Kinematics of 3-D DMO operators in transversely isotropic media

The 3-D dip-moveout (DMO) operator in homogeneous transversely Isotropic media with vertical symmetry axis (VTI media), unlike that in homogeneous isotropic media, has an out-of-plane (cross-line) component. In general, this component has a shape that is opposite to that of the cross-line component of the isotropic v(z) saddle-shaped operator. The width of the cross-line component of the VTI operator is also smaller overall than that associated with isotropic v(z) media. When both typical anisotropy and inhomogeneity are combined, the net result is an operator with a smaller cross-line component and a shape that is influenced more by the v(z) behavior. The large cost of a 3-D DMO operator, as well as the generally small cross-line components associated with the DMO operator in VTI media, suggests the possibility, as is usually done for isotropic v(z) media, of just ignoring the contribution of the out-of-plane portion of the operator.