Exercises 16 in section 175 Problem Timeconsuming picking 1 st arrival traveltimes and inverting Solution Early arrival waveform inversion EWI New Problem Estimate wavelet edit traces trialamperror ID: 534966
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Slide1
Mrinal: Maximum Entropy First Arrival Inversion
(Exercises 1-6 in section 17.5)
Problem:
Time-consuming picking 1
st
-arrival traveltimes
and inverting.
Solution
: Early arrival waveform inversion (EWI)
New Problem:
Estimate wavelet, edit traces, trial&error
testing
Better Solution?:
maximum entropy inversion of 1
st
arrivals.
1. Window about early arrivals
2. Find s(x) that maximizes migration
image at source.
If you have correct s(x) then impulsive focus,
otherwise defocused focus at source at t=0
Adv. Inv. Project: Max
Ent
. EWISlide2
Mrinal: Maximum Entropy First Arrival Inversion
(Exercises 1-6 in section 17.5)
Better Solution?:
maximum entropy inversion of 1
st
arrivals.
1. Window about early arrivals
2. Find s(x) that maximizes migration
image at source.
If you have correct s(x) then impulsive focus,
otherwise defocused focus at source at t=0
http://en.wikipedia.org/wiki/Entropy_%28information_theory%29
entropy
P(x
i
)
Almost certain
Event is at x
i
= 0,
so H(x)=-
S
P(x)
ln
(P(x))=-1ln(1
)
x
i
P(x
i
)
x
i
-S
P(x
i
)
lnP
(x )=-
S
1/n
ln
(1/n)
= -
ln
(1/n)=-
ln
(1)+
ln
(n)>-
ln
(1)
More uncertain higher entropy
More focused migration images
lead to More negative H
Adv. Inv. Project: Max
Ent
. EWI
Penalize images far from
Source locationSlide3
Mrinal: Maximum Entropy First Arrival Inversion
(Exercises 1-6 in section 17.5)
Better Solution?:
maximum entropy inversion of 1
st
arrivals.
1. Window about early arrivals
2. Find s(x) that maximizes migration
image at source.
If you have correct s(x) then impulsive focus,
otherwise defocused focus at source at t=0
x
i
3. Find s(x) that focuses migration
image at source
4. s(x)
(k+1)
= s(x)
(k)
–
a
∂
e
/
∂s(x)
Adv. Inv. Project: Max
Ent
. EWISlide4
Adv. Inv. Project: Max
Ent
. EWI
Mrinal: Maximum Entropy First Arrival Inversion
(Exercises 1-6 in section 17.5)
Better Solution?:
maximum entropy inversion of 1
st
arrivals.
1. Window about early arrivals
2. Find s(x) that maximizes migration
image at source.
If you have correct s(x) then impulsive focus,
otherwise defocused focus at source at t=0
3. Find s(x) that maximizes migration
image at source
4. s(x)
(k+1)
= s(x)
(k)
–
a
∂
e
/
∂s(x)Slide5
Adv. Inv. Projects: LSMF
Bowen: Least squares migration filtering
Problem:
Disentangle P from S waves
Solution: Moveout based ok for simple models, not ok for complex models
Better Solution?:
Least squares migration filtering.
Ls = ∫dxd(s,g,t-t
sx +txg )
Lp = ∫dxd(
s,g,t-tsx +txg )
pps
sd=Lp mp
+ Ls ms
Lp
mp Ls
[]ms
= dSlide6
Bowen: Least squares migration filtering
L
s
= ∫dx d(s,g,t-tsx +
txg )Lp =
∫
dx d(s,g,t-tsx +txg )
pps
sd=Lp m
p + Ls ms
Lp
mp Ls
[]ms
= d
2. s(x)(k+1) = s(x)
(k) – a ∂e
/∂s(x)where
∂e/∂s(x) = L
T [Lm-
d]
Adv. Inv. Projects: LSMFSlide7
Bowen: Least squares migration filtering
L
s
= ∫dx d(s,g,t-tsx +
txg )Lp =
∫
dx d(s,g,t-tsx +txg )
pps
s
Lp mp Ls
[]
ms
= d2. s(x)(k+1)
= s(x)(k) – a ∂
e/∂s(x)
where ∂e/∂s(x) =
LT [Lm
-d]
Issues: Make it fast via encoded multisource migration. Regularizer constraints to eliminate crosstalk (Yunsong’s new regulrizaer or Fomels plane wave destructor)
Adv. Inv. Projects: LSMFSlide8
Iterative migration deconvolution
m
(k+1) =
m(k) - a[LTL][ LTL
m - m(mig)]
Fast mutisource encoded
Separation of eventsVelocity updates
2. POCS separation of multisource supergather into separate shot gathers for GDM
Adv. Inv. Projects: MD or POCS
Eignevalues squared! Worse cond. #