RAY EQUATIONS

For the ray equations we need to define four new parameters, all with units of inverse velocity squared. These parameters are defined:

• M_x = W_x^-1
• M_z = W_z^-1
• M_xnmo = W_xnmo^-1
• M_znmo = W_znmo^-1

If we further define:

• $\phi$ is the angle from horizontal
• c is $\cos (\phi)$
• s is $\sin (\phi)$

then

$$M(\phi) = \frac {M_{x}^3 c^6 + M_x{x}^2 (2M_{z} + M_{znmo}) ... ...} + M_{xnmo}) c^2 s^4 + M_{z}^3 s^6}{(M_{x} c^2 + M_{z} s^2)^2}$$ (2)

Again, in a manner shown in the referenced paper, we can develop move-out equations (about the x or z axes) from this ray equation.