Operator symmetries

For orthorhombic media with a horizontal plane of symmetry there are certain symmetries to the operator. The elements of the operator will be either symmetric or anti-symmetric functions of the slowness:

$$\left[ \begin{array} {ccccc} {\rm Symm} & & {\rm Symm} & & ... ...\ {\rm Anti} & & {\rm Anti} & & {\rm Symm}\end{array}\right].$$

The exact linear operator has elements that can be expressed as polynomial functions of the horizontal slowness. By truncating the operator to low order in slowness I obtain an approximate operator that is valid for small angles of propagation (Nichols, 1989).