Least-squares Migration and Least-squares Migration and Full Waveform Inversion with Multisource Frequency Selection Yunsong Huang Yunsong Huang Sept. 5, 2013

IntroductionIntroduction Multisource Frequency SelectionMultisource Frequency Selection –Least-squares migration (LSM)  test on 2D and 3D synthetic data –Full Waveform Inversion (FWI)  test on 2D synthetic and field GOM data Resolutions for Wave Equation ImagingResolutions for Wave Equation Imaging SummarySummary Outline

Gulf of Mexico Seismic Survey m L m = d N N Time (s) 6 X (km) 4 0 d Goal: Solve overdetermined System of equations for m Predicted dataObserved data

Details of Lm = d Time (s) 6 X (km) 4 0 d G(s|x)G(x|g) G(s|x)G(x|g)m(x)dx = d(g|s) Reflectivity or velocity model Predicted data = Born approximation Solve wave eqn. to get G’s m

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

K=1 K=10 Multisource LSM & FWI Inverse problem: || d – L m || 2 ~~ 1 2 J = arg min m dd 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

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)

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

IntroductionIntroduction Multisource Frequency SelectionMultisource Frequency Selection –Least-squares migration (LSM)  test on 2D and 3D synthetic data –Full Waveform Inversion (FWI)  test on 2D synthetic and field GOM data Resolutions for Wave Equation ImagingResolutions for Wave Equation Imaging SummarySummary Outline

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

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

IntroductionIntroduction Multisource Frequency SelectionMultisource Frequency Selection –Least-squares migration (LSM)  test on 2D and 3D synthetic data –Full Waveform Inversion (FWI)  test on 2D synthetic and field GOM data Resolutions for Wave Equation ImagingResolutions for Wave Equation Imaging SummarySummary Outline

X Y Z kx ky  Phase-shift Migration Embarrassingly parallel domain decomposition ZZ  Multisource freq. sel. initially implemented here.

X (km) 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 Shots per supergather gain Computational gain Conventional migration: SNR=30dB

3D Migration Volume 6.7 km True reflectivities 3.7 km Conventional migration 13.4 km shots/super-gather, 16 iterations 40 x gain in computational efficiency of OBS data 3.7 km

IntroductionIntroduction Multisource Frequency SelectionMultisource Frequency Selection –Least-squares migration (LSM)  test on 2D and 3D synthetic data –Full Waveform Inversion (FWI)  test on 2D synthetic and field GOM data Resolutions for Wave Equation ImagingResolutions for Wave Equation Imaging SummarySummary Outline

Transients Reduction nt 2nt causal periodic steady transient t t 8 Hz 4 Hz 2nt FDTD

periodic 0-lag correlate back-propagated residual wavefield steady transient forward-propagated source wavefield steady 2nt 1 t nt transient Computing FWI’s Gradient

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

Quasi-Monte Carlo Mapping Standard Random permutation  index 1 60 Source index 1 60 Source index 1 60  index 1 60 Q.M. w/ repelling Coulomb force

Quasi-Monte Carlo Mapping 3 iterations 31 iterations

IntroductionIntroduction Multisource Frequency SelectionMultisource Frequency Selection –Least-squares migration (LSM)  test on 2D and 3D synthetic data –Full Waveform Inversion (FWI)  test on 2D synthetic and field GOM data Resolutions for Wave Equation ImagingResolutions for Wave Equation Imaging SummarySummary Outline

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

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

Convergence Rates Waveform error Log normalized Log iteration number by individual sources 1 supergather, Quasi-Monte Carlo 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

Convergence Rates Velocity error Log normalized Log iteration number 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 iterations 1 supergather, Quasi-Monte Carlo encoding

IntroductionIntroduction Multisource Frequency SelectionMultisource Frequency Selection –Least-squares migration (LSM)  test on 2D and 3D synthetic data –Full Waveform Inversion (FWI)  test on 2D synthetic and field GOM data Resolutions for Wave Equation ImagingResolutions for Wave Equation Imaging SummarySummary Outline

Source wavelet estimation 3D to 2D conversion of the data initial velocity model estimation Run FWI in multiscales Generate RTM, CIG & CSG images Workflow: FWI on GOM dataset

water surface delay:  t s r Received direct wave combined with ghost Source wavelet

Estimated w(t) Bandpass filtered to [0, 25] Hz Power spectrum of (b) 0.8 s

Source wavelet estimation 3D to 2D conversion of the data initial velocity model estimation Run FWI in multiscales Workflow: FWI on GOM dataset Generate RTM, CIG & CSG images

Source wavelet estimation 3D to 2D conversion of the data initial velocity model estimation Run FWI in multiscales Workflow: FWI on GOM dataset traveltime + semblance Generate RTM, CIG & CSG images

Source wavelet estimation 3D to 2D conversion of the data initial velocity model estimation Run FWI in multiscales Workflow: FWI on GOM dataset 0—6 Hz, 51 x 376 0—15 Hz, 101x 752 0—25 Hz, 201x 1504 Multisource Freq. Sel.: # steps: method: freq. band: grid size: Gradient descent w/ line search. Stochastic gradient descent. Step size Mini-batch size: shots  8 supergathers

Z (km) Traveltime FWI cost: 1 X (km) Z (km) FWIwMFS cost: 1/8 Velocity models obtained from:

FWIwMFS: V Q.M. – V random permutation Velocity difference due to encoding schemes: Q.M. vs standard X (km) Z (km) Model size: 18.8 x 2.5 km Source freq: Hz Shots: 496Cable length: 6km Receivers/shot: 480 Baldplate GOM Dataset The freq. sel. scheme is resilient to specifics of encoding methods

Source wavelet estimation 3D to 2D conversion of the data initial velocity model estimation Run FWI in multiscales Workflow: FWI on GOM dataset Generate RTM, CIG & CSG images

X (km) Z (km) RTM image using traveltime tomogram

Z (km) X (km) RTM image using FWI tomogram

Z (km) X (km) RTM image using FWIwMFS tomogram

Zoomed views of the RTM images

CIGs for traveltime tomogram

CIGs for FWI tomogram

CIGs for FWIwMFS tomogram

Observed CSG 7 Time (s)

FWI predicted CSG 7 Time (s)

FWIwMFS predicted CSG 7 Time (s)

TRT predicted CSG 7 Time (s)

IntroductionIntroduction Multisource Frequency SelectionMultisource Frequency Selection –Least-squares migration (LSM)  test on 2D and 3D synthetic data –Full Waveform Inversion (FWI)  test on 2D synthetic and field GOM data Resolutions for Wave Equation ImagingResolutions for Wave Equation Imaging SummarySummary Outline

g s p L W First Fresnel Zone: | | + | | = | p s | + | p g | = L + /2 Wavepath Resolution (width)

Wavepath Resolution

IntroductionIntroduction Multisource Frequency SelectionMultisource Frequency Selection –Least-squares migration (LSM)  test on 2D and 3D synthetic data –Full Waveform Inversion (FWI)  test on 2D synthetic and field GOM data Resolutions for Wave Equation ImagingResolutions for Wave Equation Imaging SummarySummary Outline

Summary

Acknowledgements I thank –my advisor, Dr. Gerard T. Schuster, for his guidance, support and encouragement; –my committee members for the supervision over my dissertation; –the sponsors of CSIM consortium for their financial support; –my fellow graduate students for the collaborations and help over last 4 years.