Spectral method of global minimum (MGM) and its application to problems of heliospheric and planetary physics

A method of spectral analysis called the method of global minimum (MGM) based on the best presentation (in the sense of minimal squares) of a given time set as a sum of sinusoids with frequencies, amplitudes and phases, which have to be determined is presented. It is shown that the method self-consistently selects from data sets polynomial trends, describes nonstationary processes, permits the investigation of data sets with gaps and has a high accuracy of the definition of the periods of harmonical oscillation. MGM allows periods to be singled out which are longer than the input data set. The formulae for an estimate of errors are given. Results of the MGM spectral analyses of the Phobos-2 magnetic field data are presented. Magnetic field data measured near Mars at circular orbits in 1989 are used. The normalized mean square error of the fitting, in the least-squares sense, of the model sine waves to the tail data Δη = 0.384%. Spectral peaks (for the modulus of the magnetic vector) are found for periods from 81.3 ± 0.9, 12.02 ± 0.04, 6.47 ± 0.02, and 4.09 ± 0.01 d down to 24.44 ± 0.03 h in that magnetic data which were taken in the Martian magnetic tail. These periods are interpreted as being related to the solar processes (which was reported earlier from solar flare observations), and as even harmonics of solar rotation period and Martian rotation period.