Multisource Least-Squares Migration Multisource Least-Squares Migration of Marine Streamer Data with Frequency-Division Encoding Yunsong Huang and Gerard Schuster Yunsong Huang and Gerard SchusterKAUST

Outline Multisource LSMMultisource LSM Problem with Marine DataProblem with Marine Data Multisource LSM with Frequency DivisionMultisource LSM with Frequency Division Numerical resultsNumerical results ConclusionsConclusions

Multisource vs Benefit: Reduction in computation and memory Liability: Crosstalk noise …

d 1 +d 2 = [L 1 +L 2 ]m =[ L +L ](d + d ) 1 TT m mig crosstalk migrate m ~ [L 1 +L 2 ](d 1 +d 2 ) TT = L 1 d 1 +L 2 d 2 + L 1 d 2 +L 2 d 1 T T T T d 1 d 2 d 1 +d 2 vs standard mig. Multisource Multisource (2) d ~ blended data L ~ blended forward modeling operator

K=1K=10 Multisource LSM Inverse problem: || d – L m || 2 ~~ 1 2 J = arg min m  misfit m (k+1) = m (k) +  L  ~T~T Iterative update:

Outline Multisource LSMMultisource LSM Problem with Marine DataProblem with Marine Data Multisource LSM with Frequency DivisionMultisource LSM with Frequency Division Numerical resultsNumerical results ConclusionsConclusions

observed data simulated data misfit = erroneous misfit Problem with Marine Data

Outline Multisource LSMMultisource LSM Problem with Marine DataProblem with Marine Data Multisource LSM with Frequency DivisionMultisource LSM with Frequency Division Numerical resultsNumerical results ConclusionsConclusions

Solution - Every source sends out a unique identifier that survives LTI operations - Every receiver acknowledge the contribution from the ‘correct’ sources. observed simulated

152 sources/group R  Group 1 N  frequency bands of source spectrum: Frequency Division 2.2 km  N  = 5 t trav f peak

Outline Multisource LSMMultisource LSM Problem with Marine DataProblem with Marine Data Multisource LSM with Frequency DivisionMultisource LSM with Frequency Division Numerical results (2D)Numerical results (2D) ConclusionsConclusions

0 Z (km) 1.48 a) Original b) Standard Migration Migration images Migration images (input SNR = 10dB) X (km) c) Standard Migration with 1/8 subsampled shots 0 Z (km) X (km) d) 304 shots/gather 26 iterations 304 shots in total an example shot and its aperture

Iteration number Convergence curves. Input SNR = 10dB data misfit Normalized data misfit 304 shots/gather 38 shots/gather Conjugate gradient Encoding anew and resetting search direction

Shots per supergather gain Computational gain Conventional migration: Sensitivity to input noise level SNR=10dB SNR=30dB SNR=20dB

Ns: # shots subsumed in a supergather Nit: # of iterations that call for new encoding (i.e., new frequency division scheme) i) If data is stored on hard disk – The I/O cost of our proposed method is Nit/Ns times that of standard migration. ii) If data is stored on tape – The I/O cost of our proposed method is 1+  times that of standard migration. I/O considerations

Conventional migration Proposed method I/O cost i)Data on hard disk ii) Data on tape

3 Stacked migration vs successive least-squares stacked migration: successive least-squares:

Outline Multisource LSMMultisource LSM Problem with Marine DataProblem with Marine Data Multisource LSM with Frequency DivisionMultisource LSM with Frequency Division Numerical results (3D)Numerical results (3D) ConclusionsConclusions

a swath swaths, 50% overlap 16 cables 100 m 6 6 km m sources 20 m 4096 sources in total SEG/EAGE Model+Marine Data 13.4 km 3.7 km

Numerical Results 3.7 km 6.7 km True reflectivities Conventional migration 13.4 km shots/super-gather, 16 iterations 8 x gain in computational efficiency

IO 1 ~1/36 Cost Resolution dx 1 ~double Migration SNR Stnd. Mig Multsrc. LSM Stnd. Mig Multsrc. LSM ~1 1 ~ 0.1 Cost vs Quality: Can I<<S? Yes. What have we empirically learned? 1