Holography Applied to Artificial Data

1. Holography Applied to Artificial Data A. Birch D. Braun NWRA, CoRA Division S. Hanasoge (Stanford)

2. Outline • Simulated Data • Background models • Power spectra • Holography Results • Frequency dependence • Positive travel-time shifts

3. Numerical Simulations • Code by Shravan Hanasoge (Hanasoge et al. 2007) • Propagate linear waves through arbitrary backgrounds (restrictions: must be convectively stable) • 256x256x300 grid (200 Mm^2 x 36 Mm)

4. Background Models Sound Speed (cm/s) Stabalized S Polytrope + iso Model S Density (cgs) Acoustic Cutoff (mHz)

5. Power Spectra: Stabilized Model S

6. Power Spectra Model MDI

7. Sound-Speed Perturbations Fan, Braun, & Chou (1995) for the sound-speed perturbation Use epsilon=0.1. For the “shallow” case: D=1 Mm For the “deep” case: D=10 Mm In both cases: R=20 Mm Note that epsilon=1, D=1 was a good match to Hankel analysis phase shifts

8. Travel-Time Shifts Shallow Deep

9. Frequency Dependence Shallow, D=1 Mm Deep, D=10 Mm 3 mHz 4 mHz 5 mHz

10. Polytrope with isothermal atmo. Shallow, D=1 Mm Deep, D=10 Mm 3 mHz 4 mHz 5 mHz

11. Positive Travel-Time Shifts (?) (Braun & Birch 2007, Sol Phys. submitted)

12. Compare D=1 with MDI observations 3 mHz 4 mHz 5 mHz

13. Conclusions • Frequency dependence is a useful constraint on models • In simple models, a shallow sound-speed perturbation produces something like the observed frequency dependence • Increase in sound-speed can lead to increased travel times ! • Lots of work to do: modeling & theory supportNASA (NNG07EI5IC)NASA/Stanford/HMI project

14. Power Spectra Sun (MDI Full Disk) Simulation (Polytrope)

15. Positive Travel-Time Shifts Ridge-Like Filter Phase-Speed Filter