48,06,2005misc 989 ANNALS OF GEOPHYSICS, VOL. 48, N. 6, December 2005 Key words shift Doppler – ionosphere – plasma drift 1. Introduction The measurement techniques of Drift Dop- pler follow the ionospheric vertical sounding where the return signal is analysed in frequen- cy domain. A wave carrier of angular frequency ω is sent toward to the ionosphere where it is reflected. In the frequency range of 2-15 MHz the solid beam angle of the employed antenna is very wide and the gain as low as 1-3 dB de- pending on the frequency so that an area of hundreds of square kilometers is illuminated. Because of the rippled ionospheric surfaces and the volume inhomogeneities the signal is re- flected back from various point sources that sat- isfy the reflection law. These point sources if moving are considered Doppler sources that su- perimpose a Doppler shift (∆ω1, ∆ω2, ... ) on the signal. In first approximation the angular pulsation shift ∆ω is (1.1) where V is the radial velocity of the reflecting point, c is the light velocity. Dividing by 2π both side of the above equation and replacing ω with c⋅k and 2π f we obtain (1.2) where, f is the frequency, ∆fD is the frequency shift due to the Doppler effect, and k wave vec- tor (Bibl et al., 1975; Hunsucker, 1991). The moving source (s) assigns a shift in fre- quency according with the above equations and in the antenna we receive a composite signal with different ∆ωs that are the contribution of the s significant sources. In case of a single re- ceiving antenna the spectral analysis (typically a complex FFT) furnishes all the spectral com- ponents and the related phases and cannot dis- criminate the spatial distribution of the different sources. In case of 3 or more antennas it is pos- D∆ /kf V= - r /V c2= -~ ~∆ Ionospheric Doppler measurements by means of HF-radar techniques Cesidio Bianchi (1) and David Altadill (2) (1) Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy (2) Observatori de l’Ebre, Roquetes, Spain Abstract Studies of the dynamics of the ionosphere and its related phenomena are mainly based on Doppler Drift meas- urements. The time variation (ionisation/recombination) of plasma density, thermospheric wind and others can be observed by means of HF-radars. The technique of Doppler Drift measurements is a quite complex technique that is now affordable by means of an advanced ionospheric sounder. The combination of vertical sounding and interferometric Doppler detection discloses the Doppler sources. The echo signal contains the Doppler shift in frequency imposed on the wave carrier by each point source where the signal is reflected. Other phenomena like environmental noise and the intrinsic error of the measurements that, together with the change in time of the re- fractive index, affect the measurements in various ways impeding to better quantify the results. Mailing address: Dr. Cesidio Bianchi, Istituto Naziona- le di Geofisica e Vulcanologia, Via di Vigna Murata 605, 00143 Roma, Italy; e-mail: bianchi@ingv.it 990 Cesidio Bianchi and David Altadill sible with a interferometric Doppler technique to resolve the spatial distribution of the signifi- cant sources (Davies, 1990). 2. Principle of Doppler interferometry In principle the interferometric Doppler techniques rely on the frequency and phase analysis of the signal picked-up from spaced antennas lying in a plane at appropriate dis- tance. In our description we refer to 4 antennas placed in the geometric barycentre and in ver- texes of an equilateral triangle as in fig. 1. In or- der to better discriminate the phase contribu- tions it is important to maximize the triangle size (more than 50 m) and to eliminate the phase ambiguity the distances between the an- tenna in the centre of the triangle must not be more than the wavelength λ employed in the sounding system. Now, as in ionospheric vertical sounding, suppose a Radio Frequency (RF) pulse is sent to illuminate a large area, the various ionos- pheric moving isodensity surfaces reflect the RF signal with a superimposed shift Doppler. A single reflector s contributes with an echo sig- nal that in the receiving antenna 1 has an ampli- tude A given by (2.1) where, A01 and φ1s are respectively the maxi- mum amplitude and the phase at the receiving antenna 1. For the generic antenna a the time varying amplitude will be (2.2) The phase term due to the source s in the anten- na 1 is (2.3) where k is the wave vector, r1s is the oriented vector for the antenna 1 and the source s, and δ is the phase value at the level of the source s. If we assume as reference point antenna 1, the phase for the generic antenna a is (2.4) where la is the oriented vector from antenna 1 and antenna a. It means that the phase differ- ences between antenna 1 and the generic anten- na a is ks ⋅ la. It must be also noted that because of the dis- tance the r1s compared with the distance be- tween the antennas the vector ks has the orien- tation in all the antenna points. Referring to fig. 2 the phase difference be- tween antenna 1 and the generic antenna a is (2.5) where θ is the angle between ks and la. For a given source that the phase difference between the antenna 1 and the generic antenna a, ac- cording with the above equation, is a function of the angle θ between the vector k and l. It is worth noting that different Doppler sources are distinguishable by different ∆ωs values (where s is the number of sources). For a given Doppler source ∆ω, once the phase difference is meas- ured knowing the range r, the wavelength λ and ( ) / ( )cos cosk k l ll 2as s a s a1 $ $= = =z i r m i k r k k llas s s s a s s a1 1$ $ $= + + +=z d z k r1s s s1 $= +z d ( ) .cosA A ta a s as0= + +~ ~ z∆7 A ( )cosA A ts s1 01 1= + +~ ~ z∆7 A Fig. 1. The receiving antenna at the vertexes and at the geometrical barycentre of an equilateral triangle in an horizontal plane. All the antennas are a the dis- tance l. 991 Ionospheric Doppler measurements by means of HF-radar techniques the distance l of separation between the consid- ered antennas it is possible to calculate the an- gle θ and consequently the horizontal position in the ionosphere. Each antenna a, neglecting the environmen- tal electromagnetic noise, will receive a com- posite signal of amplitude A given by (2.6) where s indicates all possible sources. After the quadrature sampling the signal the two follow- ing discrete-time sequences Ia (in-phase) and Qa (in-quadrature) will be obtained (2.7) (2.8) where τn is the sampling time interval. If the sampling is performed at exactly the time peri- od τn of the carrier wave ω, the sampling acts ( ) ( )senAQ ( )a n a s s n as s 0= +x ~ x z∆7 A/ ( ) ( )cosAI ( )a a s s n as s n 0= +~ x zx ∆7 A/ ( ) ( )cosA t A t( )a a s s as s 0= + +~ ~ z∆7 A/ like a filter rejecting the carrier ω and the two sequences will contain only the Doppler shift ∆ωs. Amplitude A(τ 1) and phase φ (τ 1) of the signal at a given time τ 1 are (2.9) . (2.10) The two discrete-time sequences Ia and Qa are the input of the algorithm the performs a complex Fast Fourier Transform, FFT (Oppenheim, 1999). The FFT of the N samples (where N is a power of 2) can be written as (2.11) where n is an index that runs from –N/2 to N/2, d is a dummy index to perform the operation, and fa(n) is . (2.12)( ) ( ) ( )f n I iQa a n a n= +x x ( ) ( )F d f n e / / a a i d n n N N 2 2 1 N 2 = $- = - - r/ ( ) ( )arctan Q I1 1a a= x xz 7 A ( ) ( )A I Q1 1a a 2 2= +x x Fig. 2. The signal from the same source is received by the two antennas with a phase difference depending on the source position. 992 Cesidio Bianchi and David Altadill The spectral analysis (complex FFT) furnishes d = N couple of values representing the discrete frequencies and the related phases. The fre- quency resolution is δω, being δω equal to 2π/T and T the time length of the segment of the sig- nal considered (typically less than 20 s accord- ing with the time coherence of the ionosphere). The highest frequency is related to Nyquist sampling theorem and the d ⋅ δω is the highest Doppler shift range. It is worth applying a ta- pering function (Hanning or others) to the dis- crete and finite time sequences to avoid the ringing six (x)/x after the spectral analysis. So as a result of the complex FFT for each of the 4 antennas N spectral density values A and an associated time independent phase φ will be obtained. Even if negative values of the frequen- cies have no physical meaning, in this case they represent sources that are moving in the direc- tion of r while positive values of the spectral components are related to the incoming sources. These measurements are generally affected by environmental radio noise or interferences pro- duced by other HF stations. So to evaluate the direction of k vector from eq. (2.5) a statistical anlysis must be performed (Scali, 1993). 3. Radial velocity and determination of the Doppler sources In general the observed shift for a sounding performed at a known angular frequency ω, apart from a constant factor, is the time deriva- tive of the phase path P of the radio wave . (3.1) The time derivative of the phase path depends on two terms (Dyson, 1975) (3.2) where µ is the refractive index and α is the an- gle between the wave normal and the ray direc- tion (null for isotropic medium), V is the real velocity of the reflector and pr the unit vector of the wave normal at the reflection point. Hence the quantity observed is the apparent velocity, cos dt dP pr V t dr r 0 $ 2 2 = + n a# c dt dP 2 = - ~ ~ ∆ Vapp, because the time derivative of the refrac- tive index has to be considered. If the electron density changes in time because of production or loss (especially during down and dusk) it is not possible to neglect the second term in the above equation. For that the measured veloci- ties are not real, i.e. not only dependent on the moving reflector. When performing ionospheric drift meas- urements the second term contribution on the relation (3.2) must be considered and only in stationary electron density condition are the ob- served velocities of the Doppler point sources related to the plasma motion. In this case, the radial velocity of each point sources comes di- rectly from relation (1.1) If a uniform plasma motion is considered by means of statistical method (Scali, 1995; Bibl, 1998) it is possible to determine the bulk mo- tion of the plasma (drift). The Lowell Digisonde 256 uses a least-square fit procedure described in (Dozois, 1983) in which it is possible to de- termine the vector velocity V representing a plasma drift velocity. A similar procedure is al- so described in the Digisonde Drift analysis manual DDA (Scali, 1993) and makes it possi- ble to solve the position of each point source and plot the results in a so-called sky-map. 4. Conclusions In this paper the theory on which the inter- ferometric technique relies is briefly described. The transmitting antenna has a wide beam that illuminates a large area of hundreds of square km in the ionosphere and the signals coming from different reflection points are resolved by combining Fourier transform and interferomet- ric techniques. The echo signal has a superim- posed frequency Doppler shift, hence the infor- mation of each point source where the signal is reflected. This technique is now affordable by means of the advanced ionospheric sounders that perform both on-line analysis and post pro- cessing on the recorded signal. The Doppler Drift Analysis DDA implemented as post analy- / .V c 2rs s= - ~ ~∆ Ionospheric Doppler measurements by means of HF-radar techniques sis processing in the Digisonde 256 and DPS-4 determines the Doppler shifts of signals arriv- ing from different directions and, in some par- ticular stationary conditions, measures the plas- ma drift velocity (Bibl and Reinish, 1978). REFERENCES BIBL, K. (1998): Evolution of the ionosonde, Ann. Geofis. 41 (5-6), 667-680. BIBL, K. and B.W. REINISCH (1978): The Universal Digital Ionosonde, Radio Sci., 13, 519-530. BIBL, K., W. PFISTER, B.W. REINISCH and G.S. SALES (1975): Velocities of small and medium scale ionos- pheric irregularities deduced from Doppler and arrival measurements, Adv. Space Res., XV, 405-411. DAVIES, K. (1990): Ionospheric Radio (P. Peregrinus Lon- don). DOZOIS, C.G. (1983): A high frequency radio technique for measuring plasma drift in the ionosphere (University of Massachusetts Lowell Center for Atmospheric Re- search, Lowell, U.S.), Rep. No. 6. DYSON, P.L. (1975): Relationship between the rate of change of the phase path (Doppler shift) and angle of arrival, J. Atmos. Terr. Phys., 37, 1151-1154. HUNSUCKER, R.D. (1991): Radio Technique for Probing the Terrestrial Ionosphere (Springer Verlag N.Y.). OPPENHEIM, V.A., W.R. SCHAFER and J.R. BUCK (1999): Dis- crete-Time Signal Processing, 2nd edition (New Jersey). SCALI, J. (1993): A Quality Control Package for the Digi- sonde Drift Analysis (DDA), Version 2.0 (University of Massachusetts Lowell, Center for Atmospheric Re- search). SCALI, J., B. REINISCH, C. DOZOIS, K. BIBL, D. KITROSSER, M. HAINES and T. BULLETT (1995): Digisonde Drift Analysis (University of Massachusetts Lowell Center for Atmospheric Research). (received February 23, 2005; accepted August 29, 2005) 993