1. Wave-Equation Migration Research at Los Alamos National Laboratory
Michael Fehler )
Lianjie Huang )
Wavefield snapshots from Hoelting, Seg talk, 2003

2. Objectives
Investigate and develop accurate and efficient methods for seismic migration in regions having steeply dipping interfaces and complex structure
Investigate applicability of methods to seismic migration
Develop methods to obtain more from images than geometrical information about subsurface

3. Approach: Develop methods based on
Lippman-Schwinger Equation:
integral solution of two-way wave equation
One-way wave equation:
solution requires expansion of operator Q

5. Approximate methods for imaging using one-way wave propagation
Born Approximation:
total wavefield = wavefield in homogeneous medium + scattered wavefield
Generally works well for backscattering and/or low frequencies
Rytov Approximation:
total wavefield = (wavefield in homogeneous medium) * correction term for scattering
Generally works well for forward scattering and/or high frequencies

6. Methods (1) Split Step Fourier (narrow angle Rytov)
(smooth perturbation, small angle)
(2)Local Rytov Approximation (applied in each interval)
(smooth perturbation, wide angle)

7. Methods (cont) (3) Local Born Approximation (applied in each interval)
(weak perturbation, wide angle)
Can be unstable when perturbation large
(4) Quasi-Born
(improvement on Born expansion)

8. Methods (cont) (5) Optimized Fourier Finite-Difference
(expansion of square root operator Q in one-way wave equation)
(large perturbation, wide angle)
a,b are optimized to give accurate expansion

9. Other WEM Approaches Split-Step Pade Split-Step Fourier Pade
Controlled-aperture WEM
Normal-reflection image
Offset-domain WEM
Stationary-phase WEM

13. Topics Controlled-aperture wave-equation migration
Normal reflection image
Stationary phase wave equation migration

14. Controlled-aperture Wave-equation Migration

25. Common Azimuth Migration

27. Conclusions Developed a suite of new wave-equation migration methods
Improved migration efficiency and accuracy
Obtained physical information from migration for reliable seismic reservoir characterization in addition to geometrical information