1. Time-distance: methods and results
Michael Thompson
University of Sheffield, U.K.

2. Time-distance helioseismology
Measures travel times of acoustic or surface gravity waves propagating between different surface points through the interior. The travel times depend on conditions, flow velocity and sound speed along the ray path:
Analysis proceeds by calculating cross-correlation of signal at different points on the surface:

3. Three generic steps Filter the data
Average the data (e.g. over an annulus and over a small central region)
Compute the cross-covariance (e.g. of the annular signal with the central signal)

4. Spatial averaging Choices of geometries Centre-annulus
… possibly divided into quadrants
Point to arc
Deep focussing
Point-to-point
Line-point

5. Choice of geometry as an inverse problem

6. Filtering Phase-speed filtering Filtering different modes
Frequency filtering
Choice of filters and filter parameters

7. T-D seismology around ARs
Courtesy of A. Kosovichev

8. Structure under ARs 10486 and 10488, October 31, 2003, 12:00 UT

9. Comparing old and new sunspots

12. Asymmetric cross-correlation near active regions

13. Mean travel-time
perturbation
E-W travel-time
perturbation
S-N travel-time
perturbation
Magnetogram
Amplitude
perturbation
E-W amplitude
asymmetry
S-N amplitude
asymmetry

14. Amplitude modulation in sunspots

15. Experiment with amplitude modulation

16. Aaron’s model for interaction of spatial amplitude modulation with phase-speed filtering

17. Conclusions
A multitude of choices of spatial averaging, filtering, inversion methods
Many issues – theoretical and observational – around ARs and sunspots
Modelling waves in magnetised plasma (analytical and numerical)
Amplitude suppression (may account for up to 40% of travel-time perturbation seen in sunspots)
Cross-correlation asymmetries
“Coffee-cup” behaviour under spots is a robust feature of many spots and ARs, though its interpretation is stil uncertain
Some systematic and possibly significant variation between old and new spots

18. Data products Standard data cubes that everyone can use Kernels
Intermediate products at all stages of analysis
Maps of sound-speed anomalies and flows

19. Challenges in local helioseismology
Better modelling of interaction of waves with magnetic fields and flows
Improving temporal and spatial resolution of the analyses – what are the fundamental limitations?
Pushing tomographic methods down as far as the base of the convection zone … or further … to study the tachocline, meridional circulation, etc.