- Email: [email protected]
The correlation analysis of the fading of radio signals received from satellites
Journalof Atmosphericand TerrestrialPhgsics, 1062,Vol. 24, pp. 237 to 244. PergamonPressLtd. Printedin KorthsrnIrelanfl
The correlation analysis of the fading of radio signals received from satellites P. W. JAMES Cavendish Laboratory, Cambridge (Received 9 November 1961) Abstr&-It is supposed that records of the fading of radio waves received from an artificial satellite are made at three spaced receivers, and that the auto-correlation and cross-correlation functions of the records are evaluated. The deductions which can then be made about the ionospheric irregularities which cause the fading are discussed. It is shown that it is possible to determine the mean height of these irregularities and also a parameter which measures the range of heights over which appreciable irregularities exist. It is also shown how the sizes of the irregularities can be determined. It is assumed that the height and velocity of the satellite are known.
1. INTRODUCTION IT HAS been shown (FRIHAGEN and TR~IM, 1960) that observations of the fading of radio waves received from a satellite can be used to determine the height of the irregularities in the ionosphere responsible for the fading. The principle of the method is shown in Fig. 1. If the satellite has a velocity U, assumed known, and
Fig. 1
is at a height H, and if the irregularities are confined to a thin layer at a height h, then simple arguments show that the irregular pattern of signal amplitude formed on the ground moves with a velocity V given by v= If, therefore,
-&hu.
V is measured, the height h can be determined 237
if H is known.
238
P. Iv.
JAMES
The most accurate method for the measurement of V is to set up three spaced receivers and to apply the correlation analysis of BRICGSet al. (1950)and PHILLIPS and SPENCER (1955). In this method of analysis, the auto-correlation functions between the records taken in pairs are first evaluated. By further computations, the values of certain parameters which describe the irregular pattern are then deduced. These parameters are the following: (1) The magnitude and direction of drift (8, 4); (2) The constants of a “characteristic ellipse” which indicate the size and degree of elongation of a typical irregularity in the pattern; (3) The value of a parameter Vc which measures the rate at which the pattern V, has the dimension changes with time, when the drift velocity has been removed. of velocity, and in any given direction, is the ratio of the pattern size in that direction to the life-time of a typical feature of the pattern. If the pattern drifts without change of form, then Vv, = 0. Now the velocity of the satellite is so great that any drift or random changes in the ionospheric irregularities can be neglected. It might, therefore, be thought that 8, would necessarily be zero. If, however, the irregularities are not. confined to a thin layer, but exist over a considerable range of height, there will be produced It will a whole series of diffraction patterns, each moving with a different velocity. be shown that the resultant pattern is equivalent to a single pattern moving with a certain mean velocity, but changing with time in a way which can be described by assigning an appropriate value to 8,. The value of 8, depends, as might be expected, on the range of height over which the irregularities exist. Thus it is possible to obtain information about both the mean height of the irregularities, and about the height interval over which they are spread, from the observed values of V and V’,. In addition, the characteristic ellipse for the pattern will be related to that which describes the ionospheric irregularities themselves. In the analysis which follows, it will be assumed that at each point on the ground, the change in signal amplitude from its mean value is equal to the sum of the changes which would be produced by the various component layers each acting alone. This will be justified provided that the scattering is weak, i.e. that the total phase deviation produced by the whole layer of irregularities is not more than about 1 rad. 2. CALCULATIONOF THE PARAMETERSOF THE DIFFRACTIONPATTERX DUE TO A LAYER OF IRREGULARITIESOF FIKITE THICKNESS The ionospheric irregularities will be assumed to change with time (i.e. to have a non-zero intrinsic V,), and the results will be extended to include the case when they have an overall drift. As stated above, these effects are not likely to be important in practice because of the high velocity of the satellite, but they are included for the sake of generality. In the following calculations, the curvature of the earth will be neglected. The axes Oxyz are chosen so that Oxy is the plane of the ground, and Oxx contains the satellite’s trajectory (Fig. 2). The satellite is not necessarily vertically above the point of observation. The origin 0 is any arbitrary fixed point on the ground, near the point of observation.
The correlation analysis of the fading of radio signals received from satellites
239
Let H be the satellite’s height and U its horizontal component of velocity. If the satellite has any vertical component of velocity, the height will alter during the transit; in this case, H should be taken as the average height during the period of observation. Consider a layer of irregularities at height x, of thickness 6~ and let do(z) be the standard deviation of phase shift per unit path length in this layer. Then this
tO.O,H)
Fig. 2
layer by itself would standard deviation
give rise to an amplitude
distribution
on the ground
of
f(~)#&W(~~) wheref(z) is a slowly varying function of Z; it can be shown thatf(x) is zero at x = 0 and .z = H, with a broad maximum at x = $H. If the source were at infinite height, the pattern produced by this layer alone would have a certain auto-correlation function which we shall denote by (This is defined as [A(x, y, t) A(x + 6, y + 7, t +
7) +Q21
[A2 - (A)2] where A(x, y, t) is the signal amplitude at the point (x, y, 0) at time t, and the averages are taken over x, y and t). For a source at a finite height H, moving with velocity U, this must be modified to allow for (1) the drift velocity
(2) the geometrical
[-
Uz/(H - z), 01;
magnification
by H/(H
- z) times.
P. W.
240
The modified
function
JAMES
is
PH(5, 17, 7; 2) = pm It can be readily shown from the assumption in Section 1 that the auto-correlation function ~(5, 7, T) of the pattern due to a thick layer of irregularities is given by integrating pH(E, rj, T; z) through the layer as follows (1)
P(6, ‘I, 7) = c, where C, is a normalizing
constant.
Z=h-’
”
Fig. 3
Now suppose the irregularities
have a mean height h, and that 4,,(z) varies as
do(z) = 4,(h) exp [ - GA?]. The value of 4,(h) depends on the direction of the satellite, in relation to the direction of elongation of the irregularities and to the vertical direction. It may rise to a maximum if the line of sight sweeps through the direction of the earth’s magnetic field at the height of the layer, but otherwise it will vary slowly enough to be regarded as constant. The thickness of the layer of irregularities measured between the levels at which $Jz) is l/e of its maximum value is then 4A (Fig. 3).
The correlation
Pd6, r,
7;
analysis
of the fading
of radio
signals
z) will be assumed to be independent 4(At2 + B$
P,(5> 7, 7; z) = exp [ -
received
+ 2EEq + Cb2)j.
(2)
later),
+ Bq2 + 2Etr/ = 2 log,S,
(c) the value of V, in the 6 direction Then by equation
241
of height and given by
This describes a pattern in which (a) there is no drift (this restriction will be removed (b) the characteristic ellipse [p,([, 7, 0; z) = 31 is At”
from satellites
is (~7/~4)r’~; this will be denoted
by ( VcJo.
(1)
To evaluate this integral satisfy the condition
it will be assumed that the satellite is high enough to H > h + 2A.
Also it will be assumed that h > 2A. Then f(z) is nearly constant over the range h - 2A to h + 2A, and little error is introduced by replacing the limits of integration by - co to + co. It can be shown that p(E, q, T) = exp
+2
(AE2 + By2 + 2Eb/) A U2h2
h(H -;j
- A2 (At + Ey) UT + (C + H”
Terms within the square brackets of order 14, q4 or C, has been chosen to make ~(0, 0, 0) = 1. This can be written as p(E, 7, T) = exp
--
l\H -
h)2 $ A2
2]
Hz
A(5 -
( UT)~
(H -
~(6, r, 7) = exp
i
~7)
and
I
111
A U2A2 + (H _ h)2 + A2 T2
h)2 + A2
L2 h)2 A(,$ - 2’ I(H ]
VT)~ + By2 + 2E(E -
+ 3
-
v__-u W- h) h- .A2
where
.
have been neglected
VT)~ + Bq2 + 2E([
+ [’
or
+ FIG])
’
VT)~
A U2A2 ___+ (H _ h)2
1
242
P. w.
vc -u
and
JAMES
h H
_
.
SlnCe
h,
A2 < (H -
h)‘.
(3)
Equation (3) describes a pattern in which (a) the drift is (V, 0) or [ - Uh/(H - h), 01, (b) the ellipse ~(6, 17,0) = $ is identical in shape and orientation with the original ellipse pm (6, q, 0; Z) = 4, but is linearly magnified H/(H - h) times, (c) the intrinsic time variations are described by a value of V,, in the x-direcCon, equal to
(4) In particular,
if ( VleJo is zero IUI H vc, = (H _ h)Z.
(5)
These are the main results of the present work. They show how the observed values of V and V,, can be used to find respectively the mean height h of the irregularities
U Fig. 4
and the range of heights 4A over which the irregularities exist. The analysis can be extended to the case when the irregularities are moving with a uniform drift velocity Vi, by using a system of co-ordinates moving with the irregularities. Relative to these moving axes, the satellite’s velocity is U’ = u -
vi = {U -
v7i cos CC,
- 8, sin r~}
where tl is the angle between U and Vi(Fig. 4). Then, relative to the moving axes, the auto-correlation modifying equation (3) to
~(5, l;r, T) = exp
i
- -2 ’ ‘(H ,-mH2 - h)z,A(t
-
Vz’~)2 + B(q -
function
~~‘7)2
where v’z = -(U 8,’
= -(-Vi
-
h v’, cos a) H _ h h sin M)------
U’ = IUI’ = (UZ -
H-h
2UV, cos ,X + V.2)1/2.
is obtained
by
The correlation analysis of the fading of radio signals received from satellites
The actual drift velocity
243
of the pat.tern is therefore
v = vi + f fr’,, vl,)
The value of V, in the x direction
and this expression If
is unaffected
is
by the motion of the axe8.
VcT,< U, then ET’ = U -
8, cos a
and
or
(U -
V, cos ci) AH (H -
h)”
if
(V,,),
= 0.
Note that ( V,),T is the value of V, appropriate to the direction of motion of the satellite. (I’,), is simply related to ( Vvc)v,the value of V, in the direction of pattern drift, by
where EUand I, are the radii of the characteristic ellipse in the U and V directions respectively. 3. DISCTTSSION
A satellite in a circular orbit at a height of (say) 1000 km has a speed of about 7.4 km/set. The values of V,, obtained from spaced receiver measurements using radio stars, are typically 25-500 m/see, and the values of 8, usually much less than 100 m/see. It is therefore permissible to use the simplified formulae (3) and (5) which neglect ( VeJO and Vi. Measurements of V and V, lead to values for the height and thickness of the layer of irregularities, using the relations h=Hp
and
V u+v
V, UH A=(u+v)?’
To estimate the error in neglecting Vz and (l’Cx)O, let us suppose H = 1000 km, h = 500 km, and Vi = 100 m/set. Then the error in h is at most 1.3 per cent and the error in A is at most 2.7 per cent. If ( Vcr),, = 100 m/see and A = 100 km, the error in 4 due to neglect of ( Vca}Ois only 0.2 per cent. These errors are insignificant
244
P. iv.
JAMES
compared with the probable errors in the measurements of V and V,. It must be remembered that only irregularities lower than the satellite will affect the pattern, and of these, those at height +H will be most effective. The value of h will not indicate the average height of the irregularities unless the satellite is very high, i.e. H > h. If this is not so, the value of h obtained will lie between the lower boundary of the layer of irregularities and the centre of the layer, or the satellite height, whichever is the lower: this situation will be indicated by a value of A which is not small compared with H. If
H >hh,
l’, fi g;
= QA
where 0 is the angular velocity U/H of t,he source. It is of interest to consider also the case of scintillations of a radio “star”. A radio “star” is a source with H = co, and Q, the angular velocity, is very small (due only to the rotation of the earth). If there exists a gradient of wind velocity dVC//dz, in the layer of irregularities, Ohis gradient has the same effect upon 8, as an addit’ional angular velocity
Such a wind gradient would give l’, = QA
where (Vi)Z and (V& are the velocities at heights h + 2A and h - 2A, where rj,, is l/e of its maximum value. The actually observed value of V, will be
Hence
the values of V, found
for radio star scintillations
set an upper limit to
$l(V,), - (V,)J. The correct direction in which 8, should be found is that of the vector (V,), - (V&, which is unknown. The use of the value of V, in the direction of drift gives only an approximate indication of an upper bound for / (V,)2 - (V,)ll. In practice, it is found that the value of V7, for radio star scintillation is very small or zero (JOXES, 1960), suggesting that the irregularities move bodily without the presence of velocity gradients. Acknowledgements-This work forms part of a programme of research on ionospheric irregularities supported by a grant from the Department of Scientific and Industrial Research. The author was in receipt of a maintenance grant from the same department. The author is also indebt’ed to Dr. B. H. BRIGGS for his help and advice during this investigation. REFEREKCES BRIGGS B.H.,PHILLIPS G.J.and SHINN D.H. FRIHAGEN J.and TR~IM J. JoNEsI.L. PHILLIPS G. J. and SPENCER RI.
1950 1960 1960 1955
Proc.Phys. Sot. Lond. B 63, 106. J. Atmosph. Terr. Phys. 18, 75. J. Atmosph. Terr. Phys. 19, 26. Proc. Phys. Sot. Lond. B 68, 481.
The correlation analysis of the fading of radio signals received from satellites P. W. JAMES Cavendish Laboratory, Cambridge (Received 9 November 1961) Abstr&-It is supposed that records of the fading of radio waves received from an artificial satellite are made at three spaced receivers, and that the auto-correlation and cross-correlation functions of the records are evaluated. The deductions which can then be made about the ionospheric irregularities which cause the fading are discussed. It is shown that it is possible to determine the mean height of these irregularities and also a parameter which measures the range of heights over which appreciable irregularities exist. It is also shown how the sizes of the irregularities can be determined. It is assumed that the height and velocity of the satellite are known.
1. INTRODUCTION IT HAS been shown (FRIHAGEN and TR~IM, 1960) that observations of the fading of radio waves received from a satellite can be used to determine the height of the irregularities in the ionosphere responsible for the fading. The principle of the method is shown in Fig. 1. If the satellite has a velocity U, assumed known, and
Fig. 1
is at a height H, and if the irregularities are confined to a thin layer at a height h, then simple arguments show that the irregular pattern of signal amplitude formed on the ground moves with a velocity V given by v= If, therefore,
-&hu.
V is measured, the height h can be determined 237
if H is known.
238
P. Iv.
JAMES
The most accurate method for the measurement of V is to set up three spaced receivers and to apply the correlation analysis of BRICGSet al. (1950)and PHILLIPS and SPENCER (1955). In this method of analysis, the auto-correlation functions between the records taken in pairs are first evaluated. By further computations, the values of certain parameters which describe the irregular pattern are then deduced. These parameters are the following: (1) The magnitude and direction of drift (8, 4); (2) The constants of a “characteristic ellipse” which indicate the size and degree of elongation of a typical irregularity in the pattern; (3) The value of a parameter Vc which measures the rate at which the pattern V, has the dimension changes with time, when the drift velocity has been removed. of velocity, and in any given direction, is the ratio of the pattern size in that direction to the life-time of a typical feature of the pattern. If the pattern drifts without change of form, then Vv, = 0. Now the velocity of the satellite is so great that any drift or random changes in the ionospheric irregularities can be neglected. It might, therefore, be thought that 8, would necessarily be zero. If, however, the irregularities are not. confined to a thin layer, but exist over a considerable range of height, there will be produced It will a whole series of diffraction patterns, each moving with a different velocity. be shown that the resultant pattern is equivalent to a single pattern moving with a certain mean velocity, but changing with time in a way which can be described by assigning an appropriate value to 8,. The value of 8, depends, as might be expected, on the range of height over which the irregularities exist. Thus it is possible to obtain information about both the mean height of the irregularities, and about the height interval over which they are spread, from the observed values of V and V’,. In addition, the characteristic ellipse for the pattern will be related to that which describes the ionospheric irregularities themselves. In the analysis which follows, it will be assumed that at each point on the ground, the change in signal amplitude from its mean value is equal to the sum of the changes which would be produced by the various component layers each acting alone. This will be justified provided that the scattering is weak, i.e. that the total phase deviation produced by the whole layer of irregularities is not more than about 1 rad. 2. CALCULATIONOF THE PARAMETERSOF THE DIFFRACTIONPATTERX DUE TO A LAYER OF IRREGULARITIESOF FIKITE THICKNESS The ionospheric irregularities will be assumed to change with time (i.e. to have a non-zero intrinsic V,), and the results will be extended to include the case when they have an overall drift. As stated above, these effects are not likely to be important in practice because of the high velocity of the satellite, but they are included for the sake of generality. In the following calculations, the curvature of the earth will be neglected. The axes Oxyz are chosen so that Oxy is the plane of the ground, and Oxx contains the satellite’s trajectory (Fig. 2). The satellite is not necessarily vertically above the point of observation. The origin 0 is any arbitrary fixed point on the ground, near the point of observation.
The correlation analysis of the fading of radio signals received from satellites
239
Let H be the satellite’s height and U its horizontal component of velocity. If the satellite has any vertical component of velocity, the height will alter during the transit; in this case, H should be taken as the average height during the period of observation. Consider a layer of irregularities at height x, of thickness 6~ and let do(z) be the standard deviation of phase shift per unit path length in this layer. Then this
tO.O,H)
Fig. 2
layer by itself would standard deviation
give rise to an amplitude
distribution
on the ground
of
f(~)#&W(~~) wheref(z) is a slowly varying function of Z; it can be shown thatf(x) is zero at x = 0 and .z = H, with a broad maximum at x = $H. If the source were at infinite height, the pattern produced by this layer alone would have a certain auto-correlation function which we shall denote by (This is defined as [A(x, y, t) A(x + 6, y + 7, t +
7) +Q21
[A2 - (A)2] where A(x, y, t) is the signal amplitude at the point (x, y, 0) at time t, and the averages are taken over x, y and t). For a source at a finite height H, moving with velocity U, this must be modified to allow for (1) the drift velocity
(2) the geometrical
[-
Uz/(H - z), 01;
magnification
by H/(H
- z) times.
P. W.
240
The modified
function
JAMES
is
PH(5, 17, 7; 2) = pm It can be readily shown from the assumption in Section 1 that the auto-correlation function ~(5, 7, T) of the pattern due to a thick layer of irregularities is given by integrating pH(E, rj, T; z) through the layer as follows (1)
P(6, ‘I, 7) = c, where C, is a normalizing
constant.
Z=h-’
”
Fig. 3
Now suppose the irregularities
have a mean height h, and that 4,,(z) varies as
do(z) = 4,(h) exp [ - GA?]. The value of 4,(h) depends on the direction of the satellite, in relation to the direction of elongation of the irregularities and to the vertical direction. It may rise to a maximum if the line of sight sweeps through the direction of the earth’s magnetic field at the height of the layer, but otherwise it will vary slowly enough to be regarded as constant. The thickness of the layer of irregularities measured between the levels at which $Jz) is l/e of its maximum value is then 4A (Fig. 3).
The correlation
Pd6, r,
7;
analysis
of the fading
of radio
signals
z) will be assumed to be independent 4(At2 + B$
P,(5> 7, 7; z) = exp [ -
received
+ 2EEq + Cb2)j.
(2)
later),
+ Bq2 + 2Etr/ = 2 log,S,
(c) the value of V, in the 6 direction Then by equation
241
of height and given by
This describes a pattern in which (a) there is no drift (this restriction will be removed (b) the characteristic ellipse [p,([, 7, 0; z) = 31 is At”
from satellites
is (~7/~4)r’~; this will be denoted
by ( VcJo.
(1)
To evaluate this integral satisfy the condition
it will be assumed that the satellite is high enough to H > h + 2A.
Also it will be assumed that h > 2A. Then f(z) is nearly constant over the range h - 2A to h + 2A, and little error is introduced by replacing the limits of integration by - co to + co. It can be shown that p(E, q, T) = exp
+2
(AE2 + By2 + 2Eb/) A U2h2
h(H -;j
- A2 (At + Ey) UT + (C + H”
Terms within the square brackets of order 14, q4 or C, has been chosen to make ~(0, 0, 0) = 1. This can be written as p(E, 7, T) = exp
--
l\H -
h)2 $ A2
2]
Hz
A(5 -
( UT)~
(H -
~(6, r, 7) = exp
i
~7)
and
I
111
A U2A2 + (H _ h)2 + A2 T2
h)2 + A2
L2 h)2 A(,$ - 2’ I(H ]
VT)~ + By2 + 2E(E -
+ 3
-
v__-u W- h) h- .A2
where
.
have been neglected
VT)~ + Bq2 + 2E([
+ [’
or
+ FIG])
’
VT)~
A U2A2 ___+ (H _ h)2
1
242
P. w.
vc -u
and
JAMES
h H
_
.
SlnCe
h,
A2 < (H -
h)‘.
(3)
Equation (3) describes a pattern in which (a) the drift is (V, 0) or [ - Uh/(H - h), 01, (b) the ellipse ~(6, 17,0) = $ is identical in shape and orientation with the original ellipse pm (6, q, 0; Z) = 4, but is linearly magnified H/(H - h) times, (c) the intrinsic time variations are described by a value of V,, in the x-direcCon, equal to
(4) In particular,
if ( VleJo is zero IUI H vc, = (H _ h)Z.
(5)
These are the main results of the present work. They show how the observed values of V and V,, can be used to find respectively the mean height h of the irregularities
U Fig. 4
and the range of heights 4A over which the irregularities exist. The analysis can be extended to the case when the irregularities are moving with a uniform drift velocity Vi, by using a system of co-ordinates moving with the irregularities. Relative to these moving axes, the satellite’s velocity is U’ = u -
vi = {U -
v7i cos CC,
- 8, sin r~}
where tl is the angle between U and Vi(Fig. 4). Then, relative to the moving axes, the auto-correlation modifying equation (3) to
~(5, l;r, T) = exp
i
- -2 ’ ‘(H ,-mH2 - h)z,A(t
-
Vz’~)2 + B(q -
function
~~‘7)2
where v’z = -(U 8,’
= -(-Vi
-
h v’, cos a) H _ h h sin M)------
U’ = IUI’ = (UZ -
H-h
2UV, cos ,X + V.2)1/2.
is obtained
by
The correlation analysis of the fading of radio signals received from satellites
The actual drift velocity
243
of the pat.tern is therefore
v = vi + f fr’,, vl,)
The value of V, in the x direction
and this expression If
is unaffected
is
by the motion of the axe8.
VcT,< U, then ET’ = U -
8, cos a
and
or
(U -
V, cos ci) AH (H -
h)”
if
(V,,),
= 0.
Note that ( V,),T is the value of V, appropriate to the direction of motion of the satellite. (I’,), is simply related to ( Vvc)v,the value of V, in the direction of pattern drift, by
where EUand I, are the radii of the characteristic ellipse in the U and V directions respectively. 3. DISCTTSSION
A satellite in a circular orbit at a height of (say) 1000 km has a speed of about 7.4 km/set. The values of V,, obtained from spaced receiver measurements using radio stars, are typically 25-500 m/see, and the values of 8, usually much less than 100 m/see. It is therefore permissible to use the simplified formulae (3) and (5) which neglect ( VeJO and Vi. Measurements of V and V, lead to values for the height and thickness of the layer of irregularities, using the relations h=Hp
and
V u+v
V, UH A=(u+v)?’
To estimate the error in neglecting Vz and (l’Cx)O, let us suppose H = 1000 km, h = 500 km, and Vi = 100 m/set. Then the error in h is at most 1.3 per cent and the error in A is at most 2.7 per cent. If ( Vcr),, = 100 m/see and A = 100 km, the error in 4 due to neglect of ( Vca}Ois only 0.2 per cent. These errors are insignificant
244
P. iv.
JAMES
compared with the probable errors in the measurements of V and V,. It must be remembered that only irregularities lower than the satellite will affect the pattern, and of these, those at height +H will be most effective. The value of h will not indicate the average height of the irregularities unless the satellite is very high, i.e. H > h. If this is not so, the value of h obtained will lie between the lower boundary of the layer of irregularities and the centre of the layer, or the satellite height, whichever is the lower: this situation will be indicated by a value of A which is not small compared with H. If
H >hh,
l’, fi g;
= QA
where 0 is the angular velocity U/H of t,he source. It is of interest to consider also the case of scintillations of a radio “star”. A radio “star” is a source with H = co, and Q, the angular velocity, is very small (due only to the rotation of the earth). If there exists a gradient of wind velocity dVC//dz, in the layer of irregularities, Ohis gradient has the same effect upon 8, as an addit’ional angular velocity
Such a wind gradient would give l’, = QA
where (Vi)Z and (V& are the velocities at heights h + 2A and h - 2A, where rj,, is l/e of its maximum value. The actually observed value of V, will be
Hence
the values of V, found
for radio star scintillations
set an upper limit to
$l(V,), - (V,)J. The correct direction in which 8, should be found is that of the vector (V,), - (V&, which is unknown. The use of the value of V, in the direction of drift gives only an approximate indication of an upper bound for / (V,)2 - (V,)ll. In practice, it is found that the value of V7, for radio star scintillation is very small or zero (JOXES, 1960), suggesting that the irregularities move bodily without the presence of velocity gradients. Acknowledgements-This work forms part of a programme of research on ionospheric irregularities supported by a grant from the Department of Scientific and Industrial Research. The author was in receipt of a maintenance grant from the same department. The author is also indebt’ed to Dr. B. H. BRIGGS for his help and advice during this investigation. REFEREKCES BRIGGS B.H.,PHILLIPS G.J.and SHINN D.H. FRIHAGEN J.and TR~IM J. JoNEsI.L. PHILLIPS G. J. and SPENCER RI.
1950 1960 1960 1955
Proc.Phys. Sot. Lond. B 63, 106. J. Atmosph. Terr. Phys. 18, 75. J. Atmosph. Terr. Phys. 19, 26. Proc. Phys. Sot. Lond. B 68, 481.