with Updated Velocity

9 km9 km

12601260

De

pth

(m

)D

ep

th (

m)

2 km2 km

10701070

12601260

De

pth

(m

)D

ep

th (

m)

10701070

WMVA CIGs with Initial VelocityWMVA CIGs with Initial Velocity

00

1.51.5

Dep

th (

km)

Dep

th (

km)

WMVA CIGs with Updated VelocityWMVA CIGs with Updated Velocity

KM Image with Initial VelocityKM Image with Initial Velocity 9 km9 km

12601260

De

pth

(m

)D

ep

th (

m)

2 km2 km

10701070

KM Image with KMVA Updated VelocityKM Image with KMVA Updated Velocity

12601260

De

pth

(m

)D

ep

th (

m)

10701070

KM Image with WMVA Updated VelocityKM Image with WMVA Updated Velocity

12601260

De

pth

(m

)D

ep

th (

m)

10701070

OutlineOutline



26

TheoryTheory



27

• Pre-stack migration with inaccurate velocity can bring curved events in CIGs, which provides the opportunity for migration velocity analysis.

• Iterative tomographic MVA can estimate better migration velocity and improve the migration image.


• Question: what are the advantages and disadvantages of migration velocity analysis compared to velocity estimation in data domain ?

Numerical Results

20

2D Field Data

H. Sun. 1999

00

00

18181.51.5

Initial migration velocity from NMOInitial migration velocity from NMO

Dep

th (

km

)D

epth

(k

m)

2.12.1

1.51.5

(k

m /s

)(k

m /s

)

Horizontal distance (km)Horizontal distance (km)

Numerical Results

21

2D Field Data

H. Sun. 1999

00

00

18181.51.5

KM image with the initial velocityKM image with the initial velocity

Dep

th (

km

)D

epth

(k

m)

Horizontal distance (km)Horizontal distance (km)

Numerical Results

22

2D Field Data

H. Sun. 1999

00

1.51.5

KM CIGs with the initial velocityKM CIGs with the initial velocityD

epth

(k

m)

Dep

th (

km

)

1.21.2

Numerical Results

23


00

00

1.51.5

Dep

th (

km)

Dep

th (

km)

00

1.51.5

Dep

th (

km)

Dep

th (

km)

KM Image with Updated VelocityKM Image with Updated Velocity 1818

Numerical Results

24


KM Image with Updated VelocityKM Image with Updated Velocity

9 km9 km

12601260

Dep

th (

m)

Dep

th (

m)

2 km2 km

10701070

12601260

Dep

th (

m)

Dep

th (

m)

10701070

Numerical Results

25

KMVA CIGs with Initial VelocityKMVA CIGs with Initial Velocity

00

1.51.5

Dep

th (

km

)D

epth

(k

m)

KMVA CIGs with Updated VelocityKMVA CIGs with Updated Velocity

migration velocity analysis

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