The results of observations of interplanetary scintillation (IPS) using the telescopes of EISCAT, in northern Scandinavia, and the ESR, on the Svalbard archipelago in the high Arctic, observing at frequencies of 1420 MHz, 928 MHz and 500 MHz are presented. Significant correlation is seen at time lags of 1.5–2 s when the observing frequencies of each telescope differ by a factor of almost three. Simple plane of sky solar wind speeds are also estimated and found to be consistent between single- and dual-frequency correlations.
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 The three antennas of the European Incoherent SCATter radar (EISCAT) have been used to probe the solar wind at all heliographic latitudes over distances ranging from 15R⊙ to more than 100R⊙ since 1982 [Bourgois et al., 1985] and on a regular basis since 1990. Simultaneous observations using all three of the EISCAT antennas allow a cross-correlation analysis [Coles, 1996; Canals et al., 2002] to be used to determine the solar wind speed(s) across the line of sight.
 In 2002, EISCAT was upgraded to allow measurements at an observing frequency of 1420 MHz at two sites [Wannberg et al., 2002]. The complication of a transmitting system has meant that the remaining antenna, at Tromsø, has yet to be upgraded and still uses the original observing frequency of 928 MHz. Whilst it is possible to obtain a reliable estimate of the mean solar wind velocity in the line of sight from a single-site IPS observation [Manoharan and Ananthakrishnan, 1990], cross-correlation over a long baseline provides a more accurate estimate of solar wind velocities even when more than one stream is present. Hence the ability to cross-correlate different observing frequencies assumes some importance in maintaining IPS observations with all of the baselines available at EISCAT.
 Cross-correlation between two different observing frequencies is accounted for in IPS theory [Salpeter, 1967], but has seldom been used in practice. Scott et al.  used the National Radio Astronomy Observatory in W. Virginia, USA, to make single-antenna observations at three observing frequencies simultaneously. Each pair of frequencies was cross-correlated to obtain power spectra, which were then analysed to obtain solar wind speed. The power-law nature of the density variations was also analysed. A small (0.4 ms) time lag, found to be consistent with plasma refraction due to large-scale structures in the solar wind, was seen in the cross-correlation. This effect will lead to a small but systematic bias in the time lags of cross-correlations between spaced antennas, such as those presented in this paper.
 Cross-correlation between spaced antennas has not been tried before, to the authors knowledge. Therefore the range of observing frequencies and antenna baselines over which cross-correlation is possible has yet to be quantified. In May 2003, two test observations were carried out, demonstrating that a significant correlation exists between measurements at 928 MHz and 1420 MHz. Further dual-frequency observations were carried out in September 2003. May 2004 saw the use of the EISCAT Svalbard Radar (ESR) for IPS observations for the first time. This antenna operates at the lower frequency of 500 MHz, hence allowing cross-correlation between three observing frequencies with baselines of up to 1200 km to be trialled. In this paper, the initial results from these trials are presented.
2. Background Theory
 Density fluctuations in the solar wind, which are assumed to be of turbulent origin, cause phase variations to be introduced in the radio signal from a distant source. If the rms phase difference over transverse scales equal to the radius of the first Fresnel zone Rf = are small (≪1 radian), then the level of scattering is said to be “weak” and diffraction can be modeled with the Born approximation as a linear summation of the effects of a series of “thin screens” along the line of sight between the source and receiver. The resulting intensity fluctuations have most of their energy at scales near Rf. Since Rf changes with distance z, the line of sight integration spreads the energy over a range of scales. Higher observing frequencies, sensitive to smaller density scales, which are weaker, may be used to maintain observations within a weak scattering regime as the mean solar wind density increases closer to the Sun.
 The IPS temporal power spectrum under weak scattering conditions can be expressed by the following equation: (For further details, the reader is referred to, Scott et al. , and references therein).
where: re is the classical electron radius; λ is the observing wavelength; C is a constant of proportionality; vp is the component of solar wind velocity perpendicular to the line of sight; q is the 2-dimensional spatial wavenumber; z is the distance from Earth to the scattering screen; V(q, z, θ0(λ)) is the visibility function of a radio source of size θ0(λ). sin2 () is the Fresnel filter which acts as a high-pass filter attenuating wavenumbers below the Fresnel frequency, qf = . exp(−()2 describes the dissipation and attenuates the scintillation power spectrum at wavenumbers higher than qi. In addition the source visibility function also acts as a low-pass filter attenuating wavenumbers above qs = .
Equation (1) assumes a single observing frequency and so only represents the auto-spectrum for each antenna in the case of these observations. A simple modification is needed for the cross-spectrum. Salpeter  is one of few authors on IPS theory to do this: All the λ2 terms are separated into single λ terms and the cross-spectrum becomes:
 The assumption of weak scatter must be valid for both observing frequencies. The cross correlation between different frequencies drops much more quickly in strong scattering than is the case for single-frequency cross-correlation, so this technique cannot be used as close to the Sun as the single frequency case. By contrast, any radio source is limited in how far from the Sun its scintillation can be measured at a given frequency by its strength, angular size and structure. Therefore radio sources and heliocentric distances have to be picked carefully to ensure that these restrictions are satisfied for both observing frequencies. The observations presented in this paper satisfied these conditions.
 The results presented in this paper were obtained from measurements taken in September 2003 and May 2004. The purpose of this paper is to demonstrate that cross-correlating different frequencies between spaced antennas can provide useful results. The apparent solar wind speeds presented here are plane-of-sky speeds calculated directly from the radial baseline between the lines of sight and the time lag of peak cross correlation and are not corrected for spherical divergence of the solar wind flow, the presence of multiple velocity streams or the effects of waves or random velocities. Modelling these observations to obtain more reliable estimates of solar wind speeds will be the subject of a future paper.
Figure 1 shows an EISCAT observation of 1256-057 on 1st October 2003. The receivers at both Kiruna and Sodankylä were set at 1420 MHz, while the receiver at Tromsø remained at 928 MHz.
 The time lags of the cross-correlation functions indicate that a slow stream of approximately 400 km s−1 dominates in this observation, although the extension of the cross-correlation functions to longer time lags indicate the presence of another, slower, stream as well. Cross-correlations between the two observing frequencies are slightly reduced and broadened compared to the single frequency case.
 The level of correlation between two different frequencies is expected to be lower than the level at a single frequency as the range of density scales giving rise to the scintillation at each frequency is not exactly the same.
 The second example is an EISCAT observation of 1150-003 from the same day, given in Figure 2; receiver settings are as for the first example.
 Both an intermediate and a slow stream are evident in this observation. Obvious differences can be seen between the cross-correlation functions in this example compared with the first. The single-frequency cross-correlation has a broadened peak: The main peak corresponds to a slow stream and the extension to shorter time lags corresponds to an intermediate stream. However, both dual-frequency cross-correlations show differing levels of correlation for each of these streams compared to the single-frequency case. The Tromsø-Kiruna cross-correlation clearly shows the intermediate stream dominating, with the slow stream registering as a barely-visible bump on the broad extension of the cross-correlation function to longer time lags. In contrast the Tromsø-Sodankylä correlation shows a definite twin peak in the cross-correlation function, implying an almost equal weighting to both streams.
 Since these differences are seen between all three correlations and not only between the single-frequency and dual-frequency cases, the differing observing frequencies are unlikely to be a factor in the differences seen.
 In May 2004, the EISCAT Svalbard Radar (ESR), operating at a frequency of 500 MHz, was used for the first time for IPS. The Kiruna and Sodankylä antennas were converted to 1420 MHz in the latter part of this observing campaign. Observations of two sources showed significant correlation between 500 MHz and 1420 MHz over baselines of nearly 1000 km. Figure 3 shows the correlation functions between all three observing frequencies for an observation of 0319 + 415 carried out on 12th May 2004.
 All three cross-correlations indicate a dominant fast stream in the line of sight. Some slow solar wind is also evident from the definite step and skew seen at longer time lags, most particularly in the Tromsø-Kiruna and Kiruna-ESR cross-correlations.
 The dominant stream combined with the low random spread in solar wind speeds at this solar distance make this observation relatively straightforward to model. Equations (1) and (2) were normalised and used to calculate model auto- and cross-correlation functions respectively. Density variations were assumed to be anisotropic in nature with an axial ratio of 1.5 and spectral index, α, of 3. The radio source was assumed to be a perfect point source (i.e., ∣V(q, z, θ0)∣ = 1) initially. A mean diffraction pattern drift velocity, vp, of 645 km s−1 was found to fit the cross-correlation functions best. No spread in this velocity was included. There is good agreement between the actual and model cross-correlation functions in both of the ESR cross-correlations particularly.
 However, the agreement between the actual and model auto-correlation functions is poor; the actual auto-correlation functions are much broader than the model. The source 0319+415 (3C84) is a VLA calibrator known to have an extended structure. A broad source will broaden the auto-correlation functions, but also increase the width and height of the cross-correlation function. The bottom plot in Figure 3 shows the Kiruna-ESR correlations with the same model as detailed above, but assuming a Gaussian source, ∣V∣= exp(−qzθ0). A diameter, θ0 of 0.7″ (assumed for both observing frequencies for simplicity) was found to adequately model the auto-correlation functions. The cross-correlation functions now have a poor agreement indicating that a full model fitting including the line of sight integration, random velocity components and multiple velocities in the line of sight is required. Such a fit is beyond the scope of this paper.
Table 1 summarises the main May 2004 observations. The plane of sky speeds are simple calculations based on the radial baseline and time lag for each cross-correlation and give a simple indication as to the solar wind stream(s) in the line of sight, but should not be taken as the true solar wind speed. Where two peaks exist in the correlation function, values are calculated for both. The values given are for the greatest correlation within each observation.
Table 1. Summary of Cross-Correlations From Observations in May 2004a
Speed, km s−1
Br and Bt are the baseline vectors projected in radial and tangential directions respectively onto the sky plane; Corr gives the peak height of the normalised cross-correlation function; Lag gives the time lag of the peak correlation, in seconds; Speed is the drift speed resulting from the radial baseline length divided by the time lag, figures in brackets denote an average of twin correlation peak speeds calculated according to the respective amount of correlation in each case.
 Plane of sky speeds for each observation are consistent between cross-correlations of different frequencies. This is particularly evident in the 12th May 2004 observations which were heavily dominated by one solar wind stream. In many of the remaining observations, the very long baselines between EISCAT and the ESR allow two streams to be resolved as separate peaks in the cross-correlation function. Plane of sky speeds calculated using the much shorter EISCAT baselines in these observations should represent a line of sight averaged speed of both solar wind streams. This is checked approximately by averaging the two speeds given by the separate cross-correlation peaks in the longer baseline correlations, weighting each according to its level of correlation. The figures for these calculations are given in brackets to the side of the speeds being averaged. These averages are consistent with the shorter baseline measurements.
 The results presented in this paper demonstrate that there is a clear correlation between measurements of IPS carried out at widely separated antennas, observing at different frequencies. The level of correlation depends on how much overlap there is between the density scales observed with each frequency. This will restrict the difference between observing frequencies over which it is possible to obtain correlation for a particular baseline. Nevertheless a high degree of correlation exists between frequencies differing by almost a factor of three, with a time lag of 1.5–2 seconds.
 Simple plane of sky estimates of solar wind speed have been calculated. These speed estimates are found to be consistent between single-frequency and dual-frequency correlations.
 Good agreement was found between the observed cross-correlation functions and those expected by weak-scattering theory when a point source was assumed. However this agreement was lost when the effect of a broad source, indicated by the width of the auto-correlation functions, was added. Carrying out a full model fit is beyond the scope of this paper; the simple model fits included here demonstrate that modelling these observations is possible but not trivial.
 We would like to thank the director and staff of EISCAT for their help and the quality of data over many years of observations. Three of us (RAF, MMB and RAJ) were supported by PPARC throughout the period of this research. We extend particular thanks to W. A. Coles and B. J. Rickett for making their analysis routines, expertise and advice available to us.