Wave-Equation Migration in Anisotropic Media Jianhua Yu University of Utah

Contents Motivation Anisotropic Wave-Equation Migration Numerical Examples: Cusp model Conclusions 2-D SEG/EAGE model 3-D SEG/EAGE model

Contents Motivation Anisotropic Wave-Equation Migration Numerical Examples: Cusp model Conclusions 2-D SEG/EAGE model 3-D SEG/EAGE model

What Blurs Seismic Images? Irregular acquisition geometry Bandwidth source wavelet Velocity errors Higher order phenomenon: Anisotropy

Anisotropic Imaging Ray-based anisotropic migration: Anisotropic velocity model Anisotropic wave-equation migration: ---Ristow et al, Han et al. 2003

Objective: High efficiency Improve image accuracy Develop 3-D anisotropic wave-equation migration method in orthorhombic model >78 wave propagator o

Contents Motivation Anisotropy Wave-Equation Migration Numerical Examples: Cusp model Conclusions 2-D SEG/EAGE model 3-D SEG/EAGE model

General Wave Equation Wave equation in displacement U i : displacement component C ijkl : 4th-order stiffness tensor

Eigensystem Equation Polarization components of P-P, SV, and SH waves

Orthorhombic Anisotropic

Decoupled P plane Wave Motion Equations in (x,z) and (y,z) planes and

Decoupled P plane Wave Motion Equations in (x,z) and (y,z) planes and det

Dispersion Equations (x,z) plane (y,z) plane Thomsen’s Parameters

VTI: FFD algorithm

FFD Anisotropy Migration

How to Set Velocity and Anisotropy Parameters a & b : Optimization coefficients of Pade approximation for FD Velocity: Anisotropy:

0 5 Error % 090 Pade Approximation Comparison Angle

Error % 078 Pade Approximation Comparison Angle Beyond 78 within 0.02 %

Contents Motivation Anisotropy Wave-Equation Migration Numerical Examples: Cusp model Conclusions 2-D SEG/EAGE model 3-D SEG/EAGE model

0.6 0 Kz Kx Kx Weak Anisotropy Strong Anisotropy Exact ** Approximation ** Approximation

0.3 0 Kz Kx Dispersion Equation Approximation Strong anisotropy

0 2.0 Depth (km) V/V0=3 iso New Standard

0 2.0 Depth (km) V/V0=3 Weak Aniso Strong Aniso

Contents Motivation Anisotropy Wave-Equation Migration Numerical Examples: Cusp model Conclusions 2-D SEG/EAGE model 3-D SEG/EAGE model

0 0 1 Depth (km) 1.5 X (km) Velocity ( km/s)

0 0 1 Time (s) 1.5 X (km) Velocity ( km/s) 01.5 Anisotropic data (SUSYNLVFTI) Time (s) X (km) Isotropic data (SUSYNLY)

0 0 1 Depth (km) 1.5 X (km) Isotropic data Isotropic mig (su) 01.5 Anisotropic data Isotropic mig 01.5 Anisotropic data Anisotropic mig

Contents Motivation Anisotropy Wave-Equation Migration Numerical Examples: Cusp model Conclusions 2-D SEG/EAGE model 3-D SEG/EAGE model

0 0 4 Depth (km) 5 X (km) Salt Model (VTI)

0 0 4 Depth (km) 5 X (km) Iso-mig

0 0 4 Depth (km) 5 X (km) VTI Aniso-mig

01.5 Anisotropy Error 40 % X (km) 0 4 Depth (km) 01.5 Anisotropy Error 10 % X (km) 01.5 Anisotropy Error 20 % X (km) Inaccurate Thomsen’s Parameters (VTI)

510 Anisotropy Error 40 % X (km) 3 4 Depth (km) 510 Anisotropy Error 10 % X (km) 510 Anisotropy Error 20 % X (km) Inaccurate Thomsen’s Parameters

Contents Motivation Anisotropy Wave-Equation Migration Numerical Examples: Cusp model Conclusions 2-D SEG/EAGE VTI model 3-D SEG/EAGE VTI model

0 4 Depth (km) 05 X (km) 05 VTI Aniso (y=1.5 km) Iso (y=1.5 km)

0 4 Depth (km) 05 Y (km) 05 VTI Aniso (x=1.5 km) Iso (x=1.5 km)

0 4 Depth (km) 05 Y (km) 05 VTI Aniso (x=3 km)Iso (x=3 km)

0 0 5 Y (km) 5 X (km) 05 VTI Aniso (z=0.5 km)Iso (z=0.5 km)

0 0 5 Y (km) 5 X (km) 05 VTI Aniso (z=2.5 km)Iso (z=2.5 km)

Contents Motivation Anisotropy Wave-Equation Migration Numerical Examples: Cusp model Conclusions 2-D SEG/EAGE model 3-D SEG/EAGE model

Conclusions Works for 2-D and 3-D media New > 78 Anisotropic wave propagator: Improves spatial resolution Valid for VTI and TI o 78 Propagator Cost = Cost of Standard 45^ o propagator o

Thanks To 2003 UTAM Sponsors CHPC