A statistical approach to the determination of three-dimensional ionospheric drifts

In a standard method of inferring ionospheric motions from radio soundings the random echo amplitude variations observed at spaced receivers are compared by use of their auto-and cross-correlations. Graphical procedures devised by Briggs, Phillips, and Shinn (hereafter referred to as BPS) and adapted to digital computers by Keneshea, Gardner, and Pfister permit the steady drift, random motion, and geometric properties of the echo-pattern irregularities to be extracted. The method is very powerful, but it is difficult to assess the degree to which the assumptions underlying it are fulfilled in individual cases. Furthermore, although the problem is inherently stochastic, the BPS process does not provide a ‘best fit’ of these assumptions to the available data. Finally, the BPS concepts are geometrically incomplete, since treatment of only the horizontal cross section of the ionospheric irregularities is implied. This paper describes a systematic numerical process based upon the concept of least squares that provides a best fit to the correlation functions obtainable from any number of spaced receivers deployed in any (nonsingular) manner over the ground. The analysis is developed in three spatial dimensions, anticipating new measurement methods in which vertical motions and ionospheric structure are observed by correlation of closely spaced frequencies or by other means. It is shown that the horizontal velocity components are not given correctly by the two-dimensional methods if vertical movements of anisometric irregularities occur. An example (two-dimensional) of the analysis by the new method is given and is compared with the analysis of Keneshea et al. in a case where the BPS criteria are closely met. The two methods agree well, but the new method appears to be capable of giving reasonable results in a wider variety of cases.