  In this paper we study the direct resonance problem for Rayleigh seismic
surface waves and obtain a constraint on the location of resonances and
establish a forbidden domain as the main result. In order to obtain the main
result we make a Pekeris-Markushevich transformation of the Rayleigh system
with free surface boundary condition such that we get a matrix
Schr\"odinger-type form of it. We obtain parity and analytical properties of
its fundamental solutions, which are needed to prove the main theorem. We
construct a function made up by Rayleigh determinants factors, which is proven
to be entire, of exponential type and in the Cartwright class and leads to the
constraint on the location of resonances.
