Tests of the Ring-Diagram Inversions

A. Kosovichev

Verification, testing and investigation of systematic effects are crucial for the HMI

success• Two approaches:

– Comparison of analysis results obtained by different local helioseismology methods

• Ring diagram analysis• Acoustic holography/imaging

– Using numerical simulation data• Wave propagation linearized MHD codes

– Local sunspot regions (K.Parchevsky)– Full-Sun sphere (T.Hartlep)

• Non-linear radiative MHD codes– MSU code (R.Stein)– NASA/Ames code (A.Wray)

Example: sound-speed structure below sunspots

Travel-time inversions

Born kernels Ray-path kernels

Couvidat et al (2006)

The controversies in data analysis procedures can be resolved by using

numerical simulation dataExample: phase-speed filtering is used for travel-time measurements at short travel distances to separate first- and second-bounce signals and improve S/N.

Problematic positive shifts

D=1 Mm (shallow) D=10 Mm (deep)

Testing of acoustic holography technique with phase-speed filtering revealed travel-time artifacts at short distances (Birch et al 2009)

Zhao et al (2009) repeated this test by using the standard time-distance technique with and without the phase-speed filtering and did not find such artifacts.They found a reasonably good agreement with the ray-theory predictions.

Blind tests have been done for both time-distance and holography codes using more complicated models.

Sunspot structure from Hinode (Zhao et al 2010)

Measurements of travel times without phase-speed filtering from Hinode data

Comparison time-distance and ring-diagram inversionsBasu et al (2004) Bogart et al (2008)

Comparison of ring-diagram and time-distance inversions by Gizon et al (2009) using the CT ring-diagram code and a time-

distance code (S.Zharkov)

Ring-diagram fitting formula (CT)(Basu, Antia, and Bogart, 2004)

pck

1. Specify a sound-speed sunspot model.

2. Assume that this perturbation is spherically symmetric.

3. Calculate the frequency shifts by using the variational principle, and perturbed frequencies.

4. Fit to the frequencies of the standard solar model and the model with a sunspot-type perturbations

5. Calculate the frequency difference and run the structure inversion code (OLA), assuming 0.1% measurement error.

6. Compare inversions with the initial sunspot model.

Test of CT fitting formula

pck

Frequency variations

Test for AR 9787

• Inversion of Deborah Haber’s measurements of ring-diagram frequencies (the CO fitting formula).

• Days 120-128 of 2002; one frequency measurement per day.

• Spatial grid: 15x15 with 7.5 degrees step in latitude and longitude.

• The total number of frequency sets: 1511• Inversion relative to the solar model S by the OLA

method including the surface term.

Summary• The CT ring-diagram fitting formula used by Basu et al

(2004), Bogart et al (2008) and Gizon et al. (2009) may lead to large systematic errors.

• The sound-speed inversion results obtained from the CO ring-diagram frequencies for AR 9787 are qualitatively different from the results obtained from the CT ring-diagram fitting, and are more in line with the time-distance inversion results.

• Verification and testing of the local helioseismology techniques using numerical MHD simulation data is critical for development of the HMI data analysis pipeline.

• It is important to develop of methods and standards for intercomparison of the various local techniques.