generalized differential semblance optimization
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Generalized Differential Semblance Optimization
Sanzong Zhang and Gerard SchusterKing Abdullah University of Science and Technology
Motivation
0
60 18
Z (k
m)
X (km)
Differential Semblance Inversion
0
60 18
Z (k
m)
X (km)
Problem: DSO sometimes has trouble achieving sufficient resolution
Solution: Generalized DSO = Subsurface Offset Inversion+DSOGeneralized Differential Semblance Inversion
Marmousi
Marmousi
Outline
Traveltime+waveform Inversion Generalized DSO Inversion
ε = ½∑[Dm Dh]2ε = ½∑[Dd Dt] 2
Motivation
Numerical Tests
Summary
Wave Eq. Traveltime+Waveform Inversion(Zhou et al., 1995; Luo+GTS, 1991)
Tim
e
ε = ½∑[wxDtx]2
x
Traveltime
+ ½∑[DtDd] 2
x, t
Waveform
WTW Misfit
Dtx
High wavenumber
1830 m
d(x,t)
(1-a) a
2.3
1.2
km/s
1.5
1.8
Low wavenumber
305 m
0 m
1830 mCourtesy Ge Zhan
a= 0 traveltime tomo. a= 1 FWI
e=½∑[DtxDd]2
e=½∑[DhDm]2
+ ½∑[DmDh]2
z, Dh
MVA, DSO General Differential Semblance Optimization
Tim
eε = ½∑[ Dh]
2
z
Subsurface Offset DSO
DhZ
d(x,t)
+Dh-Dh
Low wavenumber Intermediate wavenumber
Dtx
Dm
ObjectiveFunctions
Weight with offset DhWeight with amplitude Dm
z,Dhε = ½∑[Dm Dh] 2General
DSO ObjectiveFunction
General DSO Gradient
g(x) =
Low wavenumber
x,Dh ∂c(x)∂Dh ∑[ Dm Dh
2+ DmDh2 ∂Dm
∂c(x)]
Intermediate wavenumber
+Dh-Dh
Sub. offset CIG
Z
Migration
Dm
z,Dh ∂c(x)
∂(DmDh)= ∑ 2
g(x) ½
(1-a) a
(Stork, 1992; Symes & Kern, 1994;Sava & Biondi, 2004 ;Almomim, 2011;Zhang et al, 2012)
Tim
e
DhZ
d(x,t)
+Dh-Dh
Dtx
Dm+Dh-Dh
Sub. offset CIG
Z
Migration
0
60 18
Z (k
m)
X (km)
DSO Inversion0
60 18
Z (k
m)
X (km)
General DSO Inversion
MVA, DSO General Differential Semblance Optimization(Stork, 1992; Symes & Kern, 1994;Sava & Biondi, 2004 ;Almomim, 2011;Zhang et al, 2012)
+ ½∑[DmDh]2
z, Dhε = ½∑[ Dh]
2
z
Subsurface Offset DSO
Low wavenumber Intermediate wavenumber
ObjectiveFunctions
Dm (1-a) a
Outline
Traveltime+waveform Inversion Generalized DSO Inversion
ε = ½∑[Dm Dh] 2ε = ½∑[Dd Dt] 2
Motivation
Numerical Tests
Summary
Numerical Examples0
60 18
Z (k
m)
X (km)
0
10
t (s)
X (km)0 14
15 Hz Ricker wavelet 242 shots , 70 m spacing 700 receivers, 20 m spacing
(a) True velocity model
(b) CSG
Numerical Examples0
60 18
Z (k
m)
X (km)
Initial velocity model0
60 18
Z (k
m)
X (km)
True velocity model
0
60 18
Z (k
m)
X (km)
Inverted model (DSO)0
60 18
Z (k
m)
X (km)
Inverted model (Gen. DSO)
4.5
1
0
60 18
Z (k
m)
X (km)
Initial velocity model0
60 18
Z (k
m)
X (km)
Inverted model
0
30 9
Z (k
m)
X (km)
Initial velocity model0
30 9
Z (k
m)
X (km)
Inverted model (DSO)
Result Comparison
2
4
4.5
1
(Shen et al., 2001)
Numerical Examples RTM image (DSO)Z
(km
)0
60 18X (km)
RTM image (General DSO)
Z (k
m)
0
60 18X (km)
ε = a½∑[Dm Dh] +2 2
LSMGeneral DSOb½∑[ Dd]
LSM
LSRTM image (General DSO)
Z (k
m)
0
60 18X (km)
RTM image (General DSO)
Z (k
m)
0
60 18X (km)
ε = a½∑[Dm Dh] +2 2
LSMGeneral DSOb½∑[ Dd]
LSM
Numerical ExamplesAngle gathers (DSO)
Z (k
m)
0
60 18X (km)
Angle gathers (Gen. DSO) Gatthers)
Z (k
m)
0
60 18X (km)
Outline
Traveltime+waveform Inversion Generalized DSO Inversion
ε = ½∑[Dm Dh] 2ε = ½∑[Dd Dt] 2
Motivation
Numerical Tests
Summary
Summary Low+Intermediate Inversion = General DSO Inversion
Marmousi tests: DSO vs General DSO
Extension: Low+Int.+High wavenumber General DSO
ε = ½∑[Dm Dh] 2
ε = a½∑[Dm Dh] +2
b½∑[ Dd] 2
LSMGeneral DSO
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
ThanksSponsors of the CSIM (csim.kaust.edu.sa)
consortium at KAUST & KAUST HPC