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INVESTIGATIONS OF THE MOVEMENT AND STRUCTURE OF D-REGION IONOSPHERIC IRREGUI.ARITIES By I^I.K. HOCKING' B. Sc. (Hons) A Thesls presented for the degree of DOCTOR OF PHILOSOPHY at the UNIVERSITY OF ADELAIDE (Physics DeParEment) FEBRUARY I98I VOLUTIE TÏ Page CONTENTS VOLUME rI ON SIGNAI 292 CTIAPTER VI THE EFFECTS OF NOISE THE 293 6.1 Introductlon 294 6.2 Notation and AssumPtions 294 6 .2.L NotaEion 298 6.3 Complex Data 6.3.1 DetermínaÈlon of nolse usíng comPlex data 298 301 6.4 Ampli tude-onlY S arnPling 6.4.L Effect of noise on the data series 301 6.4.2 Effect of noise on the autocovariance 303 ' a. Introduction 303 b. Power (IntensiÈY) analYsis 304 c. AnPliEude-onlY analYsis 309 (f) Noise estimation 309 . (fi) Autocovariance distortion 312 6.5 Experimental Results 318 322 6.6 Conclusions 323 CHAPTER VII OBSERVATIONS USING COMPLEX DATA 324 7 1 Intro<luction 325 7 2 Some SimPle Observations (1-2 minuEes) 325 7 ,2.1 Short duration daÈa 7.2.2 Interpretation of short term daEa 327 daÈa 328 7 3 Interpretation of lonospheric scatter 7.3.1 SlmulaÈion of beam broadenÍ'ng 328 7.3.2 More accurate esÈimates of expected sPectral widths 335 7.3.3 Two unequal spectral peaks, and Èheir effect on the auto-correlaÈions ' (OR the phase of the sum of two slne waves beating together) 342 Page CONTENTS Continued. CHAPTER VII Continued 7.4 Experimental data 347 347 7 .4.L DoPPler r¿inds 7 .4.2 Spectral widths using the vertical beam 349 beam 354 7 .4.3 SpecÈral wídEhs using Èhe tilted 7 .4.4 Theoretical spectra for anisotropic turbulence 3s7 7 .4.5 Interpretatlon of specEral widths using tilEed beam 362 I'Javes 7 ,4.6 The relaEive roles of gravity and Èurbulence in the mesosPhere 373 7.5 Deconvolution 380 7.6 Conclusions 382 PROFILES CHAPTER VIII COMPARISON OF PARTIAL REFLECTION AND ROCKET MBASUREMENTS OF BLECTRON DENSITY 384 8.1 Introduction 385 8.2 ReflecÈi-on of a radío pulse in a horizontally straËified ionosPhere 386 8.2.1 TheorY 386 a. Pulse convoluÈion 386 b. Fourier Procedure 388 8.2.2 Some SimPle APPlications 39r B 3 Analysis of sirnultaneous rocket and partial ref lection me4sur emenÉs 393 8.3.1 Introduction 393 8.3.2 Experimental deLalls 394 a. Technique 394 b. Results 396 8.3.3 CompuEer símulaEion of partial reflection height Profile 400 8.3.4 Some extra observations of interest 404 a. Diffuse fluctuations in electron densitY measurements 404 b. Structure below 80 kn 405 8.4 Conclusions 407 Page CONTENTS Continued. .. OF CHAPTER IX INVESTIGATION INTO THE GENERATION THB HF SCATTERERS 408 9.1 IntroducÈion 409 9.2 Scat.terer correlations with winds 410 g.2.L Correlations between mean wind profiles and scaÈÈering LaYers 410 a. BxPerfmenÈal observations 410 b. Results from other references 413 g.2.2 Gravlty wave effects ín producing scaÈtering l-aYers 415 9.3 The relative roles of turbulence and specular scatter 420 9.3.1 Turbulence 420 g.3.2 Expected specular to isotropí-c scatLer ratios 423 9.4 Concluslons 428 429 CHAPTER X INVESTIGATIONS AT 6 lúlz 43L t_0 t_ Introduction 433 10 2 Experimental Results LO.2.L Power proflles and temporal varÍations 433 LO.2.2 Fading times and power sPectra 438 443 10. 3 TheoreÈícal InterPreËatíons 10.3.1 Theory and InterPretation 443 10 .4 Conclusions 449 450 CHAPTER XI DISCUSSION AND CONCLUSIONS 11 .1 IntroducEion 45r LL.2 Summary of Facts 4s2 11.3 Dis cussion 4s7 11.3.1 Discussion of doubÈful poínts 457 a. Product.ion of turbulence 457 b. Reasons for sPecular scatter 4s9 c. Reasons for Preferred heíghts 463 d. Seasonal varÍations 46s Page CONTENTS Continued CHAPTER XI Continued 11.3.2 The Authorrs Vi-ew 466 11.4 Inconclusive resulLs, future Projects and schematíc summarY 468 APPENDICES A The Neutral Atmosphererand Èhe Ionosphere above 100 km the B Propagation of radío waves through Ionosphere c. The Dynamical equatíons governlng the AÈmosphere D. Angular and Temporal CharacËerísÈics of Partial Reilectlon from Èhe D-Region of Ehe Ionosphere (A paper presented ín Journal of Geophysical neseârch, 84, 845, (1979) ) E Computer Program SPecPo F Computer Program ScaËPr G CompuEer Program Volsca H Co-oråinates of some ImporÈant Middle- ALmosphere Observatorj-es (Past and Present) BIBLIOGRAPHY 292, CHAPTER VI THE S OF NOISE ON THE SIGNAL 6.1 Introduction 6.2 Notation and AssumPtíons 6,2.L Notation 6.3 Complex Data 6.3.1 Determination of noíse using complex data 6.4 Arnplitude-on1y Sampling 6,4,L Effect of noise on the data seríes 6.4.2 Effect of noise on the auËocovarfance â.¿ Introduction b. Power (IntensitY) analYsis c. Amplitude-onlY analYsis (i) Noise estímation (ii) Autocovariance dístortion 6.5 Experlmental Results 6.6 Conclusíons 293. 6.1 Introduction It is of course desírable that the effects of noise be minimized in any experiment. Any noise whích is recorded should at ,least be monítored, so an idea of its mean level can be gaíned. Averaging sets of successive points can help to reduce the effective noise level. This ís a very useful technique íf complex data is used, and the averagíng length is less than about one quarter of the shortest period at which the signal varies (the procedure ís generally called "coherent l-ntegration".) However, if arnplitude-only data is recorded, great care must be taken v¡hen averaging sets of successive points. such a procedure does reduce the noise - buË also has the effect of distorting Ehe signal. The purPose of this chapter is Lo show just \'ühen averaging is allorvable, and what happens to the data if averaging is applied when Ít should not be. It is shown that the presence of noise in a signal which is sampled with amplitude-only distorts the autocovaTiance of the sígnal, but sampling with powers (intensíty) leaves the autocovariance looking similar to thaÈ for the signal alone' save for a noise spike at zelo time lag. Formulae are derived from whích the RMS noíse ca.n be calculated using the autocovariance of the íntensity of Èhe signal plus noise. The simplificatíons ín obtaining such noíse esËimates l^7hen data is recorded as complex data are also pointed out. 294. 6 2 NotaÈíon and Ass tions 6.2.I Notation In thís chapËer, the following notation will be adhered to as closely as possíble. Before detection, Èhe total received signal wíl-l be considered t,o consist of 3 contributíons. i(, (r) v (6.2.r.L) y(r) = s(t) + r(t) + e(t) 1=Y(t)e ) where (t) i0 s (6 .z.t.z¡ S(t) = S(t)e s= lql j 0"( t) (6.2.L,3) r(t) = r(t)e. El i0t (t) (6.2.L.4) e(t) = e(t)e "= lel are three complex signals. (The notation x will represent a complex vector, and x will represent its magnitude) ' s(r) sha11 be called a "specular component", though it may vary slowly in time. T(t) shall be called a "ïandom scattelil component. This is assumed to satisfy Rayleígh assumptíons, wíth RMS value kr. However, each successíve poinË of r(t) ís not assumed to be uncorrelated. IÈ is assumed that the autocorrelation of r(t) has finite r¡idth. For example, r(t) might be the signal produced by scatter from turbulence. Let jóo(t) (6. 2. 1. s) D(t) = ¡(t)e =S*r : D(t) lql S*r Thís wíll be called the "data component" of the total received signal (or the informatíon or message). IfSisaconstant' lo(t) | i" ni.. distributed. 295. The term e(t) shall be called the "external noise". It represents the unwanted component. Thís is also assumêd to satisfy Rayleigh assumpËíons (as was r(t)), with RMS value ku' (The ineorning noise on the antenna is wide-band, but becomes band-limited by the effect of the receiver. Impulsíve noise such as atmospherics ís excluded. ) Let iö (t) (6.2.I.6) I(t)e-'n' = r * e. Here n(t) = lr + el This represents the total random conlponefit of J.. It consísts of a random component carrying useful data, r(t), and an external (unwanted) noise comPonent e(t). n(t) has RMS value k'={k"2+kr2)\ (see Chapter V). Thus this situation represents the type of signal which may be received from the ionosphere, with a specular contribution, a random contributíon (e.g. turbulent scatÈer) and an unwanted external noíse contribution. The features are distinguished by Èheír fadíng times (i.e. the time for the. magnitude of their complex autocorrelation to fall to 0.5) . The external noise has a fading time defined by the receiver bandr¡ídth - if the frequency response is Gaussian and the bandwidth at halfpower Ls 25kíz (typical of the receivers used in this thesis), then the fading time is .441 (05IIO3) seconds = lBUs. At the PRFs used in thís thesís (=2OHz), the autocorrelations of this external noise will be uncorrelated after 1 shift. The random scaÈter component produces fadíng times in the region l-3s. (e.g, beam broadening, turbulent fluctuations etc) ' The specular components have much longer fading tímes' After detection an amplíÈude-on1y signal, which will be denoted as y(t) (= l¿(t) l), tirr result. 296. If there had been no external noíse, the amplitude detected would have been D(t) = lS * rl. Notice in all these definitions, a line under the symbol (e.g. such a líne A(t)) implies a complex vector, whereas the lack of means the arnplitude only (e.g.