Surface Wave Prediction and Subtraction Surface Wave Prediction and Subtraction by Interferometry + Deconvolutionby Interferometry + Deconvolution

Yanwei XueYanwei Xue

Feb. 7, 2008Feb. 7, 2008

OutlineOutline

MotivationMotivation 2D Interferometry + Deconvolution Theory and 2D Interferometry + Deconvolution Theory and

Field Data TestField Data Test 3D Proposed Algorithm and Field Data Test3D Proposed Algorithm and Field Data Test Conclusions & the Road AheadConclusions & the Road Ahead

MotivationMotivation

ProblemProblem:: Find a better way to predict and rem Find a better way to predict and remove surface waves by interferometryove surface waves by interferometry

Solution:Solution: Inteferometry + DeconvolutionInteferometry + Deconvolution

Background:Background:

Interferometric Prediction (Dong, 2005)Interferometric Prediction (Dong, 2005)

Interferometry + NLF prediction (Xue, 2006) Interferometry + NLF prediction (Xue, 2006)

OutlineOutline

MotivationMotivation 2D Interferometry + Deconvolution Theory and 2D Interferometry + Deconvolution Theory and

Field Data TestField Data Test 3D Proposed Algorithm and Field Data Test3D Proposed Algorithm and Field Data Test Conclusions & the Road AheadConclusions & the Road Ahead

U(s|g,ω)= W(s,U(s|g,ω)= W(s,ωω)G(s|g))G(s|g)

gg g’g’

u(g,g’)u(g,g’)

2D Interferometric Surface Wave Prediction2D Interferometric Surface Wave Predictionu (s,g)u (s,g) u (s,g’)u (s,g’)

g’g’SS

gg

C(g |g’,ω)C(g |g’,ω)=|W(s,ω)| G(g|g’)=|W(s,ω)| G(g|g’)Using crosscorrelation

D(g |g’)D(g |g’)= G(g|g’)= G(g|g’)Using deconvolution

U(g|g’,ω)= D(g|g’)U(g|g’,ω)= D(g|g’)W(s,ω)W(s,ω)

U(s|g’,ω)= W(s,U(s|g’,ω)= W(s,ωω)G(s|g’))G(s|g’)

Basic workflowBasic workflowWindow the surface

waves outInput data d

Interferometry + Deconvolution prediction

G

Source wavelet Predicted

d^

Least squares subtraction

d= min || d – d ||^ 2^̂

Surface waves removed completely?

Output data d̂

yes

d = d^̂

no

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Original Data Interferometric prediction of 1st Iteration

2D Field Data Test2D Field Data Test

Raw Data vs 1st Prediction

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Result after 1st IterationOriginal Data

Raw Data vs 1st Removal

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Result after 3rd IterationResult after 1st Iteration

3rd Removal vs 1st Removal

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Result after 3rd IterationOriginal Data

Raw Data vs 3Raw Data vs 3rdrd Removal Removal

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Surface Waves RemovedOriginal Data

Raw Data vs Removed SW

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Result of Interferometry+ NLF

Result of Interferometry+ Deconvolution

Interferometry + Deconvolution vs Interferometry + NLF

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Surface Waves Removed

by Interferometry + NLF

Surface Waves Removed by Interferometry + Deconvolution

SW by Interferometry + Deconvolution vs by Interferometry + NLF

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OutlineOutline

MotivationMotivation 2D Interferometry + Deconvolution Theory and 2D Interferometry + Deconvolution Theory and

Field Data TestField Data Test 3D Proposed Algorithm and Field Data Test3D Proposed Algorithm and Field Data Test Conclusions & the Road AheadConclusions & the Road Ahead

S2

S1

S3

Challenge for 3D ExtensionChallenge for 3D Extension

l1

l2

l3

l1

l2

2D: l2 - l1 = l3

3D: l2 - l1 < l3

Proposed 3D InterferometryProposed 3D Interferometry

S1

S2

S3

Physical Meaning Physical Meaning

z z

3D Test with CREWES Field Data 3D Test with CREWES Field Data 0

40000 4000X (m)

Y (

m)

Acquisition Geometry

Inline: 60 m

Crossline: 260 m

Source Interval

Total 708 Shots

Inline: 60 m

Crossline: 260 m

Receiver Interval

42 receivers per line

Interferometric Test of Line 40

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Original predicted

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Interferometric Test of Line 2

predictedOriginal

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Interferometric Test of Line 1

Original predicted

OutlineOutline

MotivationMotivation 2D Interferometry + Deconvolution Theory and 2D Interferometry + Deconvolution Theory and

Field Data TestField Data Test 3D Proposed Algorithm and Field Data Test3D Proposed Algorithm and Field Data Test Conclusions & the Road AheadConclusions & the Road Ahead

SummarySummary I developed and tested a 2D nterferometry + Deconvolution prediction scheme for surface wave removal

I proposed and tested a 3D extension of this workflow , but did not get the expected result.

Results of Interferometry + Deconvolution were compared with the results of Interferometry + NLF

The Road AheadThe Road Ahead

Improve the ability of Interferometry + Deconvolution to separate noise from signal

Use a denser data set to improve our 3D test

Thanks!