In the same paper Connolly (1999) then goes on to rearrange the basic equation to take a Vp term out of the first exponent to give the following equation:

This equation shows how elegant the elastic impedance definition is. Elastic impedance is now defined as the product of Vp and an elastic density comprised of terms in Vp, Vs and density. This definition allows elastic impedance to be used directly in conventional acoustic impedance inversion software to invert data at non-normal incidence angles. The Vp log is the usual checkshot calibrated compressional sonic log used for integration from depth to time and well ties and the elastic density term is a pseudo-density log to multiply with the Vp log to give the elastic impedance and hence appropriate reflectivity for the chosen angle theta.