Seismic observations of S velocity can be directly related to the shear modulus µ. However, P velocity is a function of both the shear and bulk moduli. For this reason, sometimes seismologists will...

Seismic observations of S velocity can be directly related to the shear modulus

µ. However, P velocity is a function of both the shear and bulk moduli. For this

reason, sometimes seismologists will compute the bulk sound speed, defined as:

which isolates the sensitivity to the bulk modulus κ. Derive an equation for Vc in

terms of the P and S velocities.