Analytical representation of offset-midpoint traveltime equation is very important for pre-stack Kirchhoff migration and velocity inversion in anisotropic media. For VTI media, the offset-midpoint traveltime resembles the shape of Cheop's pyramid. In this study, we extend the offset-midpoint traveltime pyramid to the case of 3D HTI media. We employ the stationary phase method to derive the analytical representation of traveltime equation, and then use Shanks transformation to improve the accuracy of horizontal and vertical slownesses. The traveltime pyramid is derived in both the depth- and time-domain. Numerical examples indicate that the azimuthal characteristics of both the traveltime pyramid and the migration isochrones are very obvious in HTI media due to the effect of anisotropy.
Hao, Q., Stovas, A., & Alkhalifah, T. (2013). The azimuth-dependent offset-midpoint traveltime pyramid in 3D HTI media. SEG Technical Program Expanded Abstracts 2013. doi:10.1190/segam2013-0058.1