1. holographic measurements of simulated flows
Doug Braun and Aaron Birch
using 48x48x20 Mm simulations provided by R. Stein, Å. Nordlund, D. Bensen, D. Georgobiani
NorthWest Research Associates, Inc.
Colorado Research Associates Division

2. conclusions
near-surface helioseismic holography (hh) signatures are clearly correlated with mean horizontal flows – hh “works”
hh signatures focused below surface have ~equal contributions from surface (<2Mm) and below; both decrease rapidly with depth:
surface contribution decreases due to cancellation of signals from neighboring convective cells (previously suspected and modeled in solar SG) – can cause “reversal”-like signature
subsurface contributions decrease with ratio of flow/sound-speed
assessment of noise with forward models:
flows like these can only be detected (at resolutions of ~6Mm) down to depths ~5-7 Mm
deeper assessment of solar flows (like these) may require combining many supergranules
these types of simulations are critical to helioseismology
2006 November 7
LoHCo Meeting, Boulder

3. convective flows “visible” to p modes (8 hr duration)
2006 November 7
LoHCo Meeting, Boulder

4. depth variations of mean (8-hr) flowsx x y y
2006 November 7
LoHCo Meeting, Boulder

5. “reversal” at depth > 12 Mm
slope: velocities over near-surface values
2006 November 7
LoHCo Meeting, Boulder

6. helioseismic holography (hh) of flows
“lateral vantage” N E W S
H- = ingression
H+ = egression
2006 November 7
LoHCo Meeting, Boulder

7. hh of flows (continued)
in temporal Fourier domain, correlations between egression and ingression are simply a product, e.g. the E-W correlation is:
the argument of the correlation averaged over a frequency bandpass is a phase shift:
the phase difference between E-W and W-E is sensitive to a flow in x direction :
this phase difference is equivalent to a travel-time perturbation:
2006 November 7
LoHCo Meeting, Boulder

8. power spectra
2006 November 7
LoHCo Meeting, Boulder

9. EW hh travel-time maps at different frequencies
focus depth = 0.7 Mm
3 mHz
4 mHz
mean
5 mHz
6 mHz
mean velocity Vx (0.7 Mm)
2006 November 7
LoHCo Meeting, Boulder

10. hh “calibrated” flows
calibration constant determined by introducing a known tracking rate
different calibration for each frequency bandpass
average 3,4,5, and 6 mHz bandpasses
resulting “velocities” represent weighted average over depth
2006 November 7
LoHCo Meeting, Boulder

11. hh calibrated flows, focus = 0.7 Mm
8-hr mean flows at 0.7 Mm
(smoothed to FWHM = 6 Mm)
hh calibrated flows, focus = 0.7 Mm Vx Ūx X Vy Ūy y
2006 November 7
LoHCo Meeting, Boulder

12. hh travel-time maps vs. focus depth
travel-times, focus = 0.7 Mm
focus = 0.7 – 7 Mm EW NS
2006 November 7
LoHCo Meeting, Boulder

13. decrease of hh travel-time signatures
ratio of signatures to surface values fall-off faster than actual flow speed ratios
effects of lower boundary impede measurements at and below 8 Mm
possible reversal in NS signature below 6 Mm
slope: travel times over near-surface values
2006 November 7
LoHCo Meeting, Boulder

14. reversal of supergranular hh signatures
div vh pupil
v ~ e-z/zo cos(z/z1) zo =2.5 Mm.
red crosses : no return flow (z1 ).
green circles: z1= 5 Mm
black diamonds: z1= 15 Mm.
(Braun, Birch, & Lindsey 2004 SOHO/GONG Proceedings)
2006 November 7
LoHCo Meeting, Boulder

15. observed vs. forward-modeled hh travel times
depth = 3Mm
model
obs
obs-model
3 mHz
r.m.s. = 10 s
3-6 mHz
r.m.s = 5 s
2006 November 7
LoHCo Meeting, Boulder

16. assessment of relative depth contributions
depth = 3 Mm
< 2 Mm
> 2 Mm
total
2006 November 7
LoHCo Meeting, Boulder

17. depth = 5 Mm < 2 Mm > 2 Mm total 2006 November 7
LoHCo Meeting, Boulder

18. depth = 7 Mm < 2 Mm > 2 Mm total 2006 November 7
LoHCo Meeting, Boulder

19. signal-to-noise 0.7 Mm 22 s 4.8 8.1 3 Mm 7.8 s 1.7 2.9 5 Mm 5.1 s 1.1
assumes these flows are typical of Sun
assumes smearing of ~6Mm; can sacrifice spatial resolution to increase S/N
assumes only 3-5 mHz for Sun (not 3-6 mHz)
assumes good assessment of shallower contributions
depth
r.m.s signal (“subsurface” only for > 2 Mm)
S/N (8 hr)
S/N (24 hr)
0.7 Mm
22 s
4.8
8.1
3 Mm
7.8 s
1.7
2.9
5 Mm
5.1 s
1.1
1.9
7 Mm
3.5 s
0.8
1.3
2006 November 7
LoHCo Meeting, Boulder

20. conclusions
near-surface helioseismic holography (hh) signatures are clearly correlated with mean horizontal flows – hh “works”
hh signatures focused below surface have ~equal contributions from surface (<2Mm) and below; both decrease rapidly with depth:
surface contribution decreases due to cancellation of signals from neighboring convective cells (previously suspected and modeled in solar SG) – can cause “reversal”-like signature
subsurface contributions decrease with ratio of flow/sound-speed
assessment of noise with forward models:
flows like these can only be detected (at resolutions of ~6Mm) down to depths ~5-7 Mm
deeper assessment of solar flows (like these) may require combining many supergranules
these types of simulations are critical to helioseismology
2006 November 7
LoHCo Meeting, Boulder