SuperMag: Geomagnetic Archive & Tactile Sensing

• SuperMag is a dual-use system that serves as both a standardized global archive for geomagnetic data and an algorithmic framework for tactile shape reconstruction.
• In space physics, it aggregates data from hundreds of magnetometers, employing advanced preprocessing and spherical harmonic methods for indices, forecasting, and dark-matter investigations.
• In robotics, SuperMag leverages a conditional variational auto-encoder to infer dense contact geometry from sparse magnetic readings, enhancing tactile sensing performance.

SuperMag denotes two distinct research usages. In space physics and dark-matter searches, the closely related term SuperMAG refers to a uniform, public archive and processing framework for geographically dispersed ground magnetometer measurements, with one-minute cadence since 1970 in the public archive and later one-second “high-fidelity” data products; it has been used for geomagnetic indices, global field reconstruction, network analyses, and terrestrial searches for ultralight dark matter (Fedderke et al., 2021, Friel et al., 2024). In robotic tactile sensing, SuperMag denotes a tactile shape reconstruction method for magnetic-based tactile sensors that uses high-resolution vision-based tactile supervision and a conditional variational auto-encoder (CVAE) to infer dense contact geometry from sparse magnetic taxels (Hou et al., 26 Jul 2025).

1. Terminology and scope

The two uses of the name differ in capitalization, domain, and object of study.

Term	Domain	Description
SuperMAG	Geomagnetism, space weather, dark-matter detection	A global ground-magnetometer archive and standardized preprocessing framework used to construct indices, maps, networks, and matched-filter searches (Fedderke et al., 2021)
SuperMag	Robotic tactile sensing	A tactile shape reconstruction method for magnetic tactile sensors supervised by vision-based tactile data (Hou et al., 26 Jul 2025)

In the geomagnetic usage, SuperMAG is an observational infrastructure: studies describe it as aggregating more than 300 ground magnetometers, roughly 500 ground stations, or 246 magnetometers in the high-fidelity release, depending on the dataset and epoch under discussion (Tigas et al., 2021, Fedderke et al., 2021, Friel et al., 2024). In the tactile usage, SuperMag is an algorithmic system built around co-designed hardware and a generative model rather than a geophysical observatory (Hou et al., 26 Jul 2025).

A common misconception is to treat SuperMAG only as an auroral-index provider. The literature shows a broader role: the same archive supports spherical-harmonic nowcasting and forecasting, EOF-based reanalysis, directed and undirected dynamical networks, equivalent-current inversions, and ultralight-dark-matter searches (Tigas et al., 2021, Shore et al., 2018, Orr et al., 2020, Fedderke et al., 2021).

2. SuperMAG as a geomagnetic measurement and preprocessing framework

SuperMAG provides three-component magnetic-field measurements from globally distributed ground stations at one-minute cadence, with public records extending continuously since 1970 in the low-fidelity archive (Fedderke et al., 2021). Studies using the archive variously describe the measured components as northward, eastward, and vertical; X, Y, and Z; or radial (down), north, and east after processing into a common frame (Tigas et al., 2021, Laundal et al., 2018, Fedderke et al., 2021).

The preprocessing pipeline is a central feature of the framework. Reported steps include correction for instrument offsets, rotation into a common local-magnetic coordinate system, declination-based transformation into true geographic north/east, and removal of slow baselines or quiet-day trends (Tigas et al., 2021, Oliveira et al., 2015, Fedderke et al., 2021). One description emphasizes a 17-day sliding window that forces the “east” component’s typical 17-day median to vanish before transformation to true geographic coordinates and removal of slow diurnal and annual baseline variations (Fedderke et al., 2021). Another emphasizes a three-step trend fit for quiet-day baseline removal and formation of perturbation vectors $\Delta B$ at one-minute cadence (Tigas et al., 2021). For polar-current studies, downstream analyses often re-express the data in quasi-dipole or Modified Apex coordinates and assign magnetic local time (Laundal et al., 2018).

These standardized products support the construction of geomagnetic indices. In one formulation, the SuperMAG lower auroral electrojet index is

$\mathrm{SML}(t)=\min_{i\in S} B_N^i(t),$

with $S$ the set of stations in the specified magnetic-latitude range (Oliveira et al., 2015). In another formulation, SME and SML are obtained from one-minute $\Delta H(t)$ records over $\sim 300$ high-latitude stations, with

$$\mathrm{SME}(t)=\max_i[\Delta H_i(t)],\qquad \mathrm{SML}(t)=\min_i[\Delta H_i(t)],$$

and a uniform noise in $[-0.5,+0.5]$ nT added to overcome integer rounding (Benella et al., 2022). These indices generalize AE/AL by using many more stations and therefore better sample auroral electrojets during expanded auroral-oval conditions (Benella et al., 2022).

The high-fidelity SuperMAG dataset extends the same general idea to one-second resolution. That release contains 246 magnetometers worldwide, with most stations active only part of 1998–2020; the cited dark-matter analysis restricts to 2005–2020, when at least three stations are reliably active (Friel et al., 2024). After detrending and baseline subtraction, the one-sided PSD of the combined time series is reported as $\sim 10^{-2}$–$1\,(\mathrm{nT})^2/\mathrm{Hz}$ for $$10^{-3}\,\mathrm{Hz}\lesssim f\lesssim 1\,\mathrm{Hz}$$ (Friel et al., 2024).

3. Mathematical representations and inference frameworks built on SuperMAG

A striking feature of the SuperMAG literature is the repeated use of low-dimensional global representations to regularize an intrinsically sparse and nonuniform station network. One family of methods expands geomagnetic perturbations in spherical harmonics. In “Global Earth Magnetic Field Modeling and Forecasting with Spherical Harmonics Decomposition,” the radial field is written as

$\mathrm{SML}(t)=\min_{i\in S} B_N^i(t),$0

with a deep-learning architecture that forecasts the coefficient vector from 25 minutes of one-minute-averaged OMNI solar-wind inputs using a single-layer GRU and a two-layer MLP (Tigas et al., 2021). On held-out 2013 SuperMAG data, that model achieves an RMS error of 24.23 nT on the north-component rate of change $\mathrm{SML}(t)=\min_{i\in S} B_N^i(t),$1, compared to 28.35 nT for the Weimer et al. (2013) empirical spherical-harmonic model, a 14.53 percent relative improvement (Tigas et al., 2021).

A second family of methods fits spherical-harmonic magnetic potentials to derive equivalent currents. In the IMF-$\mathrm{SML}(t)=\min_{i\in S} B_N^i(t),$2 study, averaged SuperMAG perturbations are binned on a quasi-dipole latitude–MLT grid and modeled by an external potential

$\mathrm{SML}(t)=\min_{i\in S} B_N^i(t),$3

with simultaneous fitting of internal and external potentials up to degree/order $\mathrm{SML}(t)=\min_{i\in S} B_N^i(t),$4 using linear least squares with iterative Huber weighting (Laundal et al., 2018). The equivalent current function $\mathrm{SML}(t)=\min_{i\in S} B_N^i(t),$5 then satisfies

$\mathrm{SML}(t)=\min_{i\in S} B_N^i(t),$6

so that contours of $\mathrm{SML}(t)=\min_{i\in S} B_N^i(t),$7 trace horizontal divergence-free current streamlines (Laundal et al., 2018).

A third family uses data-adaptive decompositions. The EOF reanalysis of the northern polar surface external and induced magnetic field constructs a sparse month-length data matrix from SuperMAG vectors binned into approximately $\mathrm{SML}(t)=\min_{i\in S} B_N^i(t),$8 equal-area cells, then applies a data-interpolating EOF procedure with iterative infill of missing entries (Shore et al., 2018). The first 10 modes capture 63–78 percent of the month’s total variance, with mode 1 alone approximately 30–40 percent, and graph-theoretic linking of intermonthly spatial correlations recovers the canonical DP2, DPY, DP2EC, and DP1 systems (Shore et al., 2018).

A fourth family represents SuperMAG as a dynamical graph. In quiet-time IMF-turning studies, pairwise canonical correlations are thresholded to define time-dependent unweighted networks on an MLT–MLAT grid, with global connectivity

$\mathrm{SML}(t)=\min_{i\in S} B_N^i(t),$9

and dayside–nightside subnetworks used to characterize response delays (Dods et al., 2017). In substorm studies, directed edges are inferred from the lag of peak canonical cross-correlation, so that the sign of the lag encodes leading and following stations and therefore the apparent propagation or expansion direction (Orr et al., 2020). This suggests a recurring methodological pattern: SuperMAG is routinely compressed into basis functions or network objects that preserve large-scale structure while tolerating heterogeneous station coverage.

4. Space-physics results obtained with SuperMAG

SuperMAG-derived indices and network observables have been used extensively to study shock geoeffectiveness, auroral power release, substorm evolution, and stochastic properties of the magnetosphere. A major statistical result is that strong and nearly frontal interplanetary shocks are more geoeffective than slower or more inclined shocks. Using the SuperMAG SML index as an enhanced analogue of AL, the shock-impact study reports that across all 461 shocks, $S$0 ranged from near $S$1 nT up to approximately $S$2 nT, with the majority of events producing $S$3 between $S$4 and $S$5 nT (Oliveira et al., 2015). When the shock speed is fixed and the impact angle varied, the strongest correlation is $S$6 for the strong-shock bin; when impact angle is fixed and speed varied, the correlation rises as the shocks become more frontal (Oliveira et al., 2015). The proposed interpretation is symmetric magnetospheric compression and efficient unloading of tail energy into auroral substorms (Oliveira et al., 2015).

A related study converts the SuperMAG SME index into nightside auroral power through

$S$7

and finds that the largest auroral-power jumps occur for fast shocks with nearly head-on normals (Oliveira et al., 2015). In the almost frontal bin $S$8, the correlation between $S$9 and shock speed reaches $\Delta H(t)$0, with an average $\Delta H(t)$1 GW; in the strong-shock bin $\Delta H(t)$2 km/s, the correlation of $\Delta H(t)$3 with $\Delta H(t)$4 reaches $\Delta H(t)$5, with $\Delta H(t)$6 GW (Oliveira et al., 2015). Events with $\Delta H(t)$7 GW are seen almost exclusively when $\Delta H(t)$8 km/s and $\Delta H(t)$9 (Oliveira et al., 2015).

SuperMAG network analyses also recover canonical substorm phenomenology. In the directed-network study of 86 isolated substorms, a consistent picture emerges in which the classic substorm current wedge forms, westward expansion follows, a weaker eastward expansion appears later, and finally there is evidence of substorm-enhanced convection (Orr et al., 2020). The normalized link density

$\sim 300$0

is decomposed by lag bins and subnetworks to track the timing of coherence within and between premidnight, bulge, and postmidnight regions (Orr et al., 2020). In the IMF-turning network study, the global response onset occurs approximately 8–10 minutes after the turning reaches the magnetopause, with dayside correlation peaking 2–8 minutes before nightside correlation (Dods et al., 2017).

Not all previously proposed controls are strongly supported. The IMF-$\sim 300$1 study examines three independent datasets, including SuperMAG-derived equivalent currents, and finds that reversing the sign of $\sim 300$2 changes the Birkeland currents by no more than approximately 10 percent, while the SuperMAG equivalent-current maps show only $\sim 300$3 percent differences in total current between $\sim 300$4 maxima and minima and no systematic shift in local-time morphology (Laundal et al., 2018). The paper therefore argues against a strong $\sim 300$5-driven interhemispheric current imbalance and proposes instead that solar-wind–magnetosphere coupling is more efficient when dipole tilt angle and $\sim 300$6 have the same sign (Laundal et al., 2018). This is a genuine interpretive controversy rather than a simple null result.

SuperMAG indices have also been analyzed as stochastic processes. For SME and SML, the Chapman–Kolmogorov test supports the Markov condition at scales below 60 minutes, whereas at 200 minutes the empirical and CK-predicted transition probabilities diverge clearly (Benella et al., 2022). The Kramers–Moyal analysis shows nonzero higher-order moments, so a pure diffusive process is inadequate; the proposed surrogate is a jump-diffusion SDE,

$\sim 300$7

with state-dependent drift, diffusion, and Poisson-jump rate (Benella et al., 2022). In that model, the characteristic jump-amplitude variance is $\sim 300$8 and the jump rate grows quadratically with $\sim 300$9 (Benella et al., 2022). This suggests a metastable loading–unloading dynamics on sub-hour scales and a non-Markovian, externally driven regime on longer scales.

5. SuperMAG as a terrestrial detector for ultralight dark matter

SuperMAG has been repurposed as a distributed detector for ultralight dark matter by exploiting the Earth itself as an electromagnetic transducer. For kinetically mixed dark-photon dark matter, the companion theory paper argues that the lower atmosphere behaves as a low-conductivity cavity bounded below by the conductive Earth and above by the ionosphere or interplanetary plasma, so that the observable magnetic signal is suppressed by the Earth’s radius rather than the height of the atmosphere (Fedderke et al., 2021). In the Earth-fixed frame, within one dark-matter coherence time, the expected dark-photon signal at the surface is

$$\mathrm{SME}(t)=\max_i[\Delta H_i(t)],\qquad \mathrm{SML}(t)=\min_i[\Delta H_i(t)],$$0

with the pattern dominated by the $$\mathrm{SME}(t)=\max_i[\Delta H_i(t)],\qquad \mathrm{SML}(t)=\min_i[\Delta H_i(t)],$$1 toroidal vector spherical harmonics $$\mathrm{SME}(t)=\max_i[\Delta H_i(t)],\qquad \mathrm{SML}(t)=\min_i[\Delta H_i(t)],$$2 (Fedderke et al., 2021). For $$\mathrm{SME}(t)=\max_i[\Delta H_i(t)],\qquad \mathrm{SML}(t)=\min_i[\Delta H_i(t)],$$3,

$$\mathrm{SME}(t)=\max_i[\Delta H_i(t)],\qquad \mathrm{SML}(t)=\min_i[\Delta H_i(t)],$$4

(Fedderke et al., 2021).

The one-minute SuperMAG dark-photon search uses measurements from $$\mathrm{SME}(t)=\max_i[\Delta H_i(t)],\qquad \mathrm{SML}(t)=\min_i[\Delta H_i(t)],$$5 stations with one-minute cadence since 1970 (Fedderke et al., 2021). Because the signal lives entirely in the three $$\mathrm{SME}(t)=\max_i[\Delta H_i(t)],\qquad \mathrm{SML}(t)=\min_i[\Delta H_i(t)],$$6 modes, the station data are projected into five real-valued VSH channels, weighted by year-long white-noise estimates, Fourier transformed over coherence-length subseries, and assembled into a 15-component analysis vector at frequencies $$\mathrm{SME}(t)=\max_i[\Delta H_i(t)],\qquad \mathrm{SML}(t)=\min_i[\Delta H_i(t)],$$7 and $$\mathrm{SME}(t)=\max_i[\Delta H_i(t)],\qquad \mathrm{SML}(t)=\min_i[\Delta H_i(t)],$$8 (Fedderke et al., 2021). A Bayesian likelihood is then marginalized over stochastic polarization amplitudes and stacked incoherently over coherence times (Fedderke et al., 2021). No robust and significant evidence for a dark-photon signal is found, and the resulting 95 percent credible upper limits exclude

$$\mathrm{SME}(t)=\max_i[\Delta H_i(t)],\qquad \mathrm{SML}(t)=\min_i[\Delta H_i(t)],$$9

after a 25 percent post-hoc degradation to account for finite linewidth (Fedderke et al., 2021).

The same transducer concept has been applied to axion dark matter. In the presence of the geomagnetic background field, the leading axion-induced surface signal is written as

$[-0.5,+0.5]$0

with $[-0.5,+0.5]$1 determined from IGRF-13 coefficients and the dominant contribution from low $[-0.5,+0.5]$2 (Arza et al., 2021). The SuperMAG search finds no strong evidence for an axion signal in the mass range $[-0.5,+0.5]$3 and sets limits on $[-0.5,+0.5]$4 that, at their strongest, reach

$[-0.5,+0.5]$5

comparable to the CAST helioscope in that window (Arza et al., 2021).

The later high-fidelity search extends the frequency range by using one-second data from 246 magnetometers (Friel et al., 2024). Its preprocessing includes spike removal, manual corrections for offsets and clock errors, bias and gain correction, coordinate rotation from local magnetic coordinates to true geographic, and annual and diurnal baseline subtraction (Friel et al., 2024). The search covers

$[-0.5,+0.5]$6

finds no surviving candidates with $[-0.5,+0.5]$7 and at least $[-0.5,+0.5]$8 global significance, and reports the leading direct constraints on both dark-photon and axion dark matter in that mass range (Friel et al., 2024). For dark photons, the paper states that the constraint surpasses the leading astrophysical bound in a narrow range around $[-0.5,+0.5]$9 (Friel et al., 2024). This is a notable example of SuperMAG functioning not merely as a geophysical archive but as a global precision instrument.

6. SuperMag in robotic tactile sensing

In robotic manipulation, “SuperMag” denotes an unrelated system for high-resolution tactile shape reconstruction from magnetic tactile measurements (Hou et al., 26 Jul 2025). The hardware is explicitly co-designed: the magnetic-based tactile sensor (MBTS) uses a $\sim 10^{-2}$0 mm silicone contact module, a $\sim 10^{-2}$1 array of MLX90393 magnetometers with 5 mm spacing, an ESP32PICO MCU, and a sampling rate of 125 Hz, whereas the vision-based tactile sensor (VBTS) uses a $\sim 10^{-2}$2 mm semi-transparent Ecoflex layer over a PDMS base, a USB camera, and a frame rate of 30 Hz (Hou et al., 26 Jul 2025). A symmetric calibration setup with co-located contact modules yields synchronized pairs of low-resolution magnetic readings and high-resolution depth images, with raw VBTS resolution $\sim 10^{-2}$3 px downsampled to $\sim 10^{-2}$4 px and MBTS output represented as a $\sim 10^{-2}$5 tensor (Hou et al., 26 Jul 2025).

The learning problem is formulated as conditional generation. With $\sim 10^{-2}$6 the MBTS reading and $\sim 10^{-2}$7 the VBTS depth image, the model targets

$\sim 10^{-2}$8

and trains a CVAE by maximizing the ELBO

$\sim 10^{-2}$9

The architecture contains 47.2 M parameters, a latent dimension of 512, six convolutional blocks in the encoder, four transposed-convolution blocks plus eight plain convolutional blocks in the decoder, and multiplicative fusion of the magnetic input at two depths in both encoder and decoder (Hou et al., 26 Jul 2025).

The dataset contains 2025 pairs for an Allen key and 2025 pairs for the letter “R,” for 4050 total examples; 3645 are used for training and 405 held out for testing (Hou et al., 26 Jul 2025). At run time, the MBTS streams $1\,(\mathrm{nT})^2/\mathrm{Hz}$0 at 125 Hz over UART and a single forward pass takes approximately 2.5 ms on an NVIDIA RTX 3090, with total system throughput approximately 95 Hz including 8 ms for sensor readout and communication (Hou et al., 26 Jul 2025).

On unseen test objects, the paper compares bilinear upsampling, bicubic upsampling, a z-axis-only variant, an Allen-key-only model, and the full multi-axis multi-object model (Hou et al., 26 Jul 2025). Reported results are:

• FID: Bilinear 402.63, Bicubic 309.10, z-axis 234.16, AK 213.43, Ours 210.10.
• PSNR: Bilinear $1\,(\mathrm{nT})^2/\mathrm{Hz}$1 dB, Bicubic $1\,(\mathrm{nT})^2/\mathrm{Hz}$2 dB, z-axis $1\,(\mathrm{nT})^2/\mathrm{Hz}$3 dB, AK $1\,(\mathrm{nT})^2/\mathrm{Hz}$4 dB, Ours $1\,(\mathrm{nT})^2/\mathrm{Hz}$5 dB.
• SSIM: Bilinear $1\,(\mathrm{nT})^2/\mathrm{Hz}$6, Bicubic $1\,(\mathrm{nT})^2/\mathrm{Hz}$7, z-axis $1\,(\mathrm{nT})^2/\mathrm{Hz}$8, AK $1\,(\mathrm{nT})^2/\mathrm{Hz}$9, Ours $$10^{-3}\,\mathrm{Hz}\lesssim f\lesssim 1\,\mathrm{Hz}$$0 (Hou et al., 26 Jul 2025).

The downstream demonstration is in-hand pose estimation: SuperMag reconstruction, followed by Gaussian smoothing and PCA, yields a 100 percent success rate in 6/6 trials, versus 16.7 percent for baseline upsampling (Hou et al., 26 Jul 2025). In this context, SuperMag names neither an archive nor an indexing framework, but a cross-modality tactile super-resolution system. The shared name with SuperMAG is nominal only; the two literatures are methodologically and scientifically disjoint.