In this paper, we study an extension of the standard ray-theoretical transport equation. We include a higher-order term of the ray series and obtain a modified frequency-dependent transport equation. This equation is solved analytically and numerically for an elastic 1-D model. The analysis of the results documents that the ray series diverges just at the boundary of applicability of the underlying high-frequency approximation. This implies that taking into account higher-order terms in the ray series neither improves accuracy nor allows a shift of the boundary of its applicability towards lower frequencies.