The chain rule of differentiation leads to the equality
(24) |
(25) |
Using the expression for from the main text, we can write equation (A-2) as a quadratic polynomial in p_{x}^{2} as follows
a p_{x}^{4} +b p_{x}^{2} +c=0, | (26) |
Since can be small (as small as zero for isotropic media), we use the following form of solution to the quadratic equation
Press et al. (1992). This form does not go to infinity as approaches . We choose the solution with the negative sign in front of the square root, because this solution complies with the isotropic result when is equal to zero.