Normal moveout velocities in 3D arbitrary anisotropic media

Abstract

We present analytical expressions for normal-moveout velocities of reflections from a horizontal reflector for homogeneous models of general anisotropy. The formulae are valid for strong anisotropy and can be applied inside and outside of symmetry planes. They are expressed either in terms of first derivatives of ray (group) velocity vector or in terms of second derivatives of phase velocity. The results can be reduced to the particular cases of symmetry planes or to the case of weak anisotropy by using perturbation theory. Numerical examples for triclinic Lavoux limestone with phase velocity anisotropy of about 10% are presented. The exact NMO-formulae allow to investigate the accuracy of the weak anisotropy approximation of the NMO-velocity. The weak anisotropy approximation of NMO velocity performs less good than the weak anisotropy approximation of the phase velocity. For phase velocity variations in the order of 10% relative errors of the NMO velocities are about 1.5%. This appears to be sufficient for a velocity analysis. graph and the normal moveout velocity corresponds to the slope of this line. As a starting point we use the expression of Grechka & Tsvankin (1996):