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fiber optics elastic imaging

Ivan Lim Chen Ning 1

Paul Sava 1, Whitney Schultz 2, Jim Simmons 2

1Center for Wave Phenomena2Reservoir Characterization Program

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equation of motion

ρ u−∇ · t = f

stress− strain relation

−t + c : e = m

u = displacement

t = stress tensor

f = volume force density

ρ = density

c = stiffness tensor

m = deformation density

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G p = q

G = wave propagator

p = [ f, m ]

q = [ u, t ]

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I =∑

t ( ρ us · ur − ts · er )

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I =

([ρ1/2 B 0

0 I

] [us

ts

])ᵀ [ρ1/2 B 0

0 I

] [ur

−er

]

B = time derivative

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I =

([ρ1/2 B 0

0 I

] [us

ts

])ᵀ [ρ1/2 B 0

0 I

] [ur

−er

]

B = time derivative

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I = ( � ws )ᵀ � wr

� =

[ρ1/2 B 0

0 I

]

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I = ( �ᵀ �ws )ᵀ wr

� =

[ρ1/2 B 0

0 I

]

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I = Eᵀwr

E = energy demigration operator

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G p = q

I = Eᵀwr

G = wave propagator

E = energy demigration operator

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G p = q

I = EᵀGᵀKᵀdr

G = wave propagator

E = energy demigration operator

K = data extraction

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I = Lᵀdr

L = demigration operator

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I = Lᵀdr

dr = L I

L = demigration operator

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I = LᵀSᵀWᵀdr

dr = W S L I

L = demigration operator

S = compliance operator

W = windowing operator

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vertical sourceVp = 2.0 km/s

receiversVs = 1.5 km/s

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migration

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least− squares

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S P

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upgoing

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migration

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migration

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migration

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least− squares

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initialresidual

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finalresidual

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migration

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least− squares

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conclusions

introduce new operators

avoid strain to displacement

match DAS data

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future work

regularize shot data

calculate optimal stacking

perform velocity tomography

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acknowledgement

CWP Sponsors

Devon Energy Corporation

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