The problem of Rayleigh waves in an orthotropic elastic medium under the influence of gravity
and initial stress was investigated by Abd-Alla [A. M. Abd-Alla, Propagation of Rayleigh waves in an
elastic half-space of orthotropic material, Appl. Math. Comput. 99 (1999) 61-69], and the secular equation
of the wave in the implicit form was derived. However, due to the uncorrect representation of the solution,
the secular equation is not right. The main aim of the present paper is to reconsider this problem. We find
the secular equation of the wave in explicit form. By considering some special cases, we obtain the exact
explicit secular equations of Rayleigh waves under the effect of gravity of some previous studies, in which
only implicit secular equations were derived. ?? 2009 Elsevier Inc. All rights reserved.
