Interpolating and Extrapolating Marine Data with Interferometry Sherif M. Hanafy January 2010

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: Interpolation 3D layered velocity model 3D SEG/EAGE model Extrapolation 2D SEG/EAGE model Reverse time migration and waveform inversion Conclusions and future work

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: Interpolation 3D layered velocity model 3D SEG/EAGE model Extrapolation 2D SEG/EAGE model Reverse time migration and waveform inversion Conclusions and future work

Problem In marine surveys the receiver array could be irregular, sparsely distributed and contain gaps Solution: Use interferometric interpolation and extrapolation

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: Interpolation 3D layered velocity model 3D SEG/EAGE model Extrapolation 2D SEG/EAGE model Reverse time migration and waveform inversion Conclusions and future work

Natural Green’s function Theory SSP Data SSP Data SSP Data Virtual receiver Virtual source Sea bed Ocean Surface Reflectors Sea bed Ocean Surface Sea bed Reflectors Ocean Surface x A x B A x A B h Water Velocity (V) G(x|B) Model based data G(x|A) Natural Green’s function G(B|A) Interpolated data

Generate GF for Water Multiples Interpolate/Extrapolate Missing Data Workflow G(x|B) Input Data Time (s) 3.0 X (km) 4.5 Water Layer Thickness Input Field Data G(x|A) Sea bed Ocean Surface Generate GF for Water Multiples Unfiltered Virtual Time (s) 3.0 X (km) 4.5 Interpolate/Extrapolate Missing Data Filtered Virtual Get Virtual CSG Time (s) 3.0 X (km) 4.5 G(B|A) Matching Filter N Max. Itr (MF) Y N Max Iteration Y Final CSG

Local Matching Filter dtrue dvirtual dtrue = dvirtual * f Time (s) 3.0 3.0 X (km) 4.5 Time (s) 3.0 X (km) 4.5 dtrue = dvirtual * f

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: Interpolation 3D layered velocity model 3D SEG/EAGE model Extrapolation 2D SEG/EAGE model Reverse time migration and waveform inversion Conclusions and future work

Numerical Results 3D velocity model is used to test the interpolation approach 3000 x 3000 x 1400 m3 in x, y, and z directions Source is at (10,10,30) (x,y,z) 300 by 300 receiver points are used with dx=dy=10 m Sea bottom is flat @ depth of 750 m 3 km 1.4 km Source

Velocity Model Sea bed Reflector # 1 Reflector # 2 Velocity (m/s) 1500 2400

3D Example Input Goal 60 crossline Crossline interval = 50 m 100 traces/line Trace interval = 30 m Total number of traces = 6000 Goal 300 crossline Crossline interval = 10m 300 traces/line Trace interval = 10 m Total number of traces = 90,000 Dense geometry Sparse geometry

Original CSG, 300 traces, dx = 10 m SSP Data Line # 180 Line # 180 Original CSG, 300 traces, dx = 10 m Sparse CSG, 100 traces, dx = 30 m Time (s) Time (s) 5 5 X (m) X (m) 3000 3000

Iterations: 1 interpolation and 8 MF SSP Virtual Data Line # 180 Iterations: 1 interpolation and 8 MF 5 Time (s) 3000 X (m) Sparse CSG, 100 traces, dx = 30 m 5 Time (s) 3000 X (m) Virtual CSG, 300 trace, dx = 10 m

Iterations: 3 interpolation and 8 MF/interpolation SSP Virtual Data Line # 180 Iterations: 3 interpolation and 8 MF/interpolation 5 Time (s) 3000 X (m) Sparse CSG, 100 traces, dx = 30 m Original CSG, 300 trace, dx = 10 m Time (s) 5 X (m) 3000

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: Interpolation 3D layered velocity model 3D SEG/EAGE model Extrapolation 2D SEG/EAGE model Reverse time migration and waveform inversion Conclusions and future work

SEG/EAGE Velocity Model Velocity (m/s) 1500 4500

Acquisition Parameters Goal 34 Streamers Crossline offset is 50 m Inline offset is 12.5 m 619 receivers/streamer Total number of receivers 21046 Input 12 Streamers Crossline offset is 150 m Inline offset is 25 m 310 receivers/streamer Total number of receivers 3720 Dense geometry Sparse geometry

SEG/EAGE Model – Input Data Streamer offset = 150 m No. of receiver = 310 8 Time (s) Streamer 2 1 2 1 Scale 2 km

SEG/EAGE Model – Virtual Data Streamer offset = 50 m No. of receiver = 619 8 Time (s) Streamer 2 1 2’ 1’ 2 1 2’ 1’ Scale 2 km

SEG/EAGE Model – Real Data Streamer offset = 50 m No. of receiver = 619 8 Time (s) Streamer 4 1 3 2 Scale 2 km

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: Interpolation 3D layered velocity model 3D SEG/EAGE model Extrapolation 2D SEG/EAGE model Reverse time migration and waveform inversion Conclusions and future work

Problem In marine surveys the interval between some shots and recording array is large. Solution: Use interferometric extrapolation to fill this gap

Local Matching Filter dtrue dvirtual dtrue = dvirtual * f Time (s) 3.0 3.0 X (km) 4.5 Time (s) 3.0 X (km) 4.5 dtrue = dvirtual * f

Matching Filter Apply matching filter Source Get matching filter Ocean bottom cable Geology Geology

Velocity Model

2D Extrapolation Example Time (s) 12 11 X (km) CSG with true near offset traces Time (s) 12 11 X (km) CSG with 2 km gap at the near offset Time (s) 12 11 X (km) CSG with virtual traces

Virtual CSG with 1 iteration of MF Virtual CSG with 5 iterations of MF 2D Extrapolation Example Time (s) 12 11 X (km) Virtual CSG with 1 iteration of MF Time (s) 12 11 X (km) Virtual CSG with 5 iterations of MF Time (s) 12 11 X (km) True CSG

Virtual CSG with 1 iteration of MF Virtual CSG with 5 iterations of MF 2D Extrapolation Example Time (s) 6 11 X (km) Virtual CSG with 1 iteration of MF Time (s) 6 11 X (km) Virtual CSG with 5 iterations of MF Time (s) 6 11 X (km) True CSG

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: Interpolation 3D layered velocity model 3D SEG/EAGE model Extrapolation 2D SEG/EAGE model Reverse time migration and waveform inversion Conclusions and future work

RTM image of the input data Reverse Time Migration RTM image of the input data Z (km) 3 11

RTM image of the extrapolated data RTM image of the true data Reverse Time Migration RTM image of the extrapolated data Z (km) 3 11 X (km) RTM image of the true data Z (km) 3 11 X (km)

Waveform inversion of the extrapolated data True velocity model Z (km) 3 11 X (km) Waveform inversion of the extrapolated data Z (km) 3 11 X (km)

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: Interpolation 3D layered velocity model 3D SEG/EAGE model Extrapolation 2D SEG/EAGE model Reverse time migration and waveform inversion Conclusions and future work

Conclusions Interpolation Extrapolation 3D marine SSP data can be interpolated with interferometry. Proposed approach is successfully tested on two synthetic models. Number of receivers can be increased 8 to 10 times by interferometry. Extrapolation 2D OBS extrapolation shows a promising results.

Future Work More work on the extrapolation (2D and 3D) Use down-going field and not total field Test on field data

We would like to thank the UTAM 2009 sponsors for their support. Acknowledgement We would like to thank the UTAM 2009 sponsors for their support. Thank You