A method for the determination of lower ionosphere properties by means of field measurements on sferics

Abstract

The propagatio n of a ud iofrequpncy a nd sub-a udiofrequency waves be tween t he earth a nd an ionos phere whose conductivity varies co nt inu ously with altit ude is co nsidered in deta il. The fie lds a re represe nted in te rms of t ll'O scalar potentials satisfy ing a ppropria te wa ve eq uations in spherieal coordina tes. It is s hown , on t he basis of exist in g data on t he ion osphe re, t hat waves i n th is fl'equency range can be cons idered to be confin ed to a t hin , but not s ha rp ly bounded , s pheri cal s hell abo ut t he eart h . Greatly simplified radia l wave equations in dimensionless form are deri ved in co rporatin g t hi s a pprox imation . Solu t ions of t hese equations a rc given fOI' two r egions, v iz, for t he low-altitude reg ion whe re u/W€o< < 1 a nd, in the case of cer ta in rest ri cted types of cond uct iv ity profile, for t he h igh-alti t ude reg ion where u/W€o> > 1. An itera t ive method is presented , based on a n in tegra l equatio n, which makes possib le a computation of t he radia l wave fun ction in t he transit ion region a nd a jo inin g of in te ri or and exteri or solution s for t he propagatin g TM mode. The resu lt is a direct mathematical rela t io ns hip between t he condu ctiv ity pro fi le a nd t he complex propagation constant as a funct io n of freq uency . It is demon trated t hat at freq uencies above abo u t 50 cycles t he propaga Lion cons ta nt ca n be obta ined from measure me n ts of t he horizontal co mponents of electric a nd mag netic fi elds in individ ual sferics a t air plane a lt it udes, whi le a t lower freq uencies t he sa me information can be obtained thr ougll ground-based observa t ion of cavity resonance e ffects in sferic noise. Existing data on t hcse cavity resonances a re used to calcula te t he complex p ropaga t ion co nstant as a fun ction of freq ue nc.v from 6 to 3,1. cycles. The re ults , when extrapolated to hi gher frequencies, predict atte nu a t ion rates in ex cell ent agree ment wit h currently ava ila ble data. The effect of t he diurnal vari ation in con du ctivity o n obse rvable qu anLiti es is br ir fl y examined, a nd te ntat ive co nclu sio ns as to its magni tude a re drawn.