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Efficient elastic wave-mode separation in TTI media
Jia Yan and Paul Sava
Center for Wave Phenomena Colorado School of Mines
Efficient elastic wave-mode separation in TTI media Jia Yan and - - PowerPoint PPT Presentation
Efficient elastic wave-mode separation in TTI media Jia Yan and - - PowerPoint PPT Presentation
Efficient elastic wave-mode separation in TTI media Jia Yan and Paul Sava Center for Wave Phenomena Colorado School of Mines elastic imaging anisotropic heterogeneous 3D W z P SV SH Helmholtz decomposition W = +
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Wz
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P
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SV
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SH
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Helmholtz decomposition
W = ∇θ + ∇ × ψ
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Helmholtz decomposition
W = ∇θ + ∇ × ψ P = ∇ · W S = ∇ × W
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Isotropic wave-mode separation
x-domain: stationary filtering
P = ∇ · W =
- c
Dc [Wc]
c = {x, y, z}: Cartesian coordinates
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Isotropic wave-mode separation
k-domain: vector projection
- P = i k ·
W =
- c
i kc Wc
c = {x, y, z}: Cartesian coordinates
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Anisotropic wave-mode separation
k-domain: vector projection
- qP = i u ·
W =
- c
i uc Wc
Dellinger and Etgen (1990)
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Anisotropic wave-mode separation
x-domain: non-stationary filtering
qP = ∇a · W =
- c
Lc[Wc]
Yan and Sava (2009)
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Wave-mode separation
x-domain
heterogeneous model expensive
k-domain
homogeneous model cheap
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Efficient wave-mode separation
step 1: separate in k-domain
Pr (x) = F−1 i ur (k) · W (k)
- r: reference models
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Efficient wave-mode separation
step 2: interpolate in x-domain
P (x) =
- r
wr (x) Pr (x)
r: reference models
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Multidimensional interpolation
wr = 1 m − mr m = {ǫ, δ, ν, α}
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VP
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ǫ
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δ
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ν
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Wz
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ISO
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VTI
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TTI
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Conclusions
◮ wave-mode separation is applicable in 3D ◮ k-domain separation is cheap ◮ accuracy controlled by reference selection
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