Ultra-low frequency (ULF) waves, with periods between seconds and tens of minutes, provide a mechanism for solar wind energy and momentum to be transferred into/around a planetary magnetosphere and couple the space environment to the body’s ionosphere. They are routinely recorded as time-series data both by ground-based instruments such as magnetometers or radar, as well as through in situ spacecraft observations of the magnetospheric environment. Dynamic pressure variations, either embedded in the large-scale solar wind or associated with meso-scale kinetic structures at the bow shock, may excite any of the three magnetohydrodynamic (MHD) waves—the surface, fast magnetosonic, and Alfvén modes—at locations within the magnetosphere (e.g. Sibeck et al., 1989; Hartinger et al., 2013). In addition, MHD or other plasma waves in the ULF range—such as electromagnetic ion cyclotron (EMIC) and mirror modes—may also be generated internally through fluid/kinetic instabilities or wave-particle interactions (e.g. Cornwall, 1965; Southwood et al., 1969; Hasegawa, 1975). All of these different waves may exist as incoherent broadband enhancements in wave power or at well-defined discrete, or even an entire spectrum, of coherent oscillations. Thus a zoo of ULF wave phenomena are known to occur within Earth’s magnetosphere (see the review of Nakariakov et al., 2016, for more).

Classification of magnetospheric ULF waves (Jacobs et al., 1964) has long been separated into whether pulsations qualitatively are quasi-sinusoidal (continuous pulsations, Pc) or more irregular (Pi). These two categories have then be subdivided into near-logarithmically spaced frequency bands. Unfortunately, such a classification scheme does not take into account the physical processes involved in the generation and propagation of the waves, nor how these may be reflected in their physical or morphological properties. Indeed, many studies simply consider the integrated power over one or several of these frequency bands (e.g. Mann et al., 2004), which will not distinguish between broadband, narrowband, or multi-harmonic signals. It is known, however, that the frequencies of physically different ULF waves may overlap and even occupy wildly different bands depending on the conditions present (e.g. Archer et al., 2015, 2017).

Beyond classification, even the analysis of ULF wave measurements can be quite challenging, since they are often highly nonstationary and may exhibit nonlinearity. Time-frequency analysis which can capture these variations are therefore required. Methods based on the linear Fourier transform are most commonly used, though these spectral estimators often result in a large amount of variance making it difficult to distinguish true spectral peaks to simply a realisation of an underlying stochastic process (Chatfield, 2019). While statistical tests have been developed to help address this (e.g. Di Matteo and Villante, 2018; Di Matteo et al., 2021), these are not immune to false positives (or indeed false negatives). The continuous wavelet transform (Torrence and Compo, 1998) offers some potential improvements to Fourier methods in self-consistent time-frequency analysis, e.g. enabling feature extraction. Wavelets are, like Fourier methods, still subject to the Gabor uncertainty principle in time-frequency space ( σ t σ f ≥ 1 2 , where σ _t and σ _f represent standard deviations in time and frequency respectively) due to their linear nature. Similarly large variances in spectral power again occur, which can limit the identification of discrete frequency signals. Nonlinear time-frequency analysis methods, which are not constrained to the Gabor limit, exist including the Wigner-Ville distribution (Wigner, 1932; Ville, 1948) and Empirical Mode Decomposition (Huang et al., 1998). However, these are not currently widely used for the analysis of ULF waves and their associated artifacts, mode mixing, or stability in these applications are not fully understood (Chi and Russell, 2008; Piersanti et al., 2018). Ultimately, few studies employ fully automated detection, with visual inspection still often used either for identification or confirmation of ULF wave signals in real data (e.g. Takahashi et al., 2015). However, oscillatory time-series data naturally lends itself most to another of our senses—sound.

Sonification refers to the use of non-speech audio to convey information or perceptualise data (Kramer, 1994). The human auditory system has many advantages over visualization in terms of temporal, spatial, amplitude, and frequency resolution. For example, the human hearing range of 20–20,000 Hz spans three orders of magnitude in frequency and at least 13 orders of magnitude in sound pressure level (Suzuki, 2004), compared to the human visual system’s only a quarter order of magnitude in wavelengths and no more than 4 orders of magnitude in luminance (Kunkel and Reinhard, 2010). Human hearing is also highly nonlinear, hence is not subject to the Gabor limit, thus can identify the pitch and timing of sound signals much more precisely than linear methods (Oppenheim and Magnasco, 2013). Furthermore, the human auditory system’s ability to separate sounds corresponding to different sources far outperforms even some of the most sophisticated blind source separation algorithms developed (e.g. Qian et al., 2018).

The simplest method of converting an oscillatory time-series into sound is a one-to-one mapping of data samples to audio samples, known as audification (e.g. Alexander et al., 2011, 2014). The benefit of this technique is that no information is lost and the audio is therefore a true representation of the original data. Other highly-used sonification techniques require the mapping of data values (or the outputs of some analysis on them) to discrete synthesised musical notes (Bearman and Brown, 2012; Phillips and Cabrera, 2019). This necessarily loses some information in the process and may also impose the user’s desired aesthetics on the data, meaning that it is arguable whether the audio is truly representative of the underlying data. In direct audification the only free choices are the amplitude to normalise the original data (audio is stored as dimensionless values between −1 and +1) and the sampling rate with which to output the audio. There is a straightforward relationship between time durations in the audio and their corresponding durations in the original data, given by Δ A u d i o t i m e = Δ S p a c e c r a f t t i m e × S p a c e c r a f t s a m p l i n g r a t e A u d i o s a m p l i n g r a t e (1) , where the spacecraft time represents the actual time of the spacecraft observations (e.g. in UTC) when events took place. Since frequency is the reciprocal of the time period, audio and spacecraft frequencies are related by A u d i o f r e q u e n c y = S p a c e c r a f t f r e q u e n c y × A u d i o s a m p l i n g r a t e S p a c e c r a f t s a m p l i n g r a t e (2)

Figure 1 demonstrates these relationships, indicating how various choices in the ratio of the audio to spacecraft sampling rates renders different frequency ranges in the original data audible. It is clear that for the Pc3–6 bands of ULF waves, where MHD waves largely fall, then an audio to spacecraft sampling rate ratio of order 10⁵ is required (corresponding to the thicker line in the figure). Since space plasma missions typically produce data with cadences of a few seconds, this means that typical audio sampling rates (such as 44,100 Hz) may be used. The large ratio means that timescales of the audio are dramatically reduced, which is advantageous as data navigation, mining and analysis will have a reduced processing time through listening (Hermann, 2002).

Alexander et al. (2011, 2014) and Wicks et al. (2016) showed that researchers using audification applied to Wind magnetometer data in the solar wind aided in the identification of subtle features present that were not necessarily clear from standard visual analysis. Archer et al. (2018) similarly showed that audification of GOES magnetic field observations enabled high school students to identify numerous long-lasting decreasing-frequency poloidal field line resonances during the recovery phase of geomagnetic storms. Such events were previously thought to be rare, but through exploration of the audio they were in fact demonstrated to be relatively common. These preliminary studies into the use of audification of the ULF wave bands within heliophysics show promise in its potential scientific applications.

Direct audification may not, however, be suitable for all space plasma missions and/or ULF wave events. Figure 1 indicates that to make the ULF bands audible necessarily renders a day of data into about one second of audio. In geostationary orbit the background plasma and magnetic field conditions, which affect the eigenfrequencies of the ULF modes, are relatively stable across the orbit (Takahashi et al., 2010). This makes identifying the local time patterns in frequency and occurrence of ULF waves relatively straightforward (Archer et al., 2018). However, for more eccentric orbits with similar orbital periods the conditions, frequencies, and occurrence of ULF waves will rapidly change throughout the orbit (Archer et al., 2015, 2017). Therefore, the rate at which ULF waves’ properties may be changing in the audio will be very fast. This is demonstrated in the audio in Supplementary Data S1 of Archer et al. (2022), where audification is applied to idealised and real events from the THEMIS mission. It is clear from this audio that changes are occurring too quickly to effectively listen to and analyse. Another potential issue in audification is that ULF waves can be highly transient, occuring for only several oscillations due to intermittent driving and/or damping (e.g. Zong et al., 2009; Wang et al., 2015; Archer et al., 2019). This means that ULF wave events which persist for only ∼ 10 – 30 m i n will last only ∼ 60 – 200 m s in the audio. Furthermore, effective pitch discrimination by the auditory system often requires several tens of (and even up to a hundred) oscillations (Fyk, 1987), which is not always the case with ULF waves. Thus, improvements to the sonification process over simple audification are clearly required for application to magnetospheric ULF waves more widely.

In this transdisciplinary paper we introduce several potential improved sonification methods for ULF waves, borrowing techniques from the fields of audio and music. The properties of the resulting audio from these different methods are assessed through a public dialogue with stakeholder groups to arrive at recommendations for ULF wave researchers on how best to render these waves audible. Finally, we discuss the scientific and educational possibilities that might be enabled by these new methods.

Taking existing techniques from the fields of audio and music, we have developed new potential sonification methods for magnetospheric ULF waves which we detail throughout this section. In this work we focus on Alfvén waves (Southwood, 1974), arguably the most intensely studied mode of ULF waves (e.g. the review of Keiling et al., 2016). Further justifying this choice is the fact that significant coupling occurs within the magnetosphere from compressional to Alfvén modes due to plasma inhomogeneity, curvilinear magnetic geometry, and hot plasma effects (Southwood and Kivelson, 1984). However, this focus does not preclude that sonification might also render other types of ULF waves that also occupy the same Pc3–6 frequency bands, such as surface (e.g. Archer et al., 2019) or waveguide (e.g. Hartinger et al., 2013) modes, effectively audible, though these applications are beyond the scope of this paper. The natural frequencies of Alfvén waves vary with local time and L-shell, with the spectrum of frequencies with location being known as the Alfvén continuum. The typically reported trend is that, outside of the plasmasphere or plumes, Alfvén wave frequencies tend to decrease with radial distance from the Earth (Takahashi et al., 2015), hence spacecraft observations often show tones whose frequencies sweep from high to low as the probe follows its orbit from perigee to apogee (and vice versa as the orbit continues from apogee back to perigee). It is worth noting though that the Alfvén continuum can vary considerably, both in terms of absolute values and morphology, with solar wind and magnetospheric driving conditions (Archer et al., 2015, 2017).

The full sonification process developed here is outlined as a flow chart in Figure 2. Throughout we apply the methods to NASA THEMIS observations (Angelopoulos, 2008), chosen due to the highly eccentric equatorial orbits of its spacecraft with the inner three probes having apogees r ∼ 12–15 R_E and perigee r ∼ 1.5 R_E over the course of the mission. Spin-resolution data is used, with one data point every 3 s (any data gaps or irregular samples are regularised by interpolation). As with Archer et al. (2018) we focus only on waves in the magnetic field, using fluxgate magnetometer data (Auster et al., 2008; electron plasma data, McFadden et al., 2008, is also used for discriminating between magnetosphere and magnetosheath intervals). Other physical quantities such as the plasma velocity (e.g. Takahashi et al., 2015) or electric field (e.g. Hartinger et al., 2013) could also be used in the sonification of ULF waves—a prospect we leave to future work. How the different potential sonification methods affect the sound of the resulting audio is assessed in Section 3. The software developed incorporating all of these methods is available at https://github.com/Shirling-VT/HARP_sonification.

It was felt that in order to provide recommendations to ULF wave researchers on the best method of rendering these waves audible that we should seek input from various stakeholder communities outside of the space sciences. This is because these communities either have expertise in audio and its usage, or form intended target audiences for the sonified ULF waves. We therefore undertook a public dialogue on the different sonification methods presented. The study gained ethical approval through Imperial College London’s Science Engineering Technology Research Ethics Committee process (reference 21IC7145).

While time-series data of magnetospheric ultra-low frequency (ULF) waves are often still analysed visually (at least in part), this form of data lends itself more naturally to our sense of sound. Direct audification is the simplest sonification method, providing a true representation of the original data. When applied to ULF waves though this can result in changes occurring too rapidly for effective analysis by the human auditory system. Therefore, we detail several existing audio time scale modification (TSM) techniques which have been applied to ULF wave data. Through a public dialogue with stakeholder groups, we arrive at recommendations on which sonification methods should be used to best render the Alfvén waves present audible, which are summarised in Table 2. We have implemented these final recommendations, applying them to the three THEMIS example events yielding the audio in Supplementary Data S5 of Archer et al. (2022).

Figure 7 shows a typical spectrogram representation of ULF waves for the three examples, where the logarithmic colour scale has been spectrally whitened and the limits of the colour scale in each individual event have been set at the 50% (corresponding to the noise level) and 95% (corresponding to the peaks) percentiles in power in order to capture the range present. In the idealised data (event 1) the Alfvén continuum, with frequencies decreasing from perigee to apogee, is very clear. In contrast, in the real data (events 2–3) identifying discrete peaks even by visual inspection is much more difficult. Even in the dawn sector under active geomagnetic conditions, where standing toroidal Alfvén waves are more common and their frequency profiles should be simpler (i.e. similar to event 1; Takahashi et al., 2016; Archer et al., 2017), the continuum is still subtle, especially for the first orbit where significant incoherent broadband wave power is also clearly present. In contrast, the Alfvén continuum is clearly audible in Supplementary Data S5 (Archer et al., 2022) throughout portions of the orbits for all three events. The auditory system’s ability to identify these subtle sweeping frequency tones in the presence of significant noise and other potential signals is likely thanks to its nonlinear nature and impressive ability at blind source separation. It is well known that all wave analysis techniques have their advantages and drawbacks, which will depend on the nature of the precise oscillations present (Chi and Russell, 2008; Piersanti et al., 2018). Sonification can thus provide an additional supportive tool for researchers in identifying different ULF waves (Alexander et al., 2011, 2014; Wicks et al., 2016; Archer et al., 2018) that may complement other techniques. By maximising the audibility of ULF waves for more challenging orbits/environments/events, the methods presented here should hopefully improve further the utility of sonification in this science topic.

Another benefit to sonification is that it renders scientific data more accessible and lowers the barrier to entry for students and the public to contribute to space science through citizen science (Archer et al., 2018). With the growing number of space plasma spacecraft in orbit around Earth and the networks of ground magnetometers globally, we are continually producing big data that poses a challenge to efficiently navigate, mine, and analyse. Machine learning is typically the emerging solution to dealing with big data in general, with supervised machine learning techniques being applied to a variety of space physics tasks (e.g. Breuillard et al., 2020; Lenouvel et al., 2021). However, current challenges in ULF wave research mean that many simple tasks (e.g. classifying ULF wave events) are still not easily tackled by these methods due to the lack of good (e.g. classified) training sets of events. Until ULF wave research can be fully automated, clearly it is not feasible for a single researcher to visually inspect all the ULF wave data that is, being produced. The dramatically reduced analysis processing time associated with listening to sonified data (even with moderate TSM applied) certainly helps. However, any manual process applied by a single researcher is potentially subject to biases and concerns over reliability. On the other hand, mobilising citizen scientists en masse to cover these vast datasets and arrive at a statistical consensus for each interval/event may in fact be more robust (e.g. Barnard et al., 2014). Therefore, there is a lot of potential in applying the sonification methods presented here to arrive at new scientific results through citizen science. A simple example is that already discussed, identifying how the properties and excitation of the Alfvén continuum vary under different solar wind and geomagnetic driving conditions—an important and still unresolved issue (e.g. Rae et al., 2019). Another possibility is that citizen scientists collectively may be able to arrive at more data-driven classifications of ULF waves that take into account further properties of the waves than simply frequency, which may better distinguish between the different physical processes at play than the current scheme (Jacobs et al., 1964). Countless other scientific questions into the sources and propagation of ULF waves in planetary magnetospheres could be addressed through citizen science with sonified data. Indeed the pilot “Heliophysics Audified: Resonances in Plasmas” (HARP) citizen science project (http://listen.spacescience.org/) is already building on the work presented by Archer et al. (2018) in this area, developing more streamlined interfaces for citizen scientists to interact with the audible data and record scientific results. A result of increased citizen science in ULF wave research could be the very training sets required to be able to apply machine learning algorithms to the data, an approach which has successfully been done in other fields (e.g. Beaumont et al., 2014; Sullivan et al., 2014). Once trained, these machine learning algorithms would then be able to tie together multi-satellite and multi-station data of the same event at different locations, in ways which are not possible with a single audio stream, to improve our global understanding of system-scale magnetospheric dynamics under different driving regimes.

More work is required to understand the full scope of sonification in the identification, categorisation, and characterisation of the zoo of ULF waves present within Earth’s magnetosphere. The application of existing TSM methods from the field of music and audio in this paper was motivated by the short timescales associated with direct audification of ULF waves and limits in human’s pitch perception based on the number of oscillations in typical ULF wave events. While this work has certainly increased the audibility of ULF waves, the Alfvén continuum in particular, only through further work in applying sonification for the purposes of novel scientific results can the full benefits and limits of these tools be realised.

Beyond potential scientific benefits, there are also obvious uses of sonified ULF waves in education, engagement, and communication. Recently a number of high-profile ULF wave results have leveraged the methods presented in this paper within press releases for the media (National Centers for Environmental Information, 2018; European Space Agency, 2019; Johnson-Groh, 2019; Tran, 2021), which have gone on to successfully attract global attention. Therefore, sonification is a helpful tool in communicating our science. Archer et al. (2021a) showed that simply enabling public audiences to experience these sounds can spark innate associations and dispell common misconceptions simply through the act of listening, highlighting the power of the medium in its own right. This has similarly been reflected in many of the survey responses of synonymous sounds, e.g. the perceived water-like quality of the wavelets processed data may spark conversations about fluids and (magneto)hydrodynamics in space. More in-depth engagement projects that enable high school students to work with audible data as part of research projects (Archer et al., 2018; 2021b) have recently been shown to have immense benefits to students, teachers and schools from a variety of backgrounds (Archer, 2021; Archer and DeWitt, 2021). These include increased confidence, developed skills, raised aspirations, and greater uptake of science. Sonifications may also be used as creative elements in the production of art, thereby engaging those who might not actively seek out science otherwise (Archer, 2020; Energy et al., 2021). Therefore, the potential uses of these methods are vast.

Finally, the sonification methods beyond direct audification presented here could easily be applied to other forms of waves. Indeed, there is a long history of converting heliophysics data across different frequency bands into audible sounds. The terminology of ionospheric extremely-low frequency (ELF) and very-low frequency (VLF) radio waves, which already span the human hearing range, were largely based on their psychoacoustics when picked up by radio antenna, e.g. “whistlers” (Barkhausen, 1919) and “lion roars” (Smith et al., 1967). This tradition has continued with terms such as “tweaks,” “chorus,” “hiss” and “static” being commonly used across heliospheric research. Many examples of such higher (than ULF) frequency waves from across the Solar System, either already in the audible range or in fact pitched down to be rendered audible, are available online (e.g. http://space-audio.org/). While the specific recommendations (such as the TSM factor and audio sampling rate) made here are tailored for the Pc3–6 ULF wave bands, and the Alfvén continuum in particular, there is no reason why these choices could not be suitably adjusted for other waves/frequencies to improve their audibility also. For example, electromagnetic ion cyclotron (EMIC) waves typically are found in the Pc1–2 ULF wave bands and would require different choices of parameters to render them audible. Even electron cyclotron harmonic (ECH) waves, which already occupy the audible range, can benefit from some TSM (see an example in Phillips, 2021). There are clearly also applications to time-series data in general, not just within the space sciences. Therefore, there are potentially many ways that the scientific community and wider society can benefit from this work into sonification.