The long-range propagation of electromagnetic waves over the ground is a major topic for many applications in communication, navigation, and surveillance. In this article, we propose a wavelet-based split-step method in 3D to compute the propagation in this context. Also, using the discrete-mixed Fourier transform (DMFT), transverse invariant impedance ground conditions are taken into account, for which the ground wave propagation is accurately computed. Numerical tests show that the method is fast, accurate, and memory efficient. Finally, we show that the widely used DMFT is not valid for transverse variant ground compositions.