A least action principle for the location of PSAW's and a minimum bound on their attenuation

We address the problem of the estimation of the slowness and of the attenuation of a pseudo surface acoustic wave (PSAW) on a semi-infinite substrate. This problem is an old one and many possible solutions have been given, usually making use of a complex excitation slowness along the propagation direction. We argue that this approach gives rise to a discontinuity in the partial wave selection rule and is hence self contradictory. We then propose an alternative solution, avoiding the use of complex excitation slownesses, by analogy with the problem of the reflection of a bulk acoustic wave on the surface. Specifically, we include an optimal source term exactly compensating for the energy lost by leakage. This leads us to the minimization of a function which minimum is the PSAW slowness and which minimum value gives the attenuation.