Ionospheric Electron‐Density Profiles With Continuous Gradients and Underlying lonization Corrections. I. The Mathematical‐Physical Problem of Real‐Height Determination From lonograms

Abstract

Any numerical method for inversion of the integral equation h'(f)= p.'(/N(z),f)dz must satisfy certain requirements in order to avoid introducing features into the true‐height profile which are not indicated by the ionogram. These requirements are first investigated by considering the equation as an integral transformation of fN(z) for several model distributions. In order to satisfy the above‐mentioned criteria a second‐order lamination process was developed; its mathematical principles are presented in this paper and its implementation at the Institute for Telecommunication Sciences and Aeronomy is discussed in the two following papers.