Interferometric Interpolation of 3D SSP Data Sherif M. Hanafy Weiping Cao Gerard T. Schuster October 2009

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: –3D layered velocity model –SEG/EAGE model Conclusions and future work

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: –3D layered velocity model –SEG/EAGE model Conclusions and future work

Problem In marine surveys, receiver interval could be large (especially in cross line direction) Solution: Use interferometric interpolation Sparse geometry Dense geometry

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: –3D layered velocity model –SEG/EAGE model Conclusions and future work

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

Workflow Input Field DataWater Layer Thickness Generate GF for Water Multiples Interpolate/Extrapolate M issing D ata Max. Itr (MF ) Get Virtual CSG Max Iteration Final CSG N Matching Filter N Y Y Time (s) 03.0 X (km) 04.5 Sea bed Ocean Surface Time (s) 03.0 X (km) 04.5 Time (s) 03.0 X (km) 04.5 Input Data Unfiltered Virtual Filtered Virtual G(x|B) G(B|A) G(x|A)

Time (s) 03.0 X (km) 04.5 Time (s) 03.0 X (km) 04.5 Local Matching Filter f (t,x 0 )d Virt (t,x 0 )d Real (t,x 0 )≈*

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: –3D layered velocity model –SEG/EAGE model Future work

Numerical Results 3D velocity model is used to test the interpolation approach 3000 x 3000 x 1400 m 3 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 depth of 750 m 3 km 1.4 km Source

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

2D Example Line # 1 Source Input 60 Traces Trace interval = 50 m Goal 300 Traces Trace interval = 10 m Sparse geometryDense geometry

2D Test 0 5 Time (s) X (m) Original CSG, 300 trace, dx = 10 m Keep every 4 th trace Line # 1 Source 0 5 Time (s) X (m) Sparse CSG, 60 trace, dx = 50 m

2D Test 0 5 Time (s) X (m) Virtual CSG before matching filter, 300 trace, dx = 10 m Virtual CSG after matching filter, 300 trace, dx = 10 m 0 5 Time (s) X (m) Line # 1 Source 0 5 Time (s) X (m) Original CSG, 300 trace, dx = 10 m

3D Example Input 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 Sparse geometry Dense geometry

SSP Data Line # Time (s) X (m) Original CSG, 300 trace, dx = 10 m 0 5 Time (s) X (m) Sparse CSG, 60 trace, dx = 50 m Line # 180

SSP Virtual Data 0 5 Time (s) X (m) Virtual CSG, 300 trace, dx = 10 m 0 5 Time (s) X (m) Original CSG, 300 trace, dx = 10 m Iterations: 1 interpolation and 8 MF Line # 180

SSP Virtual Data 0 5 Time (s) X (m) 0 5 Time (s) X (m) Original CSG, 300 trace, dx = 10 m Iterations: 3 interpolation and 8 MF/interpolation Original CSG, 300 trace, dx = 10 m Line # 180

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: –3D layered velocity model –SEG/EAGE model Conclusions and future work

SEG/EAGE Velocity Model Velocity (m/s)

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

Scale 2 km Time (s) Streamer 21 SEG/EAGE Model – Input Data

Scale 2 km ’1’ 0 8 Time (s) Streamer 212’1’ SEG/EAGE Model – Virtual Data

Scale 2 km 0 SEG/EAGE Model – Real Data 0 8 Time (s) Streamer 4132

True-Virtual Traces Comparison

Outline Problem: Missing and sparse traces Theory: Interferometric interpolation and extrapolation Numerical results: –3D layered velocity model –SEG/EAGE model Conclusions and future work

Conclusions 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.

Limitation and Advantage Limitation Non-aliased data are required for better interpolation Advantage Irregular geometry can be used to generate more dense and regular geometry

Future Work Extrapolation of the data Test on field data

Acknowledgement We would like to thank the UTAM 2008 sponsors for their support. Thank You

Input Field DataWater Layer Thickness Generate GF for Water Multiples Interpolate/Extrapolate M issing D ata Max. Itr (MF ) Get Virtual CSG Max Iteration Final CSG N Matching Filter N Y Y