3D shot-profile migration in ellipsoidal coordinates

Conclusions

This paper presents a 3D shot-profile migration approach in ellipsoidal coordinates. The common form of ellipsoidal coordinates generates confocal ellipsoidal shells well-positioned for propagating turning waves in all azimuths. The numerical aspects of implementing the corresponding dispersion relationship, though, are somewhat problematic. We use an integral transform to recast the problem in a way that facilitates numerical implementation. We note that the similarity between the new ellipsoidal and elliptically anisotropic media dispersion relationships allows us to use existing implicit finite-difference extrapolation implementations. The impulse responses demonstrate that the numerical solution is both accurate and stable. Future work will focus on generating 3D shot-profile migration results in the ellipsoidal coordinate system.