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Multisource Full Waveform Inversion of Marine Streamer Data with Frequency Selection Multisource Full Waveform Inversion of Marine Streamer Data with Frequency Selection Yunsong Huang and Gerard Schuster Yunsong Huang and Gerard SchusterKAUST

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Goal of the studyGoal of the study MultisourceMultisource –Mismatch solution with marine data Low-discrepancy frequency codingLow-discrepancy frequency coding Numerical resultsNumerical results ConclusionsConclusions Outline

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Standard optimization for FWI Goal of the Study Multisource optimization for marine FWI Speed and quality comparison

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Aim of the studyAim of the study Multisource MigrationMultisource Migration –Least Squares Multisource Migration Low-discrepancy frequency codingLow-discrepancy frequency coding Numerical resultsNumerical results ConclusionsConclusions Outline

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Standard Migration vs Multisource Migration Benefit: Reduced computation and memory Liability: Crosstalk noise … Given: d 1 and d 2 Find: m Soln: m=L 1 d 1 + L 2 d 2 TT Given: d 1 + d 2 Find: m = L 1 d 1 + L 2 d 2 TT + L 1 d 2 + L 2 d 1 TT Soln: m = (L 1 + L 2 )(d 1 +d 2 ) T Romero, Ghiglia, Ober, & Morton, Geophysics, (2000) Src. imaging cond. xtalk

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

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Brief Early History Multisource Phase Encoded Imaging Romero, Ghiglia, Ober, & Morton, Geophysics, (2000) Krebs, Anderson, Hinkley, Neelamani, Lee, Baumstein, Lacasse, SEG Zhan+GTS, (2009) Virieux and Operto, EAGE, (2009) Dai, and GTS, SEG, (2009) Migration Waveform Inversion and Least Squares Migration Biondi, SEG, (2009)

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Aim of the studyAim of the study Multisource MigrationMultisource Migration –Mismatch solution with marine data Low-discrepancy frequency codingLow-discrepancy frequency coding Numerical resultsNumerical results ConclusionsConclusions Outline

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Land Multisource FWI Fixed spread Simulation geometry must be consistent with the acquisition geometry

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4 Hz8 Hz Marine Multisource FWI Simulated land data Observed marine data Mismatch solution with marine data wrong misfit Freq. encoding 8 Hz 4 Hz Blend Decode & mute purify 4 Hz8 Hz F.T., freq. selec. 4 Hz8 Hz

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Multisource FWI Freq. Sel. Workflow m (k+1) = m (k) + L d ~T~T For k=1:K end Filter and blend observed data: d d d Purify predicted data: d pred d pred d pred Data residual: d=d pred -d Select unique frequency for each src

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Aim of the studyAim of the study MultisourceMultisource –Mismatch solution with marine data Low-discrepancy frequency codingLow-discrepancy frequency coding Numerical resultsNumerical results ConclusionsConclusions Outline

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Low-discrepancy Frequency Encoding Frequency index 1 60 Source index 1 60 Source index 1 60 Low-discrepancy encoding Standard Frequency index 1 60 Frequency index 1 60

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Aim of the studyAim of the study MultisourceMultisource –Mismatch solution with marine data Low-discrepancy frequency codingLow-discrepancy frequency coding Numerical resultsNumerical results ConclusionsConclusions Outline

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Frequency-selection FWI of 2D Marine Data Source freq: 8 Hz Shots: 60 Receivers/shot: 84 Cable length: 2.3 km Z (km) 0 1.5 0 6.8X (km) 4.5 1.5 (km/s)

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FWI images Starting model Actual model Z (km) 0 1.5 Standard FWI (69 iterations) Z (km) 0 1.5 0 X (km) 6.8 Multisource FWI (262 iterations) 0 X (km) 6.8

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Convergence Rates Waveform error Log normalized Log iteration number 1 0.025 1 262 69 by individual sources 1 supergather, low-discrepancy encoding 3.8 x 1 supergather, standard encoding Same asymptotic convergence rate of the red and white curves Faster initial convergence rate of the white curve

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Convergence Rates Velocity error Log normalized Log iteration number 1 0.35 1 262 69 1 supergather, standard encoding by individual sources 3.8 x Speedup 60 / 2 / 2 / 3.8 = 4 Gain 60: sources Overhead factors: 2 x FDTD steps 2 x domain size 3.8 x iteration number 1 supergather, low-discrepancy encoding

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Convergence Rates Velocity error (normalized) 1 0.75 iteration number 1 10 standard encoding Low-discrepancy encoding is 12% to 3 x faster initially than Standard encoding

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Frequency selection is implemented in FDTDFrequency selection is implemented in FDTD –2 x time steps per forward or backward modeling Low-discrepancy frequency encodingLow-discrepancy frequency encoding –affects no asymptotic rate of convergence –helps to reduce model error in the beginning of simulation 4x speedup for the multisource FWI on the synthetic marine model4x speedup for the multisource FWI on the synthetic marine model Conclusions

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Thanks Sponsors of the CSIM (csim.kaust.edu.sa) consortium at KAUST & KAUST HPC

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Thank you!

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At lower (say 1/2) frequencies, the frequency selection strategy sees fewer frequency resources, butAt lower (say 1/2) frequencies, the frequency selection strategy sees fewer frequency resources, but Computation cost: Computation cost: –(Nx x Nz) x Ns x Nt is reduced by 1/16, –since each factor is halved. This part does not degrade the overall speedup much. In the case of multiscale

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Convergence Rates Velocity error (normalized) 1 0.75 iteration number 1 10 by individual sources 1 supergather, standard encoding H L Slew rate = H/L 1 supergather, low-discrepancy encoding

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encoding Standard Frequency index 1 60 Freq. #60 assigned to source #31 crowded vacant Low-discrepancy Frequency Encoding Source index 1 60 Prefers uniformity in freq. assignment / encoding.

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