VTI migration velocity analysis using RTM |

The first-order two-way VTI wave-equation can be derived from Hooke's law
and Newton's law using Thomson anisotropy parameters (
,
) and setting shear wave velocity
(Duveneck et al., 2008). The first-order system reads as follows:

where is the density, is the velocity, is the particle velocity vector, and and are pressure in the vertical and horizontal directions, respectively. The source term and are defined by the source wavelet as follows:

It is straightforward to see that when , and , the first-order system 1 is equivalent to the familiar isotropic acoustic second-order wave-equation:

For simplicity, we can rewrite system 1 in a matrix-vector notation:

where , , and

VTI migration velocity analysis using RTM |

2012-05-10