Surface wave phase velocities for an inhomogeneous medium are usually given as eigenvalues of the wave equation. This is a differential equation (Love waves) or pair of differential equations (Rayleigh waves) of the second order. By means of a change of variable the problem is reducible to finding the zeros of a first‐order differential equation or pair of differential equations of first order. The solution can be obtained in any order of surface waves, and the eigenfunctions can be obtained as well by means of this transformation. The solution is thus amenable to computatio