Elastic wave-mode separation for VTI media |

In the wavenumber domain, for isotropic media, as shown by the black line in Figure 2(b), the exact difference operator is . Appendix A shows the domain equivalents of the , , , and order finite difference operators, and they are plotted in Figure 2(b). The higher order operators have responses closer to the exact operator (black line). To obtain vertical and horizontal derivatives of different orders of accuracy, I weight the polarization vector components and by the weights shown in Figure 2(c). For VTI media, similarly, I weight the anisotropic polarization vector components and by these same weights. The weighted vectors are then transformed back to space domain to obtain the anisotropic stencils.

operator
Comparison of
derivative operators of different orders of accuracy (
,
,
, and
orders in space, as well as the
approximation applied in Dellinger and Etgen (1990)-cosine taper)
in both (a) the
domain and (b) the
domain. (c) Weights to
apply to the components of the polarization vectors.
Figure 2. |
---|

iop2,mop2,iop4,mop4,iop6,mop6,iop8,mop8
,
,
, and
order derivative operators for an isotropic medium (
km/s and
km/s) and a VTI medium (
km/s,
km/s,
and
). The left column includes
isotropic operators, and the right column includes anisotropic
operators. From top to bottom are operators with increasing orders of
accuracy.
Figure 3. |
---|

Elastic wave-mode separation for VTI media |

2013-08-29