Calculation of true thickness of the bed

 56. For an earth material with both the lame parameters equal (λ=μ), the ratio of P-wave to S-wave velocities is

 (Thanks to Pragnath, AU)

Solution: we know that the velocity of the P-wave is

 

$\alpha=\sqrt{\frac{\lambda+2\mu}{\rho}}$  

 The velocity of S-wave is

$\beta=\sqrt{\frac{\mu}{\rho}}$

 

Given that (λ=μ) so on substituting that value we get

$V_{p}$ or $\alpha$=$\sqrt{\frac{3\mu}{\rho}}$

 

And the ration is  

$\frac{V_{p}}{V_{s}}= \frac{{\sqrt{\frac{3\mu}{\rho}}}}{\sqrt{{{\frac{\mu}{\rho}}}}}$

 

$\frac{V_{p}}{V_{s}}=\sqrt{\frac{3\mu \rho}{\mu \rho}}$

 

Therefore,

 

$\frac{V_{p}}{V_{s}}=\sqrt{3}$