Elena García Broock^{1, 2}, T. Felipe^{1, 2}, and A. Asensio Ramos^{1, 2}

1 Instituto de Astrofísica de Canarias, 38205, C/ Vía Láctea, s/n, La Laguna, Tenerife, Spain

2 Departamento de Astrofísica, Universidad de La Laguna, 38205, La Laguna, Tenerife, Spain

The standard helioseismic methods for far-side activity detection use data from a surface region on the near side of the Sun to infer the properties of a region on the far side. The presence of strong far-side active regions is routinely detected using Stanford’s Strong-Active-Region Discriminator (SARD) on far-side phase-shift maps processed with five days of HMI Doppler data. The method searches for far-side regions that imprint a phase-shift greater than 0.085 rad (4 s time-shift) on waves with a chosen range of frequencies and calculates their corresponding seismic strength (S), which is given by the integrated negative phase-shift over the area of the region. A signal is classified as a reliable detection if the seismic strength (S) exceeds a threshold of 400 μHem rad^{[1]}. This technique is limited to strong active regions due to the limited signal-to-noise. The neural network Farnet^{[2]} was developed to improve that approach. We tested the network method and compared its results with those obtained from the standard criteria to determine the presence of far-side active region in seismic maps computed with phase-sensitive helioseismic holography^{[3]}. We found that the network greatly improves the detections.

FarNet^{[2]} is a fully convolutional neural network with a U-net architecture^{[4]}. It takes as input 11 consecutive phase-shift maps with a temporal cadence of 12 hours, each of which is obtained from 24 hours of HMI Doppler observations. The outputs of the neural network are probability maps. The strength of the detections is quantified with the integrated probability (Pi) of the output blobs, with units of deg. A threshold of Pi>100 has been taken as a real detection in previous work^{[2]}. Figure 1 shows examples of inputs for the network and outputs from the standard method and the network.

Figure 1| Top: Eleven consecutive phase-shift maps used as input to FarNet. Each map is computed with 24 h of Doppler observations. The time cadence of the seismic maps is 12 h. Color scale indicates the phase shift, ranging from -0.28 rad (dark blue) to 0.17 rad (yellow). Bottom: Five days cumulative phase-shift map (a) computed for the central time of the series (input time 0 h, December 25, 2013) and prediction of FarNet for the same time; (b) using the eleven phase-shift maps.

We studied the performance of SARD and FarNet using the data from April 2011 to May 2016. We compared the outputs of both methods with STEREO/SDO 304 Å EUV Carrington maps from the Solar Museum Server of NASA^{[5]}. EUV emission is linked with magnetic activity and has been used as an activity proxy by previous works. The seismic predictions of far-side active regions require data from a wide range of dates (6 days in the case of the neural network and 5 in the case of the standard approach) and, thus, there are uncertainties in the dates where the seismically-detected far-side active regions are present. Given this, we compare the outputs of both methods with 3, 7, and 11 STEREO/SDO images (spanning 24, 72, and 120 hours, respectively). From these images, far-side activity masks were defined in where those regions with EUV intensity above a certain threshold were met. Then, we compared the blobs of the outputs of both methods with the blobs on the generated activity masks.

Figure 2| Visual comparison between methods applied on the data from April 13, 2011 (top), June 8, 2013 (middle), and April 1, 2014 (bottom). From left to right, square-root of resized STEREO/SDO image, EUV mask, seismic map computed with 5 days of Doppler data, and FarNet output. Yellow and green lines show the standard seismic method detections with S>400 and FarNet detections with Pi>100, respectively.

For S>400, the standard method detected 1334 active regions, with 52 (3.75%) false positives. For Pi>113 and a false positive percentage of 3.74% (nearest to the standard method result for S>400), the network detected 1958 active regions. For the same percentage of false positives, the neural network can provide a 47% increase in the number of far-side active region detections confirmed by the STEREO observations. Figure 2 exhibits some indications of the increased sensitivity of the network. Figure 3 shows the number of true detections from both methods as a function of the ratio of false positives to total positives, proving that the network is capable of more detections for almost the whole false-positive ratio range.

Figure 3| Number of true detections from both methods as a function of the ratio of false positives to total positives. Second row shows a close-up of the results from thresholds higher than S=400 (standard seismic method) and Pi=100 (FarNet). Each column represents the results of the comparison with 24 h (first column), 72 h (second column), and 120 h (third column) of STEREO data.

These results prove the neural network is a promising approach to improve the interpretation of the seismic maps provided by local helioseismic techniques. For more details of this work, please refer to our recent publication: https://arxiv.org/abs/2106.09365.

### References

[1] Liewer, P. C., Qiu, J., & Lindsey, C. 2017, *Sol. Phys.*, **292**, 146

[2] Felipe, T. & Asensio Ramos, A. 2019, *Astronomy & Astrophysics*, **632**, A82

[3] Lindsey, C. & Braun, D. C. 2000b, *Science*, **287**, 1799

[4] Ronneberger, O., Fischer, P., & Brox, T. 2015, *arXiv e-prints*, arXiv:1505.04597

[5] Liewer, P. C., González Hernández, I., Hall, J. R., Lindsey, C., & Lin, X. 2014, *Sol. Phys.*, **289**, 3617