Migration Deconvolution

1
I.1 Diffraction Stack Modeling
1. Forward modeling operator L
2
Forward Modeling
3
Forward Modeling Sum of Weighted Hyperbolas
4
GREENs FUNCTION
G(xx)
5
ASYMPTOTIC GREENs FUNCTION
G(xx)
A(x,x)
6
ASYMPTOTIC GREENs FUNCTION
e
G(xx)
A(x,x)
7
Diffraction Stack Modeling ZO Modeling
8
Diffraction Stack Modeling ZO Modeling
Dipping Reflector
9
Diffraction Stack Modeling ZO Modeling If c for
DS is ½ that for ZO Modeling
10
ASYMPTOTIC GREENs FUNCTION

e
d(x)
A(x,x)
11
QUICK REVIEW FOURIER TRANSFORM
? (t)
12
Forward Modeling Operator
d(x,t)
R(x)
A(x,x)
13
Forward Modeling Operator
d(x,t)
R(x)
A(x,x)
14
SUMMARY
1. Exploding Reflector Modeling Diffraction
Stack Modeling
R(x)
d(x,t)
Sum over reflectors
A(x,x)
Data variables
2. High Frequency Approximation (i.e c(x)
variations gt 3? )
3. Approximates Kinematics of ZO Sections, but
not Dynamics
15
MATLAB Exercise Forward Modeling
1. To account for the source wavelet W(t), we
convolve data with W(t) (recall ? (t- ? )W(t)
W(?) ) so that modeling equation becomes
(neglect A)
A). Execute MATLAB program forw.m to
generate synthetic data for a point scatterer
and a 30 Hz wavelet. B). Execute MATLAB program
forwl.m to generate synthetic data for a dipping
layer model C). Execute MATLAB program forw.m to
generate synthetic data for a syncline model.
Note diffractions and multiple arrivals. Adjust
for new models. Why the second time derivative?
16
MATLAB Exercise Forward Modeling
for ixtrace1ntrace for ixsistartiend
for izs1nz r sqrt((ixtracedx-ixs
dx)2(izsdx)2) time 1 round(
r/c/dt ) data(ixtrace,time)
migi(ixs,izs)/r data(ixtrace,time) end
end data1(ixtrace,)conv2(data(ixtrace,),ri
ck) end
Src Wave