Artificial ‘Physics-light’ Ring Data

Rachel Howe,

Irene Gonzalez-Hernandez, and

Frank Hill

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

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

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’.

Rings at bin 500/2048 (4mHz)

Wide Rings Narrow Rings

l- slices

Wide Rings Narrow Rings

Fitting/Inversion Tests

• Power spectra were fitted with the ‘doglegfit’ code used for the real data.

• RLS inversions, as for real data.

Fit results – frequencies

WideWide Narrow

Frequency differences from ‘truth’

Widths from single power spectra

Amplitudes from single power spectra

Inferred Flows (wide rings)

Inferred Flows (narrow rings)

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.

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

Wavefield in action

• 256 frames of the time series

• Takes about 8 hours compute time for 64 patches.

Flows from time series (narrow)

Modes with consistently ‘sensible’ widths in 8 patches

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!

Time Distance from Artificial Data

Shukur Kholikov and Rachel Howe

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.

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.

Time-distance curve

Phase

Envelope