Multi-Ridge Fitting for Ring-Diagram Helioseismology

Abstract

Inferences of sub-surface flow velocities using local domain ring-diagram helioseismology depend on measuring the frequency splittings of oscillation modes seen in acoustic power spectra. Current methods for making these measurements utilize maximum-likelihood fitting techniques to match a model of modal power to the spectra. The model typically describes a single oscillation mode, and each mode in a given power spectrum is fit independently. We present a new method that produces measurements with greater reliability and accuracy by fitting multiple modes simultaneously. We demonstrate how this method permits measurements of sub-surface flows deeper into the Sun while providing higher uniformity in data coverage and velocity response closer to the limb of the solar disk. While the previous fitting method performs better for some measurements of low-phase-speed modes, we find this new method to be particularly useful for high phase-speed modes and small spatial areas.

An improved multi-ridge fitting method for ring-diagram helioseismic analysis

“…In the updated code, we use a least-squares fitting to fit the logarithm of the model power to the logarithm of the remapped and smoothed power. Following Greer et al (2014), the fitting is carried out independently at each horizontal wavenumber k. As the amount of smoothing is increased, the probability distribution function (PDF) of the power, as well as its logarithm, approaches a normal distribution (see Appendix B.4 for more details), and it is therefore appropriate to use a least-squares fit . The logarithm of the smoothed power has the convenient property that the variance of the logarithm of power (σ N in Eq.…”

“…Methods. We updated the multi-ridge fitting code developed by Greer et al (2014, Sol. Phys., 289, 2823 to solve several problems we identified through our inspection of the code.…”

“…Sun: helioseismology -Methods: data analysis Schou et al 2012) onboard the Solar Dynamics Observatory (SDO; Pesnell et al 2012) are automatically computed by the SDO/HMI ring-diagram pipeline (Bogart et al 2011a,b) on a daily basis since the SDO launch in 2010.The HMI ring pipeline codes separately fit each single ridge (single radial order n) in the power in slices at constant horizontal wavenumber or slices in temporal frequency. Greer et al (2014) developed an alternative approach based on simultaneously fitting multiple ridges (multiple radial orders) at each horizontal wavenumber. Greer et al (2015) introduced another in-Article number, page 1 of 18…”

Helioseismic Imaging of Supergranulation Throughout the Sun’s Near-Surface Shear Layer

“…From the power spectrum of each analysis tile, the set of Doppler shifts, u x k; n i ( ), is measured by using the Multi-Ridge Fitting code presented by Greer et al (2014) and detailed extensively in Greer (2015). With this procedure we measure modes with radial order n ranging from 0 to 7 and with horizontal wavenumbers k spanning k 0.…”

Helioseismic Measurements of the Rossby Number in the Sun’s Near-Surface Shear Layer

“…For each tile, a 3D data cube x y t , , ( ) of Dopplergram measurements is constructed by tracking that tile across the solar disk for 25.6 hr at the rotation rate of Snodgrass (1984). We use the Multi-Ridge Fitting (MRF) code presented by Greer et al (2014) to measure 220 different f and p modes from each data cube. The mode set ranges over radial order Î n 0, For this study we have analyzed 11 distinct analysis periods of Dopplergram data from HMI Schou et al 2012) on board the Solar Dynamics Observatory (SDO).…”