Singular value decomposition methods for wave propagation analysis

Abstract

[1] We describe several newly developed methods for propagation analysis of electromagnetic plasma waves. We make use of singular value decomposition (SVD) technique and we determine the wave vector direction, ellipticity and directions of axes of the polarization ellipse, wave refractive index, transfer function of electric antennas, estimators of the planarity of polarization, and electromagnetic planarity. Simulations of Z-mode waves, which simultaneously propagate with different wave vectors, indicate that the SVD methods give reasonable results even if the assumption on the presence of a single plane wave is invalid. Simulations of whistler mode waves show that these methods can be used to recognize cases when the waves simultaneously propagate with wave vectors in two opposite hemispheres. Finally, we show an example of analysis of natural whistler mode and Z-mode emissions measured in the high-altitude auroral region by the MEMO experiment onboard the INTERBALL spacecraft.

Systematic analysis of equatorial noise below the lower hybrid frequency

“…We use the singular value decomposition technique from Eq. (13) of Santolík et al (2003), defining L p =w 2 /w 1 , where w 1 and w 2 are the two largest singular values of the magnetic spectral matrix. In the idealized case of exactly planar polarization, the result represents the ratio of the lengths of the minor and major axes of the polarization ellipse.…”

“…Figure 1d represents the planarity F of the polarization of magnetic field fluctuations from Eq. (12) of Santolík et al (2003). It is defined as F =1− √ w 3 / √ w 1 , where w 1 and w 3 are, respectively, the maximum and the minimum singular values of the magnetic spectral matrix.…”

Whistler mode waves at magnetotail dipolarization fronts

“…Although we present only data from C1 in Figure 1, the same wave structure was observed by all four SC in this specific event; the characteristic spacecraft separation was 1100 km in GSM-X. The spectra in Figures 1f-1i are obtained from the STAFF SA instrument and are calculated onboard Cluster using the PRASSADCO algorithm [Santolík, 2000;Santolík et al, 2003]. …”

“…In this letter we present statistics of whistlers in relation to DFs observed by Cluster [Escoubet et al, 1997] [Balogh et al, 2001], (b) electron density from PEACE [Owen et al, 2001], (c) ion velocity (X GSM) from both CIS [Rème et al, 2001] and v E×B using Electric Fields and Waves (EFW) [Gustafsson et al, 2001], (d) electron differential energy flux, (e) pitch angle distribution for energies of 3-10 keV, (f ) power spectral density of the wave magnetic field, (g) the degree of polarization, (h) the ellipticity, and (i) the wave angle with respect to the magnetic field. Data for Figures 1f-1i are calculated from spectral matrices produced by onboard STAFF Spectrum Analyzer [Cornilleau-Wehrlin et al, 2003], using the PRASSADCO program [Santolík, 2000;Santolík et al, 2003]. The black lines in Figures 1f-1i show f ce and 0.5 f ce , respectively.…”

Cluster observations of mid-latitude hiss near the plasmapause

“…5 display STAFF data and related data products from 60 Hz to 4 kHz, in logarithmic scale: (b) electric field spectrogram, (c) magnetic field spectrogram, (d) polarization planarity F , (e) parallel component of the Poynting vector, normalized by its standard variation, (f) polarization ellipticity L and (g) angle between the wave normal direction and the DC magnetic field. The calculations of the last four quantities are based on methods detailed in the following papers and references therein (Santolík et al, 2001(Santolík et al, , 2003.…”