Based on new advance in the multiple forward scattering theory of radio propagation in a random meidum

formula are derived for the study of mean arrival time of pulse signal propagating through the ionospheric irregularities

which takes into account of the refractive and dispersive effects of the background ionosphere on the mean arrival time

and of the multiple scattering and dispersive effects of the ionospheric electron density irregularities embeded in the background ionosphere. Under high-freqency approximation and asumption of a horizontally stratified background ionosphere

formula are given for calculating the refractive effect of the background ionosphere

the first order dispersive effect of the background ionosphere

the multiple forward scattering effect of the ionospheric electron density irregularities and its first order dispersive effect on the mean arrival time.With a specified background ionosphere

above ionospheric effects on the mean arrival time are studied with emphesis to variations of the scattering effect with the spectrum index

inner size and outer size of irrgularities. Results demonstrate that the scattering effect of irregularities is relatively important with respect to the refractive effect of the background ionosphere in certain cases

and that it is must taken into account in practical applications.