Surface Wave Prediction and Subtraction by Interferometry + Deconvolution Yanwei Xue Feb. 7, 2008

Outline  Motivation  2D Interferometry + Deconvolution Theory and Field Data Test  3D Proposed Algorithm and Field Data Test  Conclusions & the Road Ahead

Motivation  Problem: Find a better way to predict and remove surface waves by interferometry  Solution: Inteferometry + Deconvolution  Background: Interferometric Prediction (Dong, 2005) Interferometric Prediction (Dong, 2005) Interferometry + NLF prediction (Xue, 2006) Interferometry + NLF prediction (Xue, 2006)

Outline  Motivation  2D Interferometry + Deconvolution Theory and Field Data Test  3D Proposed Algorithm and Field Data Test  Conclusions & the Road Ahead

U(s|g,ω)= W(s, ω )G(s|g) gg’ u(g,g’) 2D Interferometric Surface Wave Prediction u (s,g) u (s,g’) g’Sg U(s|g’,ω)= W(s, ω )G(s|g’) C(g |g’,ω)=|W(s,ω)| G(g|g’) Using crosscorrelation D(g |g’)= G(g|g’) Using deconvolution U(g|g’,ω)= D(g|g’) W(s,ω) U(s|g’,ω)= W(s, ω )G(s|g’)

Basic workflow Window the surface waves out Input data d Interferometry + Deconvolution prediction G Source wavelet Predicted d ^ Least squares subtraction d= min || d – d || ^ 2 ^ ^ Surface waves removed completely? Output data d ^ yes d = d ^ ^ no

X (m) Time (s) Original DataInterferometric prediction of 1 st Iteration 2D Field Data Test Raw Data vs 1 st Prediction X (m) Time (s)

Result after 1 st IterationOriginal Data Raw Data vs 1 st Removal X (m) Time (s) X (m) Time (s)

Result after 3 rd Iteration Result after 1 st Iteration 3 rd Removal vs 1 st Removal X (m) Time (s) X (m) Time (s)

Result after 3 rd Iteration Original Data Raw Data vs 3 rd Removal X (m) Time (s) X (m) Time (s)

Surface Waves RemovedOriginal Data Raw Data vs Removed SW X (m) Time (s) X (m) Time (s)

Result of Interferometry + NLF Result of Interferometry + Deconvolution Interferometry + Deconvolution vs Interferometry + NLF X (m) Time (s) X (m) Time (s)

Surface Waves Removed by Interferometry + NLF Surface Waves Removed by Interferometry + Deconvolution SW by Interferometry + Deconvolution vs by Interferometry + NLF X (m) Time (s) X (m) Time (s)

Outline  Motivation  2D Interferometry + Deconvolution Theory and Field Data Test  3D Proposed Algorithm and Field Data Test  Conclusions & the Road Ahead

S2S2 S1S1 S3S3 Challenge for 3D Extension l1l1 l2l2 l3l3 l1l1 l2l2 2D: l 2 - l 1 = l 3 3D: l 2 - l 1 < l 3

Proposed 3D Interferometry

S1S1 S2S2 S3S3 Physical Meaning z z

3D Test with CREWES Field Data X (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 X (m) Time (s) X (m) Time (s) Original predicted

X (m) Time (s) X (m) Time (s) Interferometric Test of Line 2 predicted Original

X (m) Time (s) X (m) Time (s) Interferometric Test of Line 1 Original predicted

Outline  Motivation  2D Interferometry + Deconvolution Theory and Field Data Test  3D Proposed Algorithm and Field Data Test  Conclusions & the Road Ahead

Summary  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 Ahead  Improve the ability of Interferometry + Deconvolution to separate noise from signal  Use a denser data set to improve our 3D test

Thanks!