Discrepancies in energy calculations for inhomogeneous waves

Abstract

Summary. Two apparently equivalent methods used in the literature for calculating the mean energy flux and other properties of harmonic plane waves in a viscoelastic medium are shown to give slightly different results when applied to inhomogeneous P/SV-waves. The discrepant results of the two methods have appeared in recent papers and textbooks. Hence, it is important to point out and explain them. It is also shown that the discrepancies occur even for perfect elasticity. The first method makes use of the familiar classical formulae for the energy flux and other quantities, which can be derived from first principles. However, in the second method, the formulae for these quantities are inferred from a specifically derived conservation relation_ The validity of the results of the first method cannot be questioned. It is shown that the errors in the results of the second method are due to the presence of a certain mathematical non-uniqueness.