Generalized Differential Semblance Optimization Sanzong Zhang and Gerard Schuster King Abdullah University of Science and Technology
Feb 22, 2016
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