Helioseismic Far-side Active Region Model (FARM)

• Helioseismic Far-side Active Region Model is a framework that augments full-surface solar magnetic maps using helioseismic methods and surface flux transport modeling.
• It combines time–distance helioseismology, holography, and machine learning to calibrate seismic signals into quantitative magnetic flux estimates.
• The approach enhances space weather predictions by improving solar wind forecasts and the modeling of coronal and heliospheric structures.

The Helioseismic Far-side Active Region Model (FARM) is a framework for augmenting full-surface solar magnetic field maps with information about active regions on the Sun’s far hemisphere, which are not directly observable from Earth. By integrating helioseismic detections from local helioseismology into a surface flux transport (SFT) model, FARM provides a more comprehensive, temporally consistent, and accurate boundary condition for data-driven coronal and heliospheric modeling. This approach addresses fundamental limitations in routine synoptic maps and is critical for improving the forecasting of solar wind, coronal mass ejections, and geomagnetic disturbances. FARM incorporates advances in time–distance and holography-based helioseismology, machine learning, and statistical calibration, resulting in improved agreement between modeled and observed solar magnetic structures and enhanced space weather prediction capability.

1. Physical and Methodological Basis

FARM is founded on the synergy between sophisticated local helioseismic imaging techniques and surface flux transport models. The key components are:

• Local helioseismology methods:
  • Time–distance helioseismology: Infers subsurface and far-side structures via cross-covariance analysis of acoustic wave travel times between surface points.
  • Helioseismic holography: Reconstructs subsurface wavefields, enabling the detection of active regions on the non-visible hemisphere from Doppler data (e.g., SDO/HMI), exploiting phase shifts and travel-time perturbations induced by magnetic concentrations.
  • These approaches yield seismic phase maps that localize and characterize far-side active regions by analyzing frequency-filtered, temporally segmented surface oscillation data (Schunker, 2010).
• SFT model:
  • Governs large-scale magnetic field evolution on the solar surface, accounting for differential rotation, meridional flow, active region inflows, and diffusion. Flux emergence is typically modeled via source terms (e.g., bipoles determined from observations or, in FARM, from helioseismology).

The workflow entails detection and parametrization of far-side active regions from seismic maps, calibration of seismic signal to inferred magnetic flux, polarity assignment consistent with Hale’s and Joy’s laws, and source-term injection into the SFT simulation to ensure flux balance and realistic spatial configuration (Yang et al., 27 Nov 2024).

2. Calibration: Seismic Signal to Magnetic Flux

A central challenge is translating helioseismic phase shifts into quantitative estimates of (locally unsigned) surface magnetic flux. FARM employs empirical calibration by correlating integrated seismic phase over identified regions with corresponding unsigned magnetic flux from well-observed near-side active regions. The calibration is expressed as

$\int_P |B_r|\,dS = C \int_P \psi\,dS$

where $P$ denotes the area of a magnetic “pole” in the seismic map, $\psi$ is the phase shift, and $C$ is the calibration constant. For the implementation in (Yang et al., 27 Nov 2024), $C = -245\,\mathrm{G\,rad}^{-1}$ provides the best fit over an extensive training interval (2010–2024). The spatial magnetic profile for each pole is modeled as

$$B_p = A\,\exp\left(\frac{2(\cos\beta-1)}{\delta^2}\right)$$

with $A$ set by the integrated flux and $\beta$ the angular distance from the pole center. In cases where direct polarity assignment is ambiguous, empirical separation and orientation are imposed following observed area relations and established solar cycle laws. For complex configurations (e.g., anti-Hale or delta-type), manual correction or improved automated algorithms may be required (Yang et al., 27 Nov 2024).

3. Data Sources, Detection Pipeline, and Machine Learning Integration

• Data inputs:
  • Near-side: Full-disk line-of-sight magnetograms from SDO/HMI (transformed to approximate B_r as needed) and high-cadence Dopplergrams.
  • Far-side: Seismic phase maps inferred from overlapping Dopplergram sequences (integration times typically 31–79 hours), processed with advanced time–distance or holography pipelines.
• Detection pipeline:
  • Seismic maps are smoothed, spatially filtered, and thresholded to identify candidate active regions.
  • Polarity centers are determined, with the number of poles and their spatial configuration guiding the subsequent bipole generation.
  • Calibration proceeds according to the empirically determined C; new flux is assigned to the SFT model at the estimated Carrington longitude and latitude and with the emergence time corresponding to the detection epoch.
• Machine learning applications:
  • Recent models use convolutional neural networks (e.g., U-net architectures) to infer maps of unsigned magnetic flux directly from seismic images, leveraging supervised learning with EUV- or magnetogram-derived targets (Chen et al., 2022).
  • Advanced deep learning (FarNet, FarNet-II with ConvLSTM and attention modules) achieves statistically significant improvements in far-side detection rates, accuracy, and temporal coherence compared to thresholded phase-shift methods (2229.14789).

4. Validation, Case Studies, and Cross-Disciplinary Evaluation

The FARM methodology, including signal calibration and regional mapping, is validated through multiple cross-disciplinary comparisons:

• Direct validation with far-side magnetograms: Solar Orbiter/PHI provides contemporaneous far-side line-of-sight magnetograms, enabling direct comparison with seismic phase maps. A linear relation between area-averaged phase shift and magnetic field ($$\langle\Phi\rangle_{ar} = a (\langle || \rangle_{ar} - 5\,\mathrm{G}),\ a = -0.2\,\mathrm{deg}/\mathrm{G}$$) confirms the efficacy of seismic calibration (Yang et al., 2023).
• EUV and white-light imaging: Modeled open-field areas and streamer locations show substantial improvement in agreement with SDO/AIA, STEREO EUV, LASCO C2, and eclipse images when FARM-inferred far-side regions are included (Shi et al., 3 Sep 2025, Yang et al., 27 Nov 2024).
• In situ heliospheric measurements: Simulations using FARM-updated magnetic maps as boundary conditions yield improved magnetic connectivity and plasma parameter correlations with spacecraft data (Solar Orbiter/MAG, Parker Solar Probe) and better reproduction of observed solar wind features (Perri et al., 10 Apr 2024, Shi et al., 3 Sep 2025, Heinemann et al., 1 Oct 2025).

5. Impact on Space Weather and Solar Wind Forecasting

By providing more timely and complete boundary conditions, FARM directly enhances coronal and heliospheric models:

• Quantitative improvements: Solar wind speed forecasts show up to 50% improvement in correlation and 3% decrease in RMSE/MAE when FARM-informed maps are used as input to the Wang-Sheeley-Arge model versus base SFTM without far-side data (Heinemann et al., 1 Oct 2025).
• 3D solar wind structure: Inclusion of far-side regions modifies the distribution of open and closed flux, streamers, and the heliospheric current sheet topography in MHD simulations (EUHFORIA, AWSoM-R). Simulations with FARM often suppress spurious high-speed streams seen with SFTM and enhance agreement with observed heliospheric conditions.
• Global and local effects: Even single far-side active regions, contributing modest fractions of surface flux, can shift the heliospheric current sheet and alter streamer structures, with local coronal hole boundaries and the Sun–Earth magnetic connectivity affected on short timescales (Perri et al., 10 Apr 2024, Shi et al., 3 Sep 2025).

6. Limitations, Future Prospects, and Theoretical Extensions

• Uncertainties and caveats:
  • Polarity assignment on the far side is often ambiguous due to the seismic phase shift’s insensitivity to field sign. Manual correction is performed for anti-Hale regions, but future developments may employ statistical or physics-based polar assignment (Yang et al., 27 Nov 2024).
  • Current spatial resolution is fundamentally limited by the acoustic wavelengths ($\sim4^\circ$ FWHM), yielding lower resolution than HMI magnetograms. Machine learning approaches show improved morphological recovery, but peak flux and polarity estimation remain less reliable than near-side direct measurements (Chen et al., 2022).
  • The calibration constant $C$ is empirically derived and may require adjustment as more far-side direct measurements (e.g., from Solar Orbiter/PHI) become available. This applies as well to modeling the temporal evolution and flux decay in newly emergent or complex regions.
• Directions for advancement:
  • Stereoscopic synoptic maps combining simultaneous near- and far-side magnetograms from Solar Orbiter, Parker Solar Probe, and future missions will further reduce boundary uncertainties (Perri et al., 10 Apr 2024, Shi et al., 3 Sep 2025).
  • Advances in helioseismic inversion, mode sensitivity kernel modeling, and time–distance and holography methodologies will sharpen detection and reduce noise and systematics associated with strong magnetic field regions (Schunker, 2010, Moradi, 2012).
  • Theoretical and computational developments enabling the assimilation of subphotospheric flow descriptors linked to flare productivity—such as kinetic helicity and converging flows—may enhance the predictive power of FARM for space weather transients (Kosovichev et al., 31 Jan 2024).

7. Significance and Connection to Broader Solar Physics

The FARM framework is now central to operational space weather prediction pipelines requiring synchronic full-sphere magnetic boundary conditions for MHD and potential field models. As validated by direct far-side magnetograms, EUV, white-light, and in situ heliospheric observations, FARM implementations systematically and quantitatively improve the model–observation agreement for solar wind speeds, current sheet structure, and coronal morphology. The methodology and its generalization are extensible to asteroseismic contexts for other solar-like oscillators, suggesting broader potential for global activity imaging in stellar physics (Howe et al., 14 Jan 2025). The approach represents a convergence of observational helioseismology, deep learning, MHD modeling, and space environment prediction, and continues to evolve rapidly as new multi-view and high-resolution datasets become available.