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 data Example: phase-speed filtering is used for travel-time measurements at short travel distances to separate firstand second-bounce signals and improve S/N.
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) Zhao et al (2009) repeated this test
by using the standard timedistance 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 timedistance 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 inversions Basu 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 timedistance code (S.Zharkov)
Ring-diagram fitting formula (CT) (Basu, Antia, and Bogart, 2004) ck
p Test of CT fitting formula
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. p 4. Fit ck 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. Frequency variations
Test for AR 9787 Inversion of Deborah Habers 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
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