Acoustic Waveform Inversion of 2D Gulf of Mexico Data

Acoustic Waveform Inversion ofAcoustic Waveform Inversion of2D Gulf of Mexico Data2D Gulf of Mexico Data

Chaiwoot BoonyasiriwatChaiwoot Boonyasiriwat

April 13, 2009April 13, 2009

OutlineOutline

1

Part I: Application of waveform inversion to Part I: Application of waveform inversion to marine datamarine data

Part II: Resolution analysis using Beylkin’s Part II: Resolution analysis using Beylkin’s formulaformula

Part I: OutlinePart I: Outline

2

Application of waveform inversion to marine Application of waveform inversion to marine datadata

• MotivationMotivation

• TheoryTheory

• Numerical ResultsNumerical Results

• 2D SEG/EAGE Salt Model2D SEG/EAGE Salt Model

• Gulf of Mexico DataGulf of Mexico Data

• ConclusionsConclusions

MotivationMotivation

300 161644

00

Dep

th (

km)

Dep

th (

km)

Dep

th (

km)

Dep

th (

km)

00

44

X (km)X (km)

Waveform TomogramWaveform Tomogram

15001500

45004500

Vel

ocit

y (m

/s)

Vel

ocit

y (m

/s)

True ModelTrue Model

An acoustic wave equation:An acoustic wave equation:

)|,()|,()(

1)|,(

)(

12

2

sss rtstP

t

tPrrr

r

rr

r

The waveform misfit function isThe waveform misfit function is

dttPfs g

sg )|,(2

1 2 rr

4

Theory of Waveform InversionTheory of Waveform Inversion

wherewhere)(

)()(

r

rr

c


The waveform residual is defined byThe waveform residual is defined by

calcsgobssgsg tPtPtP )|,()|,()|,( rrrrrr

The steepest descent method can be used to The steepest descent method can be used to minimize the misfit function:minimize the misfit function:

)()()(1 rrr kkkk gcc

5


The gradient is calculated byThe gradient is calculated by

s

ss tPtPdtc

g )|,(')|,( )(

2)( rrrr

rr

wherewhere

)|,'()0,'|,(')|,(' ss tstGdtP rrrrrrr

)|,()()|,( sggg

s tPts rrrrrr

6


7



• TheoryTheory





8

2D SEG/EAGE Salt Model2D SEG/EAGE Salt Model

00 161644

00

Dep

th (

km)

Dep

th (

km)

X (km)X (km) 15001500

45004500

Vel

ocit

y (m

/s)

Vel

ocit

y (m

/s)

9

Initial Velocity ModelsInitial Velocity Models

00 161644

00

Dep

th (

km)

Dep

th (

km)

Dep

th (

km)

Dep

th (

km)

00

44

X (km)X (km)

v(z) Modelv(z) Model

Traveltime TomogramTraveltime Tomogram

15001500

45004500

Vel

ocit

y (m

/s)

Vel

ocit

y (m

/s)

10

Waveform Inversion ResultsWaveform Inversion Results

00 161644

00

Dep

th (

km)

Dep

th (

km)

Dep

th (

km)

Dep

th (

km)

00

44

X (km)X (km)

Using v(z) Model + FloodingUsing v(z) Model + Flooding

Using Traveltime TomogramUsing Traveltime Tomogram

15001500

45004500

Vel

ocit

y (m

/s)

Vel

ocit

y (m

/s)

10

Waveform Inversion ResultsWaveform Inversion Results

00 161644

00

Dep

th (

km)

Dep

th (

km)

X (km)X (km)

True ModelTrue Model

15001500

45004500

Vel

ocit

y (m

/s)

Vel

ocit

y (m

/s)

11

Flooding TechniqueFlooding Technique

00 161644

00

Dep

th (

km)

Dep

th (

km)

Dep

th (

km)

Dep

th (

km)

00

44

X (km)X (km)

Waveform Tomogram after Salt FloodWaveform Tomogram after Salt Flood

Using v(z) Model w/o FloodingUsing v(z) Model w/o Flooding

15001500

45004500

Vel

ocit

y (m

/s)

Vel

ocit

y (m

/s)

12

Flooding TechniqueFlooding Technique

00 161644

00

Dep

th (

km)

Dep

th (

km)

Dep

th (

km)

Dep

th (

km)

00

44

X (km)X (km)

Waveform Tomogram using v(z) and Flooding TechniqueWaveform Tomogram using v(z) and Flooding Technique

Waveform Tomogram after Sediment FloodWaveform Tomogram after Sediment Flood

15001500

45004500

Vel

ocit

y (m

/s)

Vel

ocit

y (m

/s)


13



• TheoryTheory





515 Shots480 Hydrophones

12.5 mdt = 2 msTmax = 10 s

1 1.5 2 2.5

0

0.5

1

1.5

2

2.5

3

Offset (km)

Tim

e (s)

b) Original CSG 1

1 1.5 2 2.5

0

0.5

1

1.5

2

2.5

3

Offset (km)Tim

e (s)

a) Virtual CSG 1

14

Gulf of Mexico DataGulf of Mexico Data

Data PreprocessingData Preprocessing

15

Offset (km)

Tim

e (s)

(a) Original CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

Offset (km)

Tim

e (s)

(b) 5-Hz CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

Offset (km)Tim

e (s)

(c) 10-Hz CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

(b) 0-15 Hz CSG (c) 0-25 Hz CSG

Adaptive Early-Arrival Muting WindowAdaptive Early-Arrival Muting Window

16

Offset (km)

Tim

e (s)

(a) Original CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

Offset (km)

Tim

e (s)

(b) 5-Hz CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

Offset (km)

Tim

e (s)

(c) 10-Hz CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

0-15 Hz CSG

Offset (km)

Tim

e (s)

(a) Original CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

Offset (km)

Tim

e (s)

(b) 5-Hz CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

Offset (km)

Tim

e (s)

(c) 10-Hz CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

0-25 Hz CSG

Window = 1 s Window = 1 s

17

Offset (km)

Tim

e (s)

(a) Original CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

Offset (km)

Tim

e (s)

(b) 5-Hz CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

Offset (km)

Tim

e (s)

(c) 10-Hz CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

0-15 Hz CSG

Offset (km)

Tim

e (s)

(a) Original CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

Offset (km)

Tim

e (s)

(b) 5-Hz CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

Offset (km)

Tim

e (s)

(c) 10-Hz CSG

0 2 4

0

0.5

1

1.5

2

2.5

3

3.5

4

0-25 Hz CSG

Window = 2 s Window = 2 s

Adaptive Early-Arrival Muting WindowAdaptive Early-Arrival Muting Window

1800 20202.52.5

00

Dep

th (

km)

Dep

th (

km)

X (km)X (km)

Traveltime TomogramTraveltime Tomogram

15001500

30003000

Vel

ocit

y (m

/s)

Vel

ocit

y (m

/s)

Waveform TomogramWaveform Tomogram2.52.5

00

Dep

th (

km)

Dep

th (

km)

ResultsResults

1900 2020

2.52.5

00

Dep

th (

km)

Dep

th (

km)

X (km)X (km)

Waveform TomogramWaveform Tomogram

15001500

30003000

Vel

ocit

y (m

/s)

Vel

ocit

y (m

/s)

2.52.5

00

Dep

th (

km)

Dep

th (

km)

Vertical Derivative of Waveform TomogramVertical Derivative of Waveform Tomogram

Kirchhoff Migration ImagesKirchhoff Migration Images

20

Comparing CIGsComparing CIGs

21


22

CIG from Traveltime Tomogram CIG from Waveform Tomogram


23


24



25


26



27



• TheoryTheory





ConclusionsConclusions

28

• Acoustic waveform inversion was applied to Acoustic waveform inversion was applied to both 2D synthetic and field databoth 2D synthetic and field data

• Using the traveltime tomogram, waveform Using the traveltime tomogram, waveform inversion failed to converge to an accurate inversion failed to converge to an accurate solution due to high velocity contrastsolution due to high velocity contrast

• Using v(z) model with the flooding technique, Using v(z) model with the flooding technique, an accurate result was obtainedan accurate result was obtained


29

• Acoustic waveform inversion with a dynamic Acoustic waveform inversion with a dynamic early-arrival muting window can invert the early-arrival muting window can invert the Gulf of Mexico data to obtain a velocity model Gulf of Mexico data to obtain a velocity model that is more accurate than the traveltime that is more accurate than the traveltime tomogram.tomogram.

• The accuracy of waveform tomogram was The accuracy of waveform tomogram was assessed by comparing the migration images assessed by comparing the migration images and common image gathers.and common image gathers.

Part II: OutlinePart II: Outline

1

Spatial Resolution Analysis using Beylkin’s Spatial Resolution Analysis using Beylkin’s FormulaFormula


• TheoryTheory


• Homogeneous ModelHomogeneous Model

• Smoothed 2D SEG/EAGE Salt ModelSmoothed 2D SEG/EAGE Salt Model


MotivationMotivation

2

Model with Resolution LimitsModel with Resolution Limits RTM ImageRTM Image


3



• TheoryTheory





Given:

source/receiver configuration and source frequency

Find:

spatial resolution limits

Method:

use a mapping function that maps the given information to resolution limits

4

2D Spatial Resolution Formulas2D Spatial Resolution Formulas

Why Beylkin’s resolution analysis?

• It is simple

• It can be used for heterogeneous media

• It is fast -- ray-based method

5


Source/receiver configuration can be described by coordinate

6


XX gs fixedfor )0,( and )0,( rr

2D common-shot gather can be described by

),(),(: zx kkf

Beylkin’s resolution mapping:

data image

Beylkin et al. (1985) derived the following resolution formulas:

7


),( rk

),( zx kkk

whereis the wavenumber vector in the

image domain

),( r is the traveltime surface of a diffractor at r for shot/receiver pairs described by

A diffractor traveltime can be described as

8


where

is the traveltime from surface position y to subsurface position x.

),( r

gsgs ),(),(),( rrrrr

),( yx

Similarly, k can be written as vectorial sum

gs kkk

)( gs

9

Wavenumber IlluminationWavenumber Illumination

gs kkk

rr

Horizontal and vertical resolution limits:Horizontal and vertical resolution limits:

|),,(|max

2

rxk

x

10


|),,(|max

2

rzk

z


11



• TheoryTheory





Homogeneous ModelHomogeneous Model

1200 11X (km)X (km)

11

00D

epth

(km

)D

epth

(km

)

Homogeneous Model with Resolution LimitsHomogeneous Model with Resolution Limits

Wavenumber Wavenumber IlluminationIllumination

13

Homogeneous ModelHomogeneous Model

1400 11X (km)X (km)

11

00D

epth

(km

)D

epth

(km

)

Reverse-Time Migration ImageReverse-Time Migration Image


15



• TheoryTheory





Smoothed SEG/EAGE Salt ModelSmoothed SEG/EAGE Salt Model

16

00 1616X (km)X (km)

3.53.5

00

Dep

th (

km)

Dep

th (

km)

Smoothed Salt Model with Resolution LimitsSmoothed Salt Model with Resolution Limits

15001500

60006000

Vel

ocit

y (m

/s)

Vel

ocit

y (m

/s)

Wavenumber Wavenumber IlluminationIllumination

17


18

00 1616X (km)X (km)

3.53.5

00

Dep

th (

km)

Dep

th (

km)


RTM Image Line at x = 8 kmRTM Image Line at x = 8 km

19

0.90.9 1.11.1Depth (km)Depth (km)00

11

Am

plit

ude

Am

plit

ude

z = 1 kmz = 1 km

1.91.9 2.12.1Depth (km)Depth (km)00

0.20.2

Am

plit

ude

Am

plit

ude

z = 2 kmz = 2 km

00

0.150.15

Am

plit

ude

Am

plit

ude

2.92.9 3.13.1Depth (km)Depth (km)

z = 3 kmz = 3 km


20

00 1616X (km)X (km)

3.53.5

00

Dep

th (

km)

Dep

th (

km)


RTM Image Line at z = 2 kmRTM Image Line at z = 2 km

21

1.81.8 2.22.2X (km)X (km)00

0.50.5

Am

plit

ude

Am

plit

ude

x = 2 kmx = 2 km

7.87.8 8.28.2X (km)X (km)00

0.20.2

Am

plit

ude

Am

plit

ude

x = 8 kmx = 8 km

00

0.30.3

Am

plit

ude

Am

plit

ude

13.813.8 14.214.2X (km)X (km)

x = 14 kmx = 14 km


22



• TheoryTheory






23

• Beylkin’s ray-based spatial resolution analysis can provide accurate resolution limits for both homogeneous and smooth heterogeneous models in this study.

• For a homogeneous model, vertical resolution is constant while horizontal resolution degrades with depth.

• For a heterogeneous model, both vertical and horizontal resolutions generally degrade with depth since the velocity value is getting higher.

• My advisor: Dr. Gerard Schuster• Mentors: Paul Valasek, Partha Routh, and Peng Chen• Committee members: Dr. Ron Brunh and

Dr. Richard Jarrard

AcknowledgmentsAcknowledgments

24

• UTAM alumni: Jianming Sheng, Min Zhou,

Ruiqing He, Xiang Xiao, George Jiang

• UTAM colleagues: Weiping Cao, Ge Zhan, Sherif Hanafy, Sam Brown, etc.

• UTAM sponsors• Development and Promotion of Science and

Technology (DPST) Project of Thailand

Acoustic Waveform Inversion of 2D Gulf of Mexico Data

Documents

Transcript of Acoustic Waveform Inversion of 2D Gulf of Mexico Data