## 1. Introduction

[2] Today's instrumentation for wave measurements in space often allows us to work with multicomponent data [e.g., *Lefeuvre et al.*, 1998; *Gurnett et al.*, 1995; *Cornilleau-Wehrlin et al.*, 1997]. In these devices, full magnetic field vector is measured by three orthogonal antennas, and the electric field is simultaneously measured by at least two electric antennas. With these data, the classical analysis of power spectra and spectrograms can be completed by examination of wave propagation properties. If we suppose the presence of a single plane wave at frequency *f*, the wave vector ** k** can be determined from the linearized Faraday's law:

where ω is the angular frequency ω = 2π*f*, and ** E** and

**are the vectors of complex amplitudes of electric and magnetic fields. Here we suppose that the corresponding analytic signals at a point**

*B***can be written as**

*x***ϒ**exp[ι(ω

*t*−

**·**

*k***)], where ι is , and**

*x***ϒ**stands for

**or**

*E***, respectively.**

*B*[3] From (1) it follows that ** B** is always perpendicular to both wave vector and

**. The perpendicularity to the wave vector is also a consequence of another Maxwell equation,**

*E***·**

*k***= 0. This can be used to determine the wave vector direction, for instance by the minimum variance analysis of magnetic fluctuations [e.g.,**

*B**Rezeau et al.*, 1993]. This method directly works with waveforms of measured signals. The direction of minimum variance can be attributed to the wave vector direction and the hodographs of the magnetic field plotted in the plane perpendicular to this direction can show the wave polarization. This supposes that the signal is narrow-band or that the wave vector direction does not change with the frequency.

[4] Another way to determine the wave vector directions is based on the multidimensional spectral analysis. This technique acts as a narrow-band frequency filter centered at each analyzed frequency and gives us the power-spectral densities of the measured components and their relative phase and coherency relations. Several different methods to determine propagation characteristics using this information exist in the literature [*Means*, 1972; *McPherron et al.*, 1972; *Samson*, 1973; *Samson and Olson*, 1980]. All of them are based on the multidimensional spectral analysis of a single vector of field fluctuations, and as far as we know, all known practical applications of these methods concern the magnetic field vector. More recently, *Ladreiter et al.* [1995] developed a method to estimate the propagation parameters of radio waves from the electric field measurements using the singular value decomposition (SVD). Their technique is based on determination of parameters of a theoretical model for the results of the multidimensional spectral analysis, and uses the SVD to improve the minimization procedure.

[5] The multidimensional spectral analysis is the basis of the method we are going to discuss in the present paper. We will show that it is useful and easy to take into account all the information obtained from this analysis of either a single measured vector, or of the simultaneously measured magnetic and electric field data. Based on the SVD, we have developed a new method which is very easy to implement using SVD procedures accessible from numerical libraries. This new technique is essentially different from the method of *Ladreiter et al.* [1995] and the basic idea is presented for the magnetic field data in section 2. We will also show that the new method provides us with some other useful polarization parameters such as the ellipticity, planarity, and the direction of the polarization ellipse axes. Next, we will demonstrate that the method is easily extensible to simultaneously process the electric and magnetic fields (section 3), and that this approach allows us to obtain not only the fully defined wave vector direction, but also the wave number and electromagnetic planarity. Section 4 shows several examples of the analysis results for well defined simulated data, and, finally, section 5 presents an example of the analysis of natural VLF emissions in the high-altitude auroral region.