ionospheric drift measurements

7/30/2019 Ionospheric Drift Measurements

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Ionospheric Drift Measurements(Doppler inteferometry)

Cesidio Bianchi INGV - Roma Italy


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Overview1. Vertical Ionospheric Sounding (VIS) and principle of

the measurement

2. Multipath VISs echo signal

3. Doppler frequency shift

4. Principle of Doppler Interferometry

5. Phase relation and source position/velocitydetermination

6. Conclusions


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Introduction

The technique of Doppler drift measurements is a complex techniquethat is now affordable by means of an advanced ionospheric sounder.

The echo signal contains the Doppler shift (in frequency) imposed on

the wave carrier by each point source where the signal is reflected.

The combination of vertical sounding and interferometric Dopplerdetection discloses the Doppler sources.

Studies of the dynamics of the ionosphere and its related phenomena

AGW, TID, thermospheric wind, ionization/recombination of plasmadensity and in general plasma drift.


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1-Vertical Ionospheric Sounding and principle of measurement

'2 hc

t=

Nfc 9

Reflectedray

Incidentray

ionosphere


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1-Vertical Ionospheric Sounding..

The measurement techniques of the Doppler drift in

the advanced ionosondes follows and derives fromthe VIS where the echo signal is analysed infrequency domain.

This measurement is performed at a fixedfrequency once that the height of the reflector isestablished by a normal VS (see the ionogram).

Other differences such as the use of sine pulse,signal sampling etc. will be explained later.


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1-VIS and principle of measurement

A wave carrier of angular frequency is sent toward to theionosphere where it is reflected.

In the frequency range of 2-15 MHz the solid beam angle ofthe employed antenna is very wide and the gain as low as 1-3dB depending on the frequency so that an area of hundredsof square kilometers is illuminated.

Because of the rippled ionospheric surfaces and the volumeinhomogeneities the signal is reflected back from variouspoint sources that satisfy the reflection law.

These point sources if moving are considered Doppler sourcesthat superimpose a Doppler shift on the signal carrier .


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1-VSI and principle of measurement


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2. Multipath VISs echo signal

)2cos()()( 00 tftutA =The transmitted signal of the ionosonde is:

where f0 the carrier frequency, A(t)is the time dependent amplitude,u(t)is the waveform of the HF radar signal that contains the reversalphase code.The received signal is:

= ++=)(

0

0 )()]())((2cos[))(()(

tN

s

Dsss tntttftttr

where, the sum of the sreflectors can vary during the measurementsfrom 0to N(t)take into account the N(t)multipath, the attenuateds-path containing the code that is delayed by s , Ds is the timedependent Doppler phase shift and n(t)is the noise.


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2-Multipath VISs echo signal

The above relation describes the received echo signal we have to

deal about. The composite signal presents different time delay s,while the phase change Ds due to the Doppler of the movingreflectors contributes to the short time scale variations of thepower of the received echo. The multipath echo signal is then

down converted and reduced to the baseband described of thefollowing relation:

=+=

)(

0

)()](cos[))(()(

tN

s Dss

tnttttr


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2- Multipath VISs echo signal

Considering:

- only a single flat reflector (it means only one Doppler )

- no electromagnetic noise or interferences

-non modulated wave having carrier angular frequency

- no losses

- only ordinary propagation mode

the echo signal is: A(t) = A0 cos [(+)t +]

where, is the time independent phase

For multipath signal (s sources)

A (t) = A0 cos s[(+s)t +s]


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3. Doppler frequency shift

In a moving (flat mirror reflector) with velocity v in verticaldirection, the radio wave of frequency f , is reflected back

with frequency f f. The sign is dependent on the versus

of the velocity of the reflector.


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3- Doppler frequency shift


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3-Doppler frequency shift

Vr =W = radial

componentof thevector

W


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- opp er requency s

If the wave is emitted by a moving sources or picked-upby a receiver in motion respect to the a fixed source andthe refractive index does not change in time we have:

vr.c

ff =

where rthe ray direction and vthe velocity (source orreceiving point). The velocity v (m/s) is the quantity thatusually we want to know.

vr.=W


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In radar system the previous relation is still valid if we multiply it by 2

As in the previous relation the angular pulsation shift is:

where Wis the radial velocity of the reflecting point, c is the lightvelocity. Dividing by 2 both side of the above equation and replacing= 2f with c kand we obtain:

where, fis the frequency, f is the frequency shift due to the Dopplereffect, and kwave vector.

c/W2=

/WkfD =

W2

c

ff =


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Measure of the Doppler frequency shift

By means of:

- Direct on the analog signal (heterodyneanalyzer)

- Direct by a digital Spectrum Analyzer

- PC after sampling and A/D and laterperforming a DFT or FFT


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Hz 4 (MHz) 8 (MHz) 12 (MHz) 16 (MHz) 20 (MHz)

Vr= 3 m/s 0.08 0.16 0.24 0.32 0.4

Vr=12 m/s 0.32 0.64 0.96 1.28 1.6

Vr=36 m/s 0.96 1.92 2.88 3.84 4.8

Expected Doppler frequency shift f at the variouscarrier frequency in MHz and different radial velocityof the reflector


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FFT resolution f (minimum) is related to the observation

time T. The smallest frequency is 1/T

The highest frequency in the FFTfmax is fs/2;where fsis thesampling frequency.

If we want a resolution = 0.08 Hz,

12.5 s time window is required


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4. Principle of Doppler interferometry

In principle the interferometric Doppler technique relyon the frequency and phase analysis of the signal picked-up from spaced antennas lying in a plane at anappropriate distance.

In our description we refer to 4 antennas placed in the

geometric barycentre and in vertices of equilateraltriangle as in figure. In order to better discriminate thephase contributions it is important to maximize thetriangle size (more than 50 m), anyway to eliminate the

phase ambiguity, the distances between the antennas fromthe centre of the triangle mustnt be greater than thewavelength employed in the sounding system.

(The method here presented were developed at the University of Lowell Massachusetts Center for Atmospheric Research)

4 P i i l


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4 Principle..


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4 Principle

The composite signal is received in the 4 spaced antennas.

The multipath components arrive with different time delays.

Because of the different delays the phase of thecomponents are different in each of the four antennas.

The separation of the different components and theirphase relation is the base Doppler interferometry.

The analysis of the phase relation allows us to locate eachsingle source in the horizontal plane at height R

established by VIS


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4 Principle..

The output of a singlepowerful algorithm (CFFT)furnishes Dopplerharmonics and phaseswhich analysis allows toderive thesky-map of the sources.

The distance from

the vertical is givenby the zenithal anglewhile the direction of thevelocity in the plane is

given by the azimuthalangle .

x

y

k

k

tg =)(zkk

=)cos(


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4 Principle

The moving source (s) adds a shift in frequency according tothe above equation and in the antenna we receive a composite

signal with different s that are the contribution of the ssignificant sources.

In case of a single receiving antenna the spectral analysis

furnishes all the spectral components and the related phasesand we cannot discriminate the spatial distribution of thedifferent sources.

In case of 3 or more antennas it is possible with aninterferometric Doppler technique to solve the spatialdistribution of the significant sources.


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4 Principle

Dopplercomponents and ralated

phases

4 P i i l


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4 Principle

Spectral Analysis uses complex FFT (CFFT)

- Input data of the complex FFT are couple of Nvalues or complex number (a+jb) i.e. the result of the

quadrature sampling.

- Output furnishes couple of values representing

angular frequencies and phases of the Doppler sources.- CFFT output yields a couple of N values from -N/2 toN/2 representing amplitude and phase of each spectral

line. In this context negative spectral lines have aphysical significance. They means motion of the sourceaway from the center of the reference frame.

4 Principle..


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4 Principle..

Considering only one source (it means only one Doppler ),at the antenna 1 the time varying amplitude of the echosignal is:

A1(t) = A01 cos [(+)t +1]

while at the generic antenna (a) the amplitude of the echo

signal is:Aa(t) = A0a cos [(+)t +a]

For multipath signal (s sources) we have:

Aa(t) = A0ascos [(+s)t +as]

4 P i i l


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4 Principle.

After the quadrature sampling the signal of the two followingdiscrete-time sequences a and b will be obtained:

a (n) = A0a(s) cos( (n) + a)

b (n) = A0b(s) sin ( (n) + as)

where nis the sampling time interval.

If the sampling is performed at exactly the time period ofthe carrier wave (2/), the sampling itself acts like a filterrejecting the carrier and the two sequences will contain

only the Doppler shift .

4 Principle


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p

Amplitude A(1) and phase (1) of the signalat a given time 1 are:

=tan-1[ b(1) / a(1 )]

21

21 )()( baA +=

4 Principle


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The two discrete-time sequences a (n)and b(n)are the input

of the algorithm that performs a complex Fast FourierTransform, (CFFT). The FFT of the N samples (where N is apower of 2) can be written as:

where n is an index that runs from N/2 to N/2, d is adummy index used to perform the operation, and fa (n)is:

fa (n) = a(n) + ib(n)

=A0 cos( (n))+ A0 sin( (n))

It is worth to apply a tapering function (Hanning or others) to thediscrete and finite time sequences to avoid the ringing sin (x)/x after thespectral analysis.

F d f n ea n NN

a

iN

dn

( ) ( )//= =

22 1

2

4 Principle


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p

These values are sufficient to establish the significantDoppler sources and the position in the horizontal plane

at the height first determined by the VIS (ionogram).

indicates the s Doppler

sources indicates the relative phase


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4. Principle..

5 Ph s r l ti n nd s urc p siti n/v l cit


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5. Phase relation and source position/velocitydetermination

5. Phase relation and..


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It is worth to remark that different Doppler sources

are distinguishable by different svalues (where sis the number of sources).

For a given Doppler source , knowing the range r,the wavelength , the distance l of separationbetween the considered antennas and measuring thephase differences 1as, it is possible to calculate the

two angles and and consequently the horizontalposition of the source respect to our referenceframework.

5 Ph l i d


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The phase term due to the source sin the

antenna 1is

1=k r1s+

where kis the wave vector, r1s is the orientedvector from the antenna 1 to the source s, and

is the phase value at the level of the source s.

In the next analysis we can neglect because

it is a constant value that disappear in theoperation of subtraction.



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Phase at the antenna a same Doppler source s

a=k r

as+=k r

1s+kla+

Phase difference between antenna 1 and a

We assume the antenna 1 as reference point.

Phase at the antenna a

= 1-a =kla

5 Phase relation and


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5. Phase relation and

where lais the oriented vector from the antenna 1 andthe antenna a.

It means that the phase differences between theantenna 1 and the generic antenna ais ksla.

It must also be noted that because of the huge distance

of the r1s compared with the small distance between theantennas la, the vector ks has the orientation in all the 4antennas.

5 Ph s l ti n nd


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In the choosen geometry = 1-a=kla = kla cos () = 2/ l cos()

= (2/ ) l cos()



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Referring to the previous figure the phase differencebetween the antenna 1 and the generic antenna a is:

1as=1s-as=k

sla = ks lacos ()

1as=(2/)l cos(a)

where a is the angle between ks and la The phase differencebetween the antenna 1 and the generic antenna a, according

to the above equation, is a function of the angle

betweenthe vector kand l.

5 Phase relation and


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The moving source (s), that has appropriate RCS adds ashift in frequency to the carrier wave so that theantenna array receives a composite signal with different

s that are the contribution of the s sources.

In case of 4 antennas it is possible with thisinterferometric Doppler technique to obtain the spatialdistribution of the main sources.



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Each multipath component is characterized by the wavevector ks. The phase difference between the antenna iand the antenna j, placed at li and lj is:

ji= j i= ks (lj li)

Utilizing 4 antennas (six equations) it is possible to solve

the wave vector ks (kx, ky , kz). First we are interested todetermine kx, ky, the components in the horizontal planexy then kz.

The sources position will be find as in the following.



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By applying the linear regression we can write:

We are interested only at the first two components of k. The third

component will be evaluate later knowing that |k|=2/. More explicitly

It is possible to minimize the above equating to zero the derivative ofrr respect to kx and ky . Because all the phase differences of the singlespectral component ij are measured (CFFT output), xij, yij are known

quantities while the unknown are kxand ky.

= +=

=1

1 1

2)]()[(

N

j

N

ji

ijsijrr llk

= +=

=1

1 1

2][),(

N

j

N

ji

jiyjixjiyxrr ykxkkk



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= +

= +=

=

=

1

1 1

1

1 1

),(0][2

N

j

N

j

ji

N

j

N

ji

jiyjijik

kkxykx

x

yx

0][21

1 1

1

1 1

),(=

=

= +

= +=

N

j

N

j

ji

N

j

N

ji

jijixjik

kkyyxk

y

yx

ji

N

j

N

ji

ji

ji

N

j

N

ji

ji

ji

N

j

N

j

jijix

ji

N

j

N

j

jiyji

y

x

yyxk

yykx

=+

=+

= +=

= +=

= +

= +

1

1 1

1

1 1

21

1 1

1

1 1

2 .

)(

)(

This linear system can be written in terms of matrix:

[ A] [ K] =[]



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=

y

x

k

kK][

=

= +=

= +=

1

1 1

1

1 1

][N

j

N

ji

jiji

N

j

N

ji

jiji

y

x

=

= +=

= +=

= +=

= +=

1

1 1

21

1 1

1

1 1

1

1 1

2

][N

j

N

ji

ji

N

j

N

ji

jiji

N

j

N

ji

jiji

N

j

N

ji

ji

yyx

yxx

A

where:



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Solving respect to kxand ky we obtain:

[ I] [ K] =[ A-1][ ]

where, [I] is the identity matrix [I]= [A] [A]-1. The inverse of the matrixis:

being |A| the determinant of [A] equal:

=

= +=

= +=

= +=

= +=

1

1 1

21

1 1

1

1 1

1

1 1

2

||

11][N

j

N

ji

ji

N

j

N

ji

jiji

N

j

N

ji

jiji

N

j

N

ji

ji

A

xyx

yxy

A

= +=

= +=

= +=

= +=

=1

1 1

1

1 1

1

1 1

21

1 1

2||

N

j

N

ji

jiji

N

j

N

ji

jiji

N

j

N

ji

ji

N

j

N

ji

ji yxyxyxA



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then kxand kyare:

||

..1

1 1

1

1 1

1

1 1

1

1 1

2

A

yyxxy

x

N

j

N

j

N

j

N

jji

N

j

N

jijijijiji

N

j

N

jijiji

k

= +

= +

= +=

= +=

=

||

..

1

1 1

1

1 1

1

1 1

1

1 12

A

xyxyx

y

N

j

N

j

N

j

N

jji

N

j

N

jijijijiji

N

j

N

jijiji

k

= +

= +

= +=

= +==



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The last two yield the wanted result including the azimuth angle ofthe Doppler source. In the framework of the antennas barycentre is:

While the vertical component kz is:

with k defined as 2/. In theory k= 2(f+fD)/cbut being fD


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where, is the zenith angle. These two couple of values will define thDoppler sources in the horizontal plane or sky-map.



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If we assume that the observed Doppler sourcedisplacements are the result of a single horizontal drift(bulk motion) of the ionospheric plasma it is possible todetermine its velocity. The Doppler frequency shift

caused by moving reflectors having radial velocity Wsseenin the previous relation.

where Ws is the velocity of the source and ksthe wavevector and the angular frequency .

c/Ws2=


Drift velocity Calculation


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Drift velocity Calculation

If we assume that all the sources in the horizontal planeare moving at the same velocity (V). The radial velocity Wscalculated by means of last-square fit analysis

Ws= - (sc)/2

wheres

is the source index and gs

a weightingfactor related to the number of sources

[ ]

=

ss

sss

g

WVg

err

2)(2

being V=(Vx+Vy+Vz) the searched drift velocity



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By setting the partial derivative err2/ Vx,

err2/ Vy

and err2/ Vz,

to zero three simultaneous equation are obtained from

which Vx, Vy and Vz are calculated.

( )[ ]0

22 )()()(

=

=++

ss

szsysxss

xx g

WVWVWVg

VV

err

etc..



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6. Conclusions


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Find the height of the layer and choose the frequency byVIS

Acquire the 4 temporal sequences of the echo signal with quadrature

sampling (amplitude and phase).Perform CFFT that yields both harmonics components and relatedphases (each shas different phase at the generic antenna a).

Obtain the most significant harmonic components nthat are theDoppler sources (maximum 128 o 256 ..)

Perform the best fit analysis of the phase differences that furnishes

the position of the sources in an horizontal plane (sky-map)

Perform the best fit analysis of the radial velocities that furnishesthe plasma drift direction (bulk motion)

Oth sid ti s


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Other considerationsSome more things we have to add

By means this technique it is impossible to separate two or

more sources giving the same .Environmental noise and RF interferences are very critical inthis kind of measurements and, we cannot use radar waveform

(to avoid phase ambiguity), so the signal cannot be processed.Intrinsic error of the measurements (phase incoherence ofthe system).

If the refractive index changes in time, what we measure isnot only the real velocity because of a term of apparentvelocity must be included.

Apparent velocity


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In general what we measure is not the drift

velocity

The time varying refractive index can introduce

a phase change because of the phase pathvariation

So only in particular condition we can be sureThat we are measuring the plasma drift velocity.

3b


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The detected radial component of the vector v isrelated to the shift in frequency by:

dt

dl

c

ff =

where, f is the frequency shift measured,c the light velocity,

f the frequency and(dl/dt) the time derivative of the phase path l

Phase path

3c


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=0

)(

S

drrnl

p

In general the phase path of the wave has differentdirection respect to the wave ray

=s

dsfnl0

)cos()(

where is the angle between the propagation

direction and the ray direction.

s

0

s

3d


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When the refractive index does not change in timewe have:

vr.c

ff =

where rthe ray direction and vthe drift velocity of theplasma. The velocity v (m/s) is the quantity that usuallywe want know.

ionospheric drift measurements

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