Conclusions

Group-velocity tomography

Figure 1: Time slice of Doppler data filtered for surface gravity wave energy. Cross-correlations are computed between all data and each pixel located in a ring with a certain radius, surrounding the sunspot. Black arrows indicate the two azimuths of averaging. The red circle indicates the approximate boundary of the sunspot.

Data

F-Mode Heliotomography

Sjoerd de Ridder1, Junwei Zhao2

(1) formerly at: University of Science and Technology of China, Geophysics and Planetary Sciences, Hefei, China, (2) Stanford University, W. W. Hansen Experimental Physics Laboratory, Stanford, CA, United States

Summary

The Doppler data was recorded by the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO) satellite from August 1st to 5th, 2010. The data varies considerably between sunspots and quiet portions of the sun. We removed a running alpha-mean from the data and applied a soft clip to deal with data glitches. The recordings contain energy of both flow and waves (see Poster S43A-4528 in the next booth), We used an fk-filter to isolate the energy of the f-mode.

References

Acknowledgements

Thompson, M. J. (2004). Helioseismology and the Sun's interior. Astronomy & Geophysics, 45 (4), 4-21.Junwei, Z., A.G. Kosovichev, and S. Ilonidis (2011). Toward Waveform Heliotomography: Observing Interactions of Helioseismic Waves with a Sunspot, Solar Physics 268, 429–442.Kosovichev, A. G., T.L. Duvall Jr., A.C. Birch, L. Gizon, P.H. Scherrer, and J. Zhao (2000). Heliotomography of the outer layers of the Sun, Proceedings of the SOHO 10/GONG 2000 Workshop: Helio- and asteroseismology at the dawn of the millennium, 2-6 October 2000, Santa Cruz de Tenerife, Tenerife, Spain.

Sjoerd thanks the Chinese Academy of Science for financial support through the Fellowship for Young International Scientists, and Sjoerd thanks the Stanford Exploration Project for computational resources during a visit to Stanford in July and August of 2014.

Apparent group velocity maps reveal that the f-mode velocity increases inside the sunspot, more so at higher frequencies then at lower frequencies. At the higher frequencies the apparent group velocity may different considerably from the inherent group velocity because the primary and secondary surface waves interfere to create an envelope function with a spuriously flat moveout. Although

Time-distance seismology is a popular tool to probe the sun’s interior (Thompson, 2004; Kosovichev et al. (2000)). We investigated 5 days of Doppler measurements geo-tracked for a sunspot. The data is cross -correlated to create time-distance impulse responses of wave propagation in the plasma. We focused on imaging the f-mode, which is separated from the other modes by fk-filtering. The f-mode is a dispersive surface-gravity wave.

Whereas terrestrial-seismology relies on increasing high signal-to-noise ratio (SNR) by cross-correlating long-time series, helioseismology relies on stacking over geometrically similar virtual sources. We assume there are two symmetries in the geometry of virtual sources around a sunspot. The first is a radial symmetry centered at the sunspot. The second is a radial symmetry of propagation around each virtual source. Because we are interested in the effect of sunspots on wave-propagation we keep the averaging along the second symmetry axis to a minimum, and rely almost completely on averaging each virtual source with equal distance from the sunspot.

We observe apparent speedup of the f-mode as it propagates through the sunspot (confirming results of Zhao et al. (2007). When we filter the waves for higher frequencies, we even observe a secondary f-mode arising ahead of the primary F-mode, when it passes through the sunspot. This can be an artifact of the smoothing along azimuth around the source, or perhaps a more complicated interaction with the P-modes.

Ripples remaining in the wave fronts after averaging along azimuth centered around the source point complicated applying an Eikonal tomography method.

In a time-radial distance slice we picked group traveltimes by picking the peak of the envelope after a narrow bandpass filter. We performed a straight ray tomography to image maps of apparent group velocity in a radial geometry with the sunspot at the center.

Figure 2 (above): Eight time-slices from an impulse response generated at a radius of 35 mM, t=0, 1125, 2250, 3375, 4500, 5625, 6750, 7875 seconds (Δt=18m and 45 s).

Figure 3 (below): Left panel is a time-distance gather as if there is no sunspot (extracted from Figure 2 for radii larger then 35mM). Right panel is is a time-distance gather showing the interaction with a sunspot (extracted from Figure 2 for radii smaller then 35mM). Blue lines indicate the approximate location of the sunspot.

Averaging over 360°

Averaging over 10°

Sunspot

Impulse location

Group velocity profiles

Figure 4 (above): Envelope gathers after bandpass around 2.25mHz, from a source at 15mM , 25mM and 35mM (top to bottom). Left quiet reference sun; right; sunspot interaction. Black dots and red dashes are the measured and modeled traveltimes.

Gathers at a radial distance of 10mM, 15mM, 20mM, 25mM, 30mM, and 35mM were input to a straight ray tomography kernel. Group traveltimes were picked as the peak of the envelope function of the bandpass filtered gathers. The forward kernel is a simple integration operator with the length through each grid-cell. Grid-cells were 1mM wide. In addition to fitting the picked traveltimes. In addition to fitting the traveltimes, we posed a smoothness constraint on the model using a second-order derivative operator. We performed this procedure with bandpass filters for 2.00mHz, 2.25mHz, 2.50mHz, 2.75mHz and 3.00mHz.

Cross-correlations

Figure 6: Group-velocity profiles for five frequencies.

Figure 5 (above): Envelope gathers after bandpass around 2.75mHz, from a source at 15mM , 25mM and 35mM (top to bottom). Left quiet reference sun; right; sunspot interaction. Black dots and red dashes are the measured and modeled traveltimes.

2.00mHz 2.25mHz 2.50mHz

3.00mHz2.75mHz

The sunspot region is characterized by increasing velocities. The increase is much larger for group velocities at higher frequencies then at lower frequencies. We expect an almost homogeneous velocity for the profile of the quiet reference sun, additionally there is some anomalous structure outside the sunspot region. This may be an effect of actually structure outside the sunspot, that despite the averaging, is not entirely negligible. But it can also be because we have only 6 ‘impulse responses’ to image. The anomalous structure coincides with the region of least ray coverage.

Frequency (mHz) 2.00 2.25 2.50 2.75 3.00

Group Velocity (km/s) 8.93 8.45 8.00 7.53 7.13

Table 1: Averaged group-velocity for the quiet reference sun (a pseudo group-velocity dispersion curve).