## 4. Power spectraThe next step of the data analysis was the computation of power spectra, or "diagnostic diagrams", for each of the 3D-arrays. The Fourier transform of the time-dependent velocity signal is defined as and is calculated as a discrete Fourier transform. The power spectrum is Since we have removed the solar rotation from the data, we can assume that the velocity signals do not have a preferred horizontal direction, and that, therefore, the power spectrum depends only on the horizontal wave number . The diagnostic diagrams are obtained by azimuthally averaging the power spectra in the -plane. The size of the investigated fields is 243 Mm 243 Mm on the Sun, about 1/3 of the solar radius, so the use of cartesian coordinates is justified. From the total duration ( s) and
the horizontal dimension ( Mm) we
have a frequency resolution of mHz
and a wave number resolution of
Mm Fig. 1 shows the -diagram corresponding to disk center. About a dozen modes are visible. The lowermost ridge corresponds to global surface waves (the f mode) with the dispersion relation with ms
© European Southern Observatory (ESO) 1999 Online publication: May 21, 1999 |