Artificial

1
Artificial Physics-light Ring Data

• Rachel Howe,
• Irene Gonzalez-Hernandez, and Frank Hill

2
Roadmap

• Noise free power spectra, with and without
  uniform flow field
• Power spectra with realization noise
• Inverse transform to wave fields with realization
  noise.
• Projection effects
• Seeing

3
Noise-free power spectra

• Based on Frank Hills old code
• Lorentzian peaks
• 2arcsec/pixel, 60s cadence, dk3.338e-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 c2 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)
Narrow Rings
Wide Rings
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l-n slices
Narrow Rings
Wide Rings
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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
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Frequency differences from truth
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Widths from single power spectra
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Amplitudes from single power spectra
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Inferred Flows (wide rings)
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Inferred Flows (narrow rings)
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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

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Wavefield in action

• 256 frames of the time series
• Takes about 8 hours compute time for 64 patches.

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Flows from time series (narrow)
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Modes with consistently sensible widths in 8
patches
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Conclusions

• Power spectra work reasonably well.
• Widths need fine-tuning
• Something isnt right with the time series
  precision problems with FFTs?
• Need more computers!

20
Time Distance from Artificial Data

• Shukur Kholikov and Rachel Howe

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TD-test

• 128 ? 128 ? 2048 artificial time series
• Narrow-ring version, no flows
• Set does not contain lower-l information
• S. Kholikovs time distance code
• Fit for phase and envelope travel times.

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TDmore 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