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

2. Outline Simulated Data Holography Results 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
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 support NASA (NNG07EI5IC) NASA/Stanford/HMI project
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
support NASA (NNG07EI5IC) NASA/Stanford/HMI project

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

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