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 = ∇ θ + ∇ × ψ

Helmholtz decomposition W = ∇ θ + ∇ × ψ P = ∇ · W S = ∇ × W

Isotropic wave-mode separation x-domain: stationary filtering � P = ∇ · W = D c [ W c ] c c = { x , y , z } : Cartesian coordinates

Isotropic wave-mode separation k-domain: vector projection � P = i k · � � i k c � W = W c c c = { x , y , z } : Cartesian coordinates

Anisotropic wave-mode separation k-domain: vector projection � qP = i u · � � i u c � W = W c c Dellinger and Etgen (1990)

Anisotropic wave-mode separation x-domain: non-stationary filtering � qP = ∇ a · W = L c [ W c ] c Yan and Sava (2009)

Wave-mode separation x-domain k-domain heterogeneous model homogeneous model expensive cheap

Efficient wave-mode separation step 1: separate in k-domain P r ( x ) = F − 1 � � i u r ( k ) · � W ( k ) r : reference models

Efficient wave-mode separation step 2: interpolate in x-domain � w r ( x ) P r ( x ) P ( x ) = r r : reference models

Multidimensional interpolation 1 w r = � m − m r � m = { ǫ, δ, ν, α }

V P

ǫ

δ

ν

W z

ISO

VTI

TTI

Conclusions ◮ wave-mode separation is applicable in 3D ◮ k-domain separation is cheap ◮ accuracy controlled by reference selection

Acknowledgments the sponsors of the Center for Wave Phenomena at Colorado School of Mines