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A Test of the Ring-Diagram Fitting Formula

A Test of the Ring-Diagram Fitting Formula. A. Kosovichev. Verification, testing and investigation of systematic effects are crucial for the HMI success. Two approaches: Comparison with other local helioseismology methods Ring diagram analysis Acoustic holography/imaging

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A Test of the Ring-Diagram Fitting Formula

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  1. A Test of the Ring-Diagram Fitting Formula A. Kosovichev

  2. Verification, testing and investigation of systematic effects are crucial for the HMI success • Two approaches: • Comparison with other 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)

  3. Example: sound-speed structure below sunspots Travel-time inversions Born kernels Ray-path kernels Couvidat et al (2006)

  4. The controversies in data analysis procedures can be resolved by using numerical simulation data Example: phase-speed filtering is used for travel-time measurements at short travel distances to separate first- and second-bounce signals and improve S/N.

  5. Testing of acoustic holography technique with phase-speed filtering revealed travel-time artifacts at short distances (Birch et al 2009) Problematic positive shifts D=1 Mm (shallow) D=10 Mm (deep)

  6. 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 are being done for more complicated models.

  7. Comparison with ring-diagram inversions Basu et al (2004) Bogart et al (2008)

  8. Comparison of ring-diagram and time-distance inversions by Gizon et al (2009) using the same ring-diagram code but a different time-distance code

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

  10. Test • Specify a sound-speed sunspot model. • Assume that this perturbation is spherically symmetric. • Calculate the frequency shifts by using the variational principle, and perturbed frequencies. • Fit to the frequencies of the standard solar model and the model with a sunspot-type perturbations • Calculate the frequency difference and run the structure inversion code (OLA), assuming 0.1% measurement error. • Compare inversions with the initial sunspot model.

  11. Frequency variations

  12. Sunspot model (T.Hartlep)

  13. CT ring fit True values

  14. Summary • Verification and testing of the local helioseismology techniques using numerical 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. • 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.

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