Least Squares Migration of Stacked Supergathers Wei Dai and Gerard Schuster KAUST vs

RTM Problem & Possible Soln. Problem: RTM computationally costly; IO highProblem: RTM computationally costly; IO high Solution: Multisource LSM RTMSolution: Multisource LSM RTM Preconditioning speeds up by factor 2-3 Encoded LSM reduces crosstalk. Reduced comp. cost+memory

Outline MotivationMotivation Multisource LSM theoryMultisource LSM theory Signal-to-Noise Ratio (SNR)Signal-to-Noise Ratio (SNR) Numerical resultsNumerical results ConclusionsConclusions

Multisource Migration: m mig =L T d Forward Model: Phase Encoded Multisource Migration d +d =[ L +L ]m 1221 L {d { =[ L +L ](d + d ) TT = L d +L d TT L d +L d L d +L d212 1 Crosstalk noise Standard migration TT m mig = L d +L d TT L d +L d L d +L d T T m mig = L d +L d m mig

Multisource Migration: m mig =L T d Forward Model: Phase Encoded Multisrce Least Squares Migration d +d =[ L +L ]m 1221 L {d { =[ L +L ](d + d ) TT m mig = L d +L d TT L d +L d L d +L d212 1 Crosstalk noise Standard migration TT m = m + (k+1)(k)

Outline MotivationMotivation Multisource LSM theoryMultisource LSM theory Signal-to-Noise Ratio (SNR)Signal-to-Noise Ratio (SNR) Numerical resultsNumerical results ConclusionsConclusions

Standard Migration SNR GS # geophones/CSG # CSGs SNR=... migrate SNR= d(t) = Zero-mean white noise [S(t) +N(t) ] [S(t) +N(t) ] Neglect geometric spreading Standard Migration SNR Assume: migrate stack S 1 S GS G ~ ~ iterate GI Iterative Multisrc. Mig. SNR # iterations SNR= Cost ~ O(S) Cost ~ O(I)

SNR 0 1 Number of Iterations The SNR of MLSM image grows as the square root of the number of iterations. SNR = GI

Multisource LSM Summary IO 1 1/100 Cost ~ Resolution dx 1 1/2 SNR Stnd. Mig Multsrc. LSM Stnd. Mig Multsrc. LSM GSGI S I Cost vs Quality: Can I<<S?

Outline MotivationMotivation Multisource LSM theoryMultisource LSM theory Signal-to-Noise Ratio (SNR)Signal-to-Noise Ratio (SNR) Numerical resultsNumerical results ConclusionsConclusions

0 Z k(m) 3 0X (km)16 The Marmousi2 Model The area in the white box is used for SNR calculation. 200 CSGs. Born Approximation Conventional Encoding: Static Time Shift & Polarity Statics

0X (km)16 0 Z k(m) 3 0 Z (km) 3 0X (km)16 Conventional Source: KM vs LSM (50 iterations) Conventional KM 50x 1x Conventional KLSM

0X (km)16 0 Z k(m) 3 0 Z (km) 3 0X (km)16 Multisource KM (1 iteration) 200-source Supergather: Multisrc. KM vs LSM Multisource KLSM (300 iterations) 1.5 x 1 x 200 I=1.5S

IO 1 1/200 Cost ~ Resolution dx 1 1/2 SNR~ Stnd. Mig Multsrc. LSM Stnd. Mig Multsrc. LSM Cost vs Quality: Can I<<S? What have we empirically learned? S=200 I=300

SEG/EAGE Salt Reflectivity Model Use constant velocity model with c = 2.67 km/s Center frequency of source wavelet f = 20 Hz 320 shot gathers, Born approximation Z (km) X (km) 6 Encoding: Dynamic time, polarity statics + wavelet shaping Center frequency of source wavelet f = 20 Hz 320 shot gathers, Born approximation

0X (km)6 0 Z k(m) Z (km) 1.4 0X (km)6 Standard Phase Shift Migration (320 CSGs) Standard Phase Shift Migration vs MLSM (Yunsong Huang) Multisource PLSM (320 blended CSGs, 7 iterations) 1 x 44

Single-source PSLSM (Yunsong Huang) Model Error Iteration Number Unconventional encoding Conventional encoding: Polarity+Time Shifts

IO 1 1/320 Cost ~ Resolution dx 1 1/2 SNR~ Stnd. Mig Multsrc. LSM Stnd. Mig Multsrc. LSM I=7 1 1/44 Cost vs Quality: Can I<<S? Yes. What have we empirically learned? S=320

Conclusions Mig vs MLSM Conclusions Mig vs MLSM Cost: S vs I 3. Caveat: Mig. & Modeling were adjoints of one another. LSM sensitive starting model 5.Next Step: Sensitivity analysis to starting model SNR: VS GSGI 4. Unconventional encoding: I << S 2. Memory 1 vs 1/S

Back to the Future? Back to the Future? Poststack encoded migration DMO Prestack migration 1980s1980s ? Evolution of Migration Poststack migration 1960s-1970s