Journal cover Journal topic
Annales Geophysicae An open-access journal of the European Geosciences Union
Ann. Geophys., 35, 639-644, 2017
https://doi.org/10.5194/angeo-35-639-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
ANGEO Communicates
11 May 2017
Minimum variance projection for direct measurements of power-law spectra in the wavenumber domain
Yasuhito Narita1,2,3, Yoshihiro Nishimura4, and Tohru Hada4,5 1Space Research Institute, Austrian Academy of Sciences, Schmiedlstr. 6, 8042 Graz, Austria
2Institut für Geophysik und extraterrestrische Physik, Technische Universität Braunschweig, Mendelssohnstr. 3, 38106 Braunschweig, Germany
3Institute of Physics, University of Graz, Universitätsplatz 5, 8010 Graz, Austria
4Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen 6-1, Kasuga, Fukuoka 816-8580, Japan
5International Center for Space Weather Science and Education, Kyushu University, Motooka, Nishi-Ku, Fukuoka 819-0395, Japan
Abstract. Minimum variance projection is widely used in geophysical and space plasma measurements to identify the wave propagation direction and the wavenumber of the wave fields. The advantage of the minimum variance projection is its ability to estimate the energy spectra directly in the wavenumber domain using only a limited number of spatial samplings. While the minimum variance projection is constructed for discrete signals in the data, we find that the minimum variance projection can reasonably reproduce the spectral slope of the power-law spectrum if the data represent continuous power-law signals. The spectral slope study using the minimum variance projection is tested against synthetic random data with a power-law spectrum. The method is applicable even for a small number of spatial samplings. Conversely, the spatial aliasing causes a flattening of the spectrum.

Citation: Narita, Y., Nishimura, Y., and Hada, T.: Minimum variance projection for direct measurements of power-law spectra in the wavenumber domain, Ann. Geophys., 35, 639-644, https://doi.org/10.5194/angeo-35-639-2017, 2017.
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Short summary
An algorithm is proposed to estimate the spectral index of the turbulence energy spectrum directly in the wavenumber domain using multiple-sensor-array data. In contrast to the conventional method using time series data and Fourier transform of the fluctuation energy onto the frequency domain, the proposed algorithm does not require the assumption of Taylor's frozen inflow hypothesis, enabling direct comparison of the spectra in the wavenumber domain with various theoretical predictions.
An algorithm is proposed to estimate the spectral index of the turbulence energy spectrum...
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