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Generalized Differential Semblance Optimization

Generalized Differential Semblance Optimization. Sanzong Zhang and Gerard Schuster King Abdullah University of Science and Technology. Motivation. Problem: DSO sometimes has trouble achieving sufficient resolution. Differential Semblance Inversion. 0. 0. Z (km). Z (km). Marmousi. 6.

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Generalized Differential Semblance Optimization

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  1. Generalized Differential Semblance Optimization Sanzong Zhang and Gerard Schuster King Abdullah University of Science and Technology

  2. Motivation Problem: DSO sometimes has trouble achieving sufficient resolution Differential Semblance Inversion 0 0 Z (km) Z (km) Marmousi 6 6 X (km) X (km) 18 18 0 0 Solution: Generalized DSO = Subsurface Offset Inversion+DSO Generalized Differential Semblance Inversion Marmousi

  3. Outline Motivation Traveltime+waveform Inversion Generalized DSO Inversion 2 2 ε = ½∑[DdDt] ε = ½∑[DmDh] Numerical Tests Summary

  4. d(x,t) km/s 2.3 1.8 1.5 1.2 Wave Eq. Traveltime+Waveform Inversion (Zhou et al., 1995; Luo+GTS, 1991) t x d(x,t) Time Dtx 2 2 + ½∑[DtDd] ε = ½∑[wxDtx] x,t x Traveltime Waveform 2 2 e=½∑[DtxDd] e=½∑[DhDm] a WTW Misfit (1-a) a= 0 traveltimetomo. a= 1 FWI Low wavenumber High wavenumber 0 m 305 m Courtesy Ge Zhan 0 m 0 m 183 183

  5. MVA, DSO General Differential Semblance Optimization (Stork, 1992; Symes & Kern, 1994; Sava & Biondi, 2004 ; Almomim, 2011; Zhang et al, 2012) Sub. offset CIG d(x,t) Time Dtx 2 2 2 + ½∑[DmDh] ε = ½∑[ Dh] ε = ½∑[DmDh] Migration z,Dh z Z Z Dm -Dh -Dh +Dh +Dh DSO a Subsurface Offset (1-a) Dh Dm Objective Functions ∂(DmDh) 2 ∂Dh ∑[ DmDh 2 g(x) ∂c(x) ∂c(x) Low wavenumber Intermediate wavenumber Weight with amplitude Dm Weight with offset Dh 2 ∂Dm +DmDh ] ∂c(x) x,Dh General DSO Objective Function ½ Low wavenumber Intermediate wavenumber z,Dh = ∑ z,Dh General DSO Gradient g(x) =

  6. MVA, DSO General Differential Semblance Optimization (Stork, 1992; Symes & Kern, 1994; Sava & Biondi, 2004 ; Almomim, 2011; Zhang et al, 2012) Sub. offset CIG d(x,t) Time Dtx General DSO Inversion DSOInversion 0 0 2 2 + ½∑[DmDh] ε = ½∑[ Dh] Migration z,Dh z Z Z Dm Z (km) Z (km) -Dh -Dh +Dh +Dh DSO a Subsurface Offset (1-a) 6 6 X (km) X (km) 18 18 0 0 Dh Dm Objective Functions Low wavenumber Intermediate wavenumber

  7. Outline Motivation Traveltime+waveform Inversion Generalized DSO Inversion 2 2 ε = ½∑[DdDt] ε = ½∑[DmDh] Numerical Tests Summary

  8. Numerical Examples (a) True velocity model 0 Z (km) • 15 Hz Ricker wavelet • 242 shots , 70 m spacing • 700 receivers, 20 m spacing 6 0 18 X (km) (b) CSG 0 t (s) 10 14 X (km) 0

  9. 4.5 1 Numerical Examples Inverted model (Gen. DSO) Inverted model (DSO) Initial velocity model True velocity model 0 0 0 0 Z (km) Z (km) Z (km) Z (km) 6 6 6 6 X (km) X (km) 18 18 0 0 18 18 0 0 X (km) X (km)

  10. 4.5 1 Result Comparison Inverted model (Shen et al., 2001) Inverted model (DSO) Initial velocity model Initial velocity model 0 0 0 0 4 Z (km) Z (km) Z (km) Z (km) 6 3 3 6 X (km) 18 0 18 0 0 X (km) X (km) X (km) 0 9 9 2

  11. 2 2 b½∑[Dd] ε = a½∑[DmDh] + Numerical Examples LSM LSM General DSO RTM image (General DSO) RTM image (DSO) 0 0 Z (km) Z (km) 6 6 0 0 X (km) X (km) 18 18

  12. 2 2 b½∑[Dd] ε = a½∑[DmDh] + LSM LSM General DSO LSRTM image (General DSO) RTM image (General DSO) 0 0 Z (km) Z (km) 6 6 0 0 X (km) X (km) 18 18

  13. Numerical Examples Angle gathers (Gen. DSO) Gatthers) Angle gathers (DSO) 0 0 Z (km) Z (km) 6 6 0 0 X (km) X (km) 18 18

  14. Outline Motivation Traveltime+waveform Inversion Generalized DSO Inversion 2 2 ε = ½∑[DdDt] ε = ½∑[DmDh] Numerical Tests Summary

  15. Summary • Low+Intermediate Inversion = General DSO Inversion • Marmousi tests: DSO vs General DSO • Extension: Low+Int.+High wavenumber General DSO 2 ε = ½∑[DmDh] 2 2 b½∑[Dd] ε = a½∑[DmDh] + LSM General DSO

  16. Summary • Limitations • 1. No coherent events in CIGs, then unsuccessful • 2. Expensive • 3. Infancy, still learning how to walk • 4. Low+intermediate wavenumber unless LSM or FWI

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

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