1. Artificial ‘Physics-light’ Ring Data Rachel Howe, Irene Gonzalez-Hernandez, and Frank Hill

2. Roadmap 1.Noise free power spectra, with and without uniform flow field 2.Power spectra with realization noise 3.Inverse transform to wave fields with realization noise. 4.Projection effects 5.Seeing

3. Noise-free power spectra Based on Frank Hill’s old code Lorentzian peaks 2arcsec/pixel, 60s cadence,  k=3.338e-5 128  128  2048 power spec. 0  n  11, 100  l  1440 Kernels from model S to put in flows Widths and amplitudes based on simple model Second attempt with reduced widths

4. Noisy Power Spectra Add two normally-distributed pseudo-random numbers in quadrature, multiply by power spectrum (to give   2d.o.f. statistics). Both clean and noisy spectra, with and without a flow field, are available as FITS files (67Mb) Realization noise only, no instrumental or ‘background’.

5. Rings at bin 500/2048 (4mHz) Wide Rings Narrow Rings

6. l- slices Wide Rings Narrow Rings

7. Fitting/Inversion Tests Power spectra were fitted with the ‘doglegfit’ code used for the real data. RLS inversions, as for real data.

8. Fit results – frequencies Wide Narrow

9. Frequency differences from ‘truth’

10. Widths from single power spectra

11. Amplitudes from single power spectra

12. Inferred Flows (wide rings)

13. Inferred Flows (narrow rings)

14. Thoughts on results so far Narrower rings give fewer successful fits, but better-quality ones. Narrow rings are probably too narrow to be realistic. Effects of error correlations evident in inversions of noisy results.

15. Noisy Wave Field NB – un-noisy wave fields no good, need random phases to make it work. Make 1024  1024  2048 power spectrum, one layer at a time. Make real and imaginary parts by multiplying spectrum by Gaussian random numbers 2 Fourier transforms in space, store spatial transforms. Make Hermitian and do transform in time Save as 128  128  2048 FITS files (64 off) – 134Mb each, rudimentary headers

16. Wavefield in action 256 frames of the time series Takes about 8 hours compute time for 64 patches.

17. Flows from time series (narrow)

18. Modes with consistently ‘sensible’ widths in 8 patches

19. Conclusions Power spectra work reasonably well. Widths need fine-tuning Something isn’t right with the time series – precision problems with FFTs? Need more computers!

20. Time Distance from Artificial Data Shukur Kholikov and Rachel Howe

21. TD-test 128  128  2048 artificial time series Narrow-ring version, no flows Set does not contain lower-l information S. Kholikov’s time distance code Fit for ‘phase’ and ‘envelope’ travel times.

22. TD—more details Cross-correlation function of artificial data computed for the angular distance [1.1, 3.5]. Then Gabor-fitting parameters obtained to compare travel times with GONG data. Only one realization of artificial data used (2048 min) from 15x15 region. So, using bigger region and more realizations could smooth envelope travel time curve too. Also, I found that correlation amplitude in case of artificial data is little different from real observations which can come from power distribution used to simulate artificial power spectrum.

23. Time-distance curve Phase Envelope