Impulse response for the one-dimensional inhomogeneous medium with an approximation for attenuation and dispersion

The impulse response h(z,t) for the wave equation which models the propagation in a one-dimensional inhomogeneous lossless medium is detailed, Pulse spreading and pulse hight reduction versus travel distance are then accommodated as a superposition integral with the lossless response acting as an excitation function on a dispersion model g(z,t).