Transcript Extended Diffraction-Slice Theorem for Wavepath Traveltime

Acoustic Multi-source Waveform
Inversion with Deblurring
Ge Zhan and Wei Dai
Jan. 7, 2010
Outline
• Motivation
• Theory
• Numerical Results
• Conclusions
Motivation

Problem

Waveform inversion is computer intensive due to
multiple iterations of forward modeling and backpropagation.

Phase-encoded FD simulation (Morton, 1998) with insufficient
temporal duration yields noticeable artifacts.

Solution

Preconditioned multi-source waveform inversion.

Encoded multi-source deblurring filter to limit crosstalk noise.
Outline
• Motivation
• Theory
• Numerical Results
• Conclusions

Standard Waveform Inversion Procedure
pobs

Compute the waveform residual by calculating the difference
between observed and calculated data.

Cross-correlation of the backpropagated residual wavefield
with the corresponding forward modeled source wavefield.

Update the velocity model by using the misfit gradient in
a non-linear iterative way.
pcal
S

Multi-source Waveform Inversion
g ( x, z )   S * ( x, z,  ) R( x, z,  )
Single-source gradient
R

Multi-source wavefield
N
S ( x, z,  )   a j ( ) S j ( x, z,  )
j 1
N
R( x, z,  )   a j ( ) R j ( x, z,  )
j 1
N=4
Multi-source gradient
g ( x , z )   S * ( x , z ,  ) R ( x, z ,  )

N
  | a j ( ) |2 S *j ( x, z ,  ) R j ( x, z,  ) 
j 1 
N
N
*
*
a
(

)
a
(

)
S
 j k j ( x, z,  ) Rk ( x, z,  )
j  k k 1 
Time
d1= Lm1
Z
Z
Time
Multi-source Deblurring Filter
d0= Lm0
m0
m1
X
X
Time
mmig = LT(d1-d0)
mmig* F = (m1-m0)
Z

F=
X
Outline
• Motivation
• Theory
• Numerical Results
• Conclusions
Velocity Model for Synthetic Tests
800 geophones
2D Marmousi Velocity Model
0
km/s
8 multi-source gathers
100 shots in a multisource gather
Z (km)
4.5
3.5
2.5
1.5
3
peak freq = 7.5 Hz
0
dx = 20 m
X (km)
16
Starting Model for Inversion
0
ds = 20 m
Z (km)
dg = 20 m
nsamples = 6000
dt = 0.002 s
3
0
X (km)
16
Construction of Deblurring Filter
a) Point Scatterer Model
Z (km)
0
3
b) Migration Image of Multi-source Point Scatterers
Z (km)
0
3
c) Migration Image after Deblurring Filter
Z (km)
0
3
0
X (km)
16
Application of Deblurring Filter
a) Multisource Misfit Gradient
Z (km)
0
3
b) Gradient after Deblurring
Z (km)
0
3
0
X (km)
16
a) Marmousi Velocity Model
0
km/s
Z (km)
4.5
1
3.5
2
2.5
3
1.5
b) Starting Model
Z (km)
0
1
2
3
c) Inverted velocity after 300 iterations using 8 multi-source gathers
Z (km)
0
1
2
3
0
X (km)
16
Residual Curves of Multi-source Waveform Inversion
100
Residual Percentage (%)
w/ deblurring
w/o deblurring
0
0
50
100
150
Iteration #
200
250
300
Outline
• Motivation
• Theory
• Numerical Results
• Conclusions
Conclusions
 We
present the theory of multi-source waveform inversion with
multi-source preconditioner.

Synthetic results show that use of deblurring filter provides
a good inverted model with less computational cost (1/100).
 The
deblurring filter accelerates convergence in the early
iterations and is more powerful in the shallow and middle
parts and less effective in the lower part.
 We
can speedup more than 100x by blending more than 100 shot
gathers in a multi-source gather, but stronger crosstalks are
generated and more iterations are needed as well.