LMR equations

The LMR products are popular because they expressed intrinsic elastic properties ($$\lambda, \mu, \rho$$) as parsimonious combinations of P-impedance, $$I_{p}$$, and S-Impedance $$I_{s}$$, which are usually extracted from seismic inversion and AVO processes.

$$\lambda \rho =\left ( \rho V_{p} \right)^{2}}-2\left ( \rho V_{s} \right )^{2} = I_{p}^{2}-2 I_{s}^{2} $$,

$$\mu \rho = \left ( \rho V_{s} \right )^{2}= I_{s}$$,

$$ \kappa \rho = \left ( \rho V_{p} \right)^{2}}-4/3\left ( \rho V_{s} \right )^{2}= I_{p}^{2}-4/3 I_{s}^{2}$$.