3D shot-profile migration in ellipsoidal coordinates

3D shot-profile migration in ellipsoidal coordinates

Jeff Shragge and Guojian Shan

Abstract:

We present an approach for performing 3D shot-profile migration in ellipsoidal coordinate systems. Wavefields are extrapolated on confocal ellipsoidal shells that are well suited for accurately propagating steeply dipping and turning waves in all azimuthal directions. Numerical implementation of the corresponding dispersion relationship, though, is somewhat problematic due to first-order, complex-valued wavenumbers. We show that an integral transform recasts the problem in a way that eliminates first-order wavenumbers. The corresponding dispersion relationship is similar to that in elliptically anisotropic media. This similarity allows us to use existing implementations of wavefield extrapolation in elliptically anisotropic media to propagate wavefields on ellipsoidal meshes. Impulse response tests demonstrate the stability and accuracy of the approach.