Junwei Zhao1, Dominick Hing2, Ruizhu Chen1, & Shea Hess Webber1
1. W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305-4085
2. Department of Physics, Stanford University, Stanford, CA 94305-4060
Being able to monitor active regions (ARs) on the far side of the Sun is useful to space weather forecasting and solar wind modeling. Using helioseismic holography method, Lindsey & Braun demonstrated that local helioseismology method is capable of imaging the Sun’s far-side ARs using only the near-side Doppler observations. Later, Zhao and Ilonidis et al.  developed 3-skip, 4-skip, and 5-skip time-distance helioseismic methods, greatly enhancing the signal-to-noise ratio and the reliability of the acoustic far-side AR images.
Figure 1 shows measurement schemes for the existing time-distance method. There are 1×2-scheme for 3-skip waves, 2×2- and 1×3-schemes for 4-skip waves, and 2×3-scheme for 5-skip waves. Considering that 2×4-scheme of 6-skip waves has a same surface geometry with the 1×2-scheme of 3-skip waves, 3×3-scheme of 6-skip waves and 4×4-scheme for 8-skip waves have a same surface geometry with the 2×2-scheme of 4-skip waves, and 2×6-scheme for 8-skip waves has a same surface geometry with the 1×3-scheme of 4-skip waves, we can greatly expand our calculation of far-side images with little code-developing effort. Meanwhile, considering that for waves experiencing more than 3 skips, there are two regimes of waves that can be used, one with total traveling distance greater than 360°, and the other less than 360°. With the expansion of number of wave skips and by including both distance regimes greater and less than 360°, we are able to monitor a total of 14 sets of far-side images for a given time.
Figure 1| Measurement schemes, viewed as great-circle slices through far-side target points, for (a) 1×2-scheme for 3-skip waves, (b) 2×2-scheme for 4-skip waves, (c) 1×3-scheme for 4-skip waves, and (d) 2×3-scheme for 5-skip waves.
None of the 14 sets of far-side images cover the entire far side of the Sun, and we need to combine these images. Depending on the area each image covers and the quality of these images, we use a weighted average to combine all the far-side images and form one final far-side image. Figure 2b shows one example of the far-side image. For a comparison, Figure 2d shows one EUV 304Å image of the Sun’s far side, observed by STEREO spacecraft. Dark patches in the acoustic far-side images correspond to ARs, formed due to the deficit in total acoustic travel times. One can also see some positive patches near the high-latitude regions; however, these positive patches are due to the systematic center-to-limb effect in the time-distance helioseismic measurements, and are believed not corresponding to any real solar features.
Figure 2| Comparison of near-side and far-side images taken at or near 00:00 UT of 2014 March 13. (a) SDO/HMI-observed near-side magnetic field. (b) Helioseismic acoustic far-side image. (c) SDO/AIA-observed near-side 304 Å image. (d) STEREO/EUVI-observed far-side 304 Å image.
Compared with the existing helioseismic holography method, our new method has clear advantage in mapping the ARs that are close to both of the far-side limbs, either before the ARs rotate into the Earth’s view or after the ARs just rotate into the far side. Moreover, as the example shown in Figure 3, our new method is also believed to be more sensitive in capturing newly emerged ARs. According to the STEREO observations, this far-side AR emerged on February 11. Our new time-distance method is able to unambiguously see this new AR on February 14. Although it is already 3 days after the start of the emergence, it is still 2 days ahead of the first unambiguous detection of the helioseismic holography method.
Figure 3| Comparison of helioseismic holography far-side image, our new time–distance far-side image, and the EUV images taken at 00:00 UT, 2014 February 14. Top panel: synchronic chart of helioseismic holography far-side image (color) and SDO/HMI near-side magnetic field (black and white); middle panel: similar chart composed of time–distance far-side image (color) and near-side magnetic field; bottom panel: combination of simultaneous 304 Å observations of SDO/AIA and both STEREO spacecraft.
With both the helioseismic holography method and our new time-distance helioseismology method available to simultaneously image the Sun’s far side, we can monitor the Sun’s far-side ARs with higher confidence and better reliability.
For more details of this work, please refer to our recent publication Ref. .
 Lindsey, C., & Braun, D. C. 2000, Science, 287, 1799
 Zhao, J. 2007, ApJ Lett., 664, L139
 Ilonidis, S., Zhao, J., & Hartlep, T. 2009, Solar Phys., 258, 181
 Zhao, J., Hing, D., Chen, R., & Hess Webber, S. 2019, ApJ, 887, 216