# Listening to the magnetosphere: How best to make ULF waves audible

Martin O. Archer 1,∗, Marek Cottingham 1, Michael D. Hartinger 2, Xueling Shi
3,4, Shane Coyle 3,
Ethan “Duke” Hill 3, Michael F. J. Fox 1, Emmanuel V. Masongsong 5

###### Abstract

Observations across the heliosphere typically rely on in situ spacecraft
observations producing time-series data. While often this data is analysed
visually, it lends itself more naturally to our sense of sound. The simplest
method of converting oscillatory data into audible sound is audification – a
one-to-one mapping of data samples to audio samples – which has the benefit
that no information is lost, thus is a true representation of the original
data. However, audification can make some magnetospheric ULF waves
observations pass by too quickly for someone to realistically be able to
listen to effectively. For this reason, we detail various existing audio time
scale modification techniques developed for music, applying these to ULF wave
observations by spacecraft and exploring how they affect the properties of the
resulting audio. Through a public dialogue we arrive at recommendations for
ULF wave researchers on rendering these waves audible and discuss the
scientific and educational possibilities of these new methods.

1 Department of Physics, Imperial College London, London, United Kingdom
2 Space Science Institute, Boulder, Colorado, USA
3 Department of Electrical and Computer Engineering, Virginia Polytechnic
Institute and State University, Blacksburg, Virginia, USA
4 High Altitude Observatory, National Center for Atmospheric Research,
Boulder, Colorado, USA
5 Earth, Planetary, and Space Sciences Department, University of California,
Los Angeles, California, USA

##  1 Introduction

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., 2013b). 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
($\sigma_{t}\sigma_{f}\geq\frac{1}{2}$, where $\sigma_{t}$ and $\sigma_{f}$
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., 2015a). 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

$\Delta\left(\mathrm{Audio\,time}\right)=\Delta\left(\mathrm{Spacecraft\,time}\right)\times\frac{\mathrm{Spacecraft\,sampling\,rate}}{\mathrm{Audio\,sampling\,rate}}$
(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

$\mathrm{Audio\,frequency}=\mathrm{Spacecraft\,frequency}\times\frac{\mathrm{Audio\,sampling\,rate}}{\mathrm{Spacecraft\,sampling\,rate}}$
(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 $10^{5}$ 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 1 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 $\sim 10\text{--}30\,\mathrm{min}$ will last only $\sim
60\text{--}200\,\mathrm{ms}$ 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.

##  2 Sonification

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.,
2013a) 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., 2015b), 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 $r\sim
12\text{--}15\,\mathrm{R_{E}}$ and perigee $r\sim 1.5\,\mathrm{R_{E}}$ over
the course of the mission. Spin-resolution data is used, with one data point
every $3\,\mathrm{s}$ (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., 2015b) or electric field
(e.g. Hartinger et al., 2012) 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.

###  2.1 ULF wave extraction

Before sonification, the magnetospheric ULF waves must be extracted from the
data and transformed into an appropriate coordinate system. Non-physical
spikes in the magnetometer data are first removed by identifying when
$\partial_{t}\mathbf{B}>3\,\mathrm{nT}\,\mathrm{s}^{-1}$ in any component and
removing the 10 neighbour data points from all components. Next, since
magnetospheric ULF waves are the focus of the sonification, magnetosheath
intervals are also removed. These are flagged for $r>8\,\mathrm{R_{E}}$ when
either the electron number density is greater than $10\,\mathrm{cm}^{-3}$,
antisunward component of the electron velocity is greater than
$200\,\mathrm{km}\,\mathrm{s}^{-1}$, or the perpendicular electron particle
flux is greater than $2\times 10^{7}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}$. The
three nearest neighbour points to flagged data are also removed. Interpolation
is applied to fill in the removed data, thereby preventing discontinuities in
the data which might affect the sonification. For short magnetosheath
intervals, less than the dominant ULF wave period present, the interpolation
will fill in the gaps in phase effectively. In contrast, when the intervals
are longer than ULF wave periodicities then the resulting audio during
interpolated intervals will be silent, since frequencies associated with the
interpolation will be below the audible range.

The background magnetospheric magnetic field is determined by a
$30\,\mathrm{min}$ running average, with this trend being subtracted to arrive
at the ULF waves. These are then rotated into a field-aligned coordinate
system. The field-aligned component (representative of compressional waves) is
along the previous running average, the radial component (representative of
poloidal waves) is perpendicular to this pointing radially away from Earth,
and the azimuthal component (representative of toroidal waves) is
perpendicular to both of these pointing eastwards. Since close to Earth the
instrument precision is reduced (Auster et al., 2008) and the dipole field as
measured by the spacecraft changes more rapidly than the running average
(Archer et al., 2013), we finally remove all data from geocentric distances
$r<5\,\mathrm{R_{E}}$ setting these points to zero.

###  2.2 Time scale modification

Time scale modification (TSM) refers to speeding up or slowing down audio
without affecting the frequency content, e.g. the pitch of any tones (Driedger
and Müller, 2016). It therefore modifies the link between the time of events
and frequency/periodicity of waves. This may be advantageous for the
sonification of ULF waves compared to simple audification, since it allows the
frequencies to still fall within the audible range as per equation 2 but
stretches the audio in time so that events do not occur so quickly for
listening, i.e.

$\Delta\left(\mathrm{Audio\,time}\right)=\mathrm{TSM\,factor}\times\Delta\left(\mathrm{Spacecraft\,time}\right)\times\frac{\mathrm{Spacecraft\,sampling\,rate}}{\mathrm{Audio\,sampling\,rate}}$
(3)

Here the TSM factor refers to the factor by which the audio has been stretched
in time, where values greater than one result in longer audio (in some other
sources the definition may refer to the reciprocal of this). Time stretching
necessarily increases the number of oscillations present in each event, since
the periodicities are maintained and thus equation 2 remains unaffected. This
has the consequence of also improving the audibility of short-lived waves for
purposes such as pitch detection (Fyk, 1987).

One of the benefits of direct audification is that the resulting audio is
identical in information content to the original data. While TSM methods
necessarily modify their inputs, this is done in ways which are relatively
easy to understand. In principle, it should be possible to reverse these
procedures to arrive back at the original data, which we justify for each
method in turn. However, in practice some additional artifacts may be present
when attempting this reversal.Nonetheless, key properties of the original data
are left invariant by each process and thus the time-stretched audio can still
be treated as a representation of the original data. Because different TSM
methods work differently though, it is expected that the methods will produce
audio that sounds different.

In this subsection we briefly describe several widely used TSM methods,
originally developed primarily for music, which we will apply to ULF wave
observations. For further discussion of the details behind these methods see
the review of Driedger and Müller (2016) and/or our provided software.
Throughout this subsection the input refers to the extracted ULF waves from
the original spacecraft time series, consisting of $N$ data samples (the
spacecraft time range used multiplied by the spacecraft sampling rate).
Several of the methods are based on overlap–add procedures. These take
analysis frames, highly overlapping windows spaced by the analysis hop, from
the input data. Throughout we have set the length of the analysis frames to be
512 samples ($25\,\mathrm{min}$) as this is the closest power of two to the
length of the running average used to extract the waves. The analysis frames
are individually manipulated, depending on the TSM method used, and then
relocated on the audio time axis as synthesis frames with corresponding
synthesis hop. The slightly overlapping synthesis frames are then added
together, essentially performing multiple copies of very similar parts of the
original data, yielding the output. This gives the desired TSM of the input
data by a stretch factor equal to the ratio of analysis to synthesis hops. The
output thus contains more data samples but covers the same spacecraft time
range in UTC, with the periodicities of oscillations (shorter than the frame
length) in terms of data samples having been preserved. In general one has a
freedom in what fraction of the frame length to use as the synthesis hop. This
has been tested and we report which choices seemed to yield the best results
when applied to magnetospheric ULF waves. Mathematically it is possible to
reproduce the original signal following an overlap-add procedure with no
modifications subject to some simple constraints on the windowing function
(Sharpe, 2020). Therefore, if the modifications are also invertible then
overlap-add based TSM methods should also be reversible. Figure S1 shows an
example of applying first stretching and then compression of time for each TSM
method to an idealised chirp ULF wave signal with added noise.

####  2.2.1 Waveform Similarity Overlap-Add (WSOLA)

Waveform Similarity Overlap-Add (WSOLA) is a TSM method that works in the time
domain as outlined in Figure 3. The only modification between the analysis and
synthesis frames are slight shifts in time to reduce any phase jumps present
in the output, with these shifts being determined for each successive frame
via cross correlation (Driedger and Müller, 2016). As a time-based procedure
WSOLA is known to have issues with transients much shorter than the analysis
frame length, causing these features to be repeated in the output. WSOLA is
also known to struggle when multiple harmonic sources are present, with only
the largest amplitude one being preserved in the output. For continuous
functions with no noise, the cross-correlation function should be smooth with
a well-defined peak. Therefore, the time-shifts applied in WSOLA are
invertible in principle. However, in practice the discrete-time nature of
digital data and the presence of substantial noise may hinder the
invertibility of WSOLA. The WSOLA example in Figure S1 (blue) shows that the
original periodicities are recoverable, but amplitudes and longer-term trends
may end up being rather different.

####  2.2.2 Phase vocoder

The phase vocoder TSM is a frequency domain overlap–add procedure that aims to
preserve the periodicities of all signal components. Figure 4 depicts how it
works through a Short Time Fourier Transform (STFT). Due to the coarse nature
of this transform in both time and frequency, to maintain continuity in the
output the STFT phases at each frequency need to be iteratively adjusted
(based on the phase differences between frames) before inversion, known as
phase propagation (Driedger and Müller, 2016). Therefore, the STFT spectrogram
(absolute magnitude of the transform) remains invariant under the phase
vocoder (note human hearing is relatively insensitive to phase; Meddia and
Hewitt, 1991; Moore, 2002). Transient signals tend to get somewhat smeared out
over timescales of around the frame length using this method. While locking
the phase of frequencies near peaks in the spectrum can reduce phase
artifacts, these nonetheless may still be present and are reported to have
rather distinct sounding distortions. The STFT is known to have an inverse
transform, however, again in practice the discrete application of this
transform to noisy data can result in artifacts such as time-aliasing (Allen,
1977). The example of its invertibility in Figure S1 (orange) demonstrates it
performs slightly better than WSOLA at recovering the original data.

####  2.2.3 PaulStretch

PaulStretch is an extreme sound stretching algorithm based on the phase
vocoder (Nasca, 2006). Instead of propagating the phase, which becomes
difficult for large TSM factors, the algorithm instead randomises all the STFT
phases, as shown in Figure 5. This results in a more smooth sound than the
phase vocoder method, with less repetition and distortion (Nasca, 2010).
Unlike the other methods presented here, PaulStretch is not suitable for TSM
factors less than unity (compression in time) as it will result in many phase
jumps due to the randomisation. The method may also result in the introduction
or modulation of amplitudes over timescales of the order of, or longer than,
the frame length, which while visible in the waveforms are not noticeably
audible typically. Since random numbers are applied to the phase, this method
would only be invertible if those random numbers were saved as part of the
process. Nonetheless, like the phase vocoder, PaulStretch leaves the STFT
spectrogram invariant.

####  2.2.4 Wavelet phase vocoder

The wavelet phase vocoder technique (henceforth simply wavelets) works rather
differently to the previous overlap-add procedures, as illustrated in Figure
6. It utilises a complex continuous wavelet transform of the data (Torrence
and Compo, 1998), a complete time-frequency (over) representation of the data
which consistently scales these two dimensions with one another (unlike the
STFT). This has the benefit that magnitude and phase are provided at each
frequency for all sampling times, rather than only at a small number of
specified analysis frames. The TSM procedure is simply an interpolation in
time of the wavelet coefficients (essentially different bandpasses) followed
by multiplying the unwrapped phase by the TSM factor (De Gersem et al., 1997).
The interpolation step increases the number of samples, lowering the pitch of
oscillations, which is subsequently corrected by rescaling the phases by the
same factor. The modified wavelet coefficients are then inverted back to a
time-series (Torrence and Compo, 1998). While wavelet reconstruction is
possible mathematically for continuous functions, it has been noted that this
is often not perfect in practice computationally (Lebedeva and Postnikov,
2014; Postnikov et al., 2016). The example of inversion in Figure S1 (yellow)
shows a constant phase offset has resulted, likely due to edge effects, but
otherwise the wavelet phase vocoder performs somewat similarly to its STFT
counterpart. The wavelet spectrogram is invariant under this TSM method.

###  2.3 Spectral whitening

The amplitudes of ULF wave magnetic field oscillations in general are largest
at the lowest frequencies and tend to decrease rapidly with increasing
frequency. This pattern is associated mostly with incoherent background noise,
whose overall levels vary depending on driving and magnetospheric conditions,
on top of which discrete resonances may also be present. However, because of
this trend, spectrograms tend to show undue prominence to the lowest
frequencies, making variations present at higher frequencies hard to discern.
Therefore, it is common to pre-whiten ULF wave spectra so that the background
spectrum is flat. A simple way to achieve this is through taking the time
derivative of the time-series before calculating spectra, since the amplitudes
approximately follow a $1/f$ Brownian/red noise relationship (e.g. Engebretson
et al., 1986; Russell et al., 1999). Such spectral whitening may also be
helpful for similar reasons in the sonification of ULF waves. Indeed, Archer
et al. (2018) produced audifications of both the original and time-derivatives
of the data. Here the whitening step is optionally undertaken after TSM, since
it was found that applying it beforehand had adverse effects on the time
stretching.

###  2.4 Audification

The final step is audification. To ensure that the audio waveforms are
constrained to the dimensionless range -1 to +1, the data is normalised by the
maximum absolute value. This normalised data is then written to audio using a
standard audio sampling frequency of 44,100 Hz, which as discussed earlier
renders most of the ULF wave bands audible since THEMIS measurements are made
every $3\,\mathrm{s}$ (Figure 1). While Archer et al. (2018) produced separate
mono tracks for each component of the magnetic field and a combined stereo
file containing all three components, here we only produce the separate files,
focusing in particular on the azimuthal component of the magnetic field as
this is most relevant to the Alfvén continuum (Southwood, 1974). The audio is
encoded in Waveform Audio File Format (WAV), an uncompressed and the most
common audio format. Archer et al. (2018) had used Ogg Vorbis compression,
which is near-lossless thereby reducing the file size efficiently, however, we
found that not all applications were able to robustly work with this format
(issues with the MP3 format introducing silence to the audio eliminating the
ability to relate audio time to spacecraft time were highlighted by Archer et
al., 2018).

##  3 Public dialogue

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).

###  3.1 Methods

An anonymous online survey was used for the public dialogue, where
participants were asked to rank audio clips and explain their reasoning.
Survey questions can be found in Table S1. The audio clips in each question
varied either the TSM method, TSM factor, or background noise spectrum. These
were applied to three different THEMIS events. It was deemed that having more
than three events would limit participation, due to the amount of time it
would take to complete the survey, and that the events chosen provided a good
range in ULF waves to apply the different methods to. Each event corresponds
to 3 full orbits of the THEMIS-E spacecraft starting and ending at perigees,
and thus are approximately 3 days in duration. They are shown in Figure 7.
Event 1 corresponds to a synthetic Alfvén continuum – a constant amplitude
chirp/sweep signal, i.e. $\sin\left(\Psi\left[t\right]\right)$ with
instantaneous frequency $f\left[t\right]=\partial_{t}\Psi\left[t\right]/2\pi$.
The frequencies are taken from the statistical Alfvén continuum calculations
of Archer et al. (2015, 2017) based on a large database of THEMIS density
observations. The average frequencies in the dawn sector as a function of
$L$-shell (neglecting plasmaspheric densities and assuming local azimuthal
symmetry) have been constructed and then mapped to a representative orbit. The
first orbit consists of the fundamental frequency plus low-level (standard
deviation of 10% the chirp amplitude) Brownian noise (Gardiner, 2009); the
second orbit is a superposition of the first and third harmonics (each at half
the previous amplitude) plus more intense noise (3 times greater); and the
third orbit is just the high-level of noise. The other two events correspond
to real data under different conditions. Event 2 covers 17–20 March 2012,
where THEMIS was in the dawn sector (05:40 MLT at apogee) and geomagnetic
conditions were active (minimum Dst was $-44\,\mathrm{nT}$). Event 3 covers
21–24 July 2011, where THEMIS was in the dusk sector (19:55 MLT at apogee) and
geomagnetic conditions were moderate (minimum Dst was $-20\,\mathrm{nT}$). All
the audio clips used in the survey can be found in Supplementary Data 2 of
Archer et al. (2022) or in the survey preview link provided.

####  3.1.1 Participants

Participants were recruited by advertising the study to public email lists for
those with relevant interests/expertise, such as music, citizen science, or
science communication. Social media posts were also used. A total of 140
people completed the survey over the month it was open, all of whom indicated
their consent as part of the survey itself. A breakdown of participants’ self-
identified expertise, shown in Figure S2, reveals we successfully targeted the
survey outside of the space science community, with a good mix of interest
groups.

####  3.1.2 Analysis

Both quantitative and qualitative analyses are employed, as the closed and
open questions in the survey generate different types of data.

The quantitative data comes in the form of rankings, where a rank of 1
corresponds to the most liked/favoured (i.e. the highest ranked) and $r_{max}$
corresponds to the least liked/favoured (i.e. the lowest ranked). The
proportions of all responses $p_{i}$ in each rank $r_{i}$ is determined. Based
on these, for each audio clip we construct a score calculated as

$\mathrm{Score}=\sum_{i=1}^{r_{max}}\frac{r_{max}-2r_{i}+1}{r_{max}-1}p_{i}$
(4)

where the fraction normalises each rank value to between -1 (least liked) and
+1 (most liked), hence the score is also constrained to this range. The scores
are then averaged over the three events to give an overall score for that
option. 95% confidence intervals in these overall scores are estimated by
bootstrapping the same calculations over the participants (Efron and
Tibshirani, 1993), where 5,000 different random samples with replacement are
employed.

Thematic analysis (Braun and Clarke, 2006) is used to analyse the meaning
behind the open-text questions. This finds patterns, known as qualitative
codes, in the data which are then grouped into broader related themes. The
themes and codes are defined by induction, where they are iteratively
determined by going through samples of the qualitative data rather than being
pre-defined (Silverman, 2010; Robson, 2011). Once finalised, the themes and
codes are applied to the full dataset by the primary coder and indicative
quotes are identified. A second coder independently analysed a subset of the
data (30 participants’ responses, corresponding to 21%) to check reliability.
Average agreement across the different themes ranged from 73–95%. A typical
measure of reliability in coding qualitative data is Cohen’s kappa, a
statistic between 0 and 1, given by unity minus the ratio of observed
disagreement to that expected by chance (McHugh, 2012). Average values between
0.5–0.6 were found across the themes, which correspond to 70–80% of the
maximum achievable values given the uneven distributions of the data (Umesh et
al., 1989). All these statistics therefore indicate good agreement and thus
the qualitative analysis is reliable.

###  3.2 Results

All participants’ responses to the survey question can be found in
Supplementary Data 3. The quantitative results of the survey are shown in
Figure 8, depicting the proportions in each rank for the various options as
well as their scores. No obvious trends were present in the quantitative
results between different interest groups, hence we simply present all the
data together in this paper. Table 1 summarises the themes and their
underlying codes that were determined from the qualitative data, as well as
which question topics these pertained to. The application of these qualitative
codes to the open responses can be seen in Supplementary Data 4 of Archer et
al. (2022). One of the main themes was timbre, which refers to the perceived
quality of a sound. This theme encapsulates aspects of whether the sounds were
pleasant to listen to or if potential issues around ear fatigue were raised.
The codes in this theme thus are either positive, negative, or neutral. The
second theme concerned signal-to-noise or the perceived information content
within the sounds, i.e. whether the tones were discernible from the
background. Again the codes ranged from positive, through to neutral, or
negative. Issues around potential artifacts introduced by the processing were
raised as another theme. Many respondents also commented with synonymous
sounds, i.e. what they thought the audio “sounded like”. The final
themes/codes concerned whether it was possible to hear the detail present, if
listening to the sounds evoked a sense of boredom, and if the participants
desired more context on the intended usage of the sounds. All these themes
were present across the different interest groups. Not every participant
answered all the open-text questions, with response rates between
$88\text{--}94\%$. Some answers did not fit into all of the themes either,
with the two main themes of timbre and signal-to-noise being discussed on
average in 41% and 30% of responses respectively.

####  3.2.1 TSM method

Figure 8 indicates that the wavelets technique was by far the participants’
favourite TSM method. Its timbre was deemed to be the most pleasant to the
ear, with 57 positive responses compared to only 5 neutral and 3 negative

> “The best on all counts. Good depth, and richness in texture.” (Participant
> 3)
> “This had a softer sound, easier to listen to.” (Participant 41)

Many participants (a total of 37) noted that the results of this method evoked
the sounds of water. In terms of the signal-to-noise, 26 responses indicated
that the tones were sufficiently clear

> “Conveyed the frequencies effectively.” (Participant 6)
> “Clearly isolates the components of the signals.” (Participant 56)

Only 7 expressed the wavelets method was too noisy, though 16 responses
indicated more neutral responses within this theme

> “Very ‘harmonic’ sounds, but occasionally hard to differentiate.”
> (Participant 45)

PaulStretch had the second highest overall score. Generally it’s timbre was
thought of as positive (32 responses)

> “I like it, makes sounds very smooth and kind of diffuse.” (Participant 15)
> “This was also pleasing, but a little less than Wavelets.” (Participant 84)

but more neutral (14) and negative (13) comments were made than with wavelets

> “Kind of a middle ground between the watery feel of Wavelets and the glitchy
> techno of the other two” (Participant 14)
> “Felt very static filled and hard to listen to.” (Participant 128)

The most common synonymous sounds were those of wind or “natural” sounds. The
survey results were inconclusive on the signal-to-noise ratio present with
PaulStretch.

The phase vocoder method was ranked only slightly below PaulStretch – several
participants noted similarities in the sounds of the two, which is due to
their related methods. However, open responses were more negative (36
responses) on how this method sounded

> “Sounds like really terrible radio interference and is very jarring to the
> nerves.” (Participant 35)
> “The metallic character made it less pleasant to listen to” (Participant 25)

compared to 17 neutral and 6 positive comments. Results were again mixed on
the information content, however, potential artifacts associated with this
method were more commonly raised than before (12 responses)

> “This sounds like heavily processed noise cancelling DSP [digital signal
> processessing] which maybe good at recovering spoken words but heavily masks
> fundamental random signals.” (Participant 55)
> “Most unpleasant; phasing is the culprit.” (Participant 88)

WSOLA was clearly the least liked TSM method in the rankings. Indeed, almost
all comments on the sound quality were negative (70 responses)

> “Too much distortion for my taste, hard for me to listen to.” (Participant
> 86)
> “Totally unlistenable. It sounds like 4-bit digital audio.” (Participant
> 129)
> “Lack of amplitude dynamic[s] makes it almost painful to listen.”
> (Participant 135)

Similar to with the phase vocoder, results on the signal-to-noise were
inconclusive and processing artifacts were raised several times (17 responses)

> “Distortion artifacts are probably not real” (Participant 56)
> “Too much artificial noise sounds.” (Participant 103)

Therefore, the recommendation from our survey is that the wavelet phase
vocoder method is the preferred TSM method for application to magnetospheric
ULF waves. It may be possible to improve this method even further by
compensating for the spreading effects in time-frequency due to the mother
wavelet. Examples of this are the synchrosqueezed wavelet transform
(Daubechies et al., 2011) which uses reassignment in frequency, or superlets
(Moca et al., 2021) which is a geometric combination of sets of wavelets with
different bandwidths. Further work into how one may apply these to TSM is
required.

####  3.2.2 TSM factor

The result of the rankings shown in Figure 8 shows that a TSM factor of
$8\times$ was favoured, with $4\times$ somewhat close behind (this difference
is statistically significant though). TSM factors of $2\times$ and $16\times$
were both ranked poorly and the confidence intervals in their overall scores
overlap. The reason behind these scores could be gleaned from the open-text
responses. Participants stated that larger TSM factors allowed more time to
hear the detail of the signals within the clips, which was not possible with
the shortest clips (44 responses)

> “Length of audio clips coincided with perception of individual tones and
> increased clarity of sounds as the length increased.” (Participant 5)
> “I much prefer the longer audio lengths, because it allows me to hear the
> nuances in the received sound.” (Participant 78)
> “The 2x signal goes by too fast. Listener will miss small changes in the
> signal.” (Participant 59)

However, in contrast, it was felt that the longest clips may induce boredom in
the listener (30 responses)

> “While having a 30 second clip would be ideal, it feels tedious and boring
> and not ‘fun’ to listen to. It also can be quite painful to listen to some
> of the tracks at full length.” (Participant 5)
> “Generally the $16\times$ feels dragging too slow and information can be
> obtained from faster speeds.” (Participant 20)

Thus the consensus was that the two middle options provided a compromise to
both these themes, though individuals’ preferences varied between $4\times$
and $8\times$. 11 participants raised that to best answer the question on the
TSM factor they would have preferred to know more about the context of the
sounds, their intended uses, and any tasks associated with them. We
intentionally did not provide this, however, as our aim was to arrive at broad
recommendations on the sonification of magnetospheric ULF waves that may be
applied in a variety of contexts and settings.

The recommendation on TSM factor from the survey would be to use a value of
$\sim 6\times$, based on the average (either arithmetic or geometric) TSM
factors for $4\times$ and $8\times$ using the overall scores as weights.

####  3.2.3 Noise spectrum

Participants’ preferences in terms of the background noise spectrum of the
audio were somewhat split, as shown in Figure 8, with overall 57% preferring
red noise (audification of $\mathbf{B}$) to white noise
($\partial_{t}\mathbf{B}$). The confidence intervals for the scores also are
not constrained to simply positive or negative. Therefore, the quantitative
results do not provide a clear recommendation. However, the qualitative data
provides further insight. While opinions on which had the more pleasant timbre
were again somewhat split, comments on the harshness of the white noise (23
responses) outweighed those of the red (8 responses) with many references to
the higher frequencies present being the cause of this

> “The white noise has higher frequencies, which is giving me some ear
> fatigue.” (Participant 19)
> “This noise hurts my ears and gives me a headache. It is sharper and
> tinnier.” (Participant 26)

However, it was recognised that the spectral whitening made it easier to
distinguish the signals (30 responses)

> “The tones seemed clearer against this as a backdrop.” (Participant 21)
> “This process provides a full spectrum appreciation of the underlying
> signals that are not bandwidth limited due to masking or filtering.”
> (Participant 55)

whereas the red noise sounded somewhat “muffled” and less clear.

The spectral whitening of ULF waves is used to make signals over a wide range
of frequencies clearer in spectrograms, since the background spectrum becomes
approximately constant with frequency (Engebretson et al., 1986; Russell et
al., 1999). The same power value in the spectrogram relative to the background
at different frequencies therefore can be seen as the same colour on the
chosen colourmap. However, the survey results highlight that the same level of
intensity of sound at different frequencies are not perceived as the same
loudness. Indeed, human hearing is most sensitive to higher frequencies in the
range $2\text{--}5\,\mathrm{kHz}$, which is likely the reason for the comments
on the harshness of the white noise. Equal-loudness contours have been
determined, which specify what sound pressure levels at different frequencies
are perceived as being at the same loudness level (International Organization
for Standardization, 1987; Suzuki, 2004). Therefore, rather than modifying the
spectrum of the ULF waves for sonification to be flat in intensity they should
be adjusted for equal-loudness, which should be possible through applying
appropriate filtering (e.g. by modifying the magnitudes of the Fourier
transform after stretching). This should then have the benefits of making
tones discernible but not being too harsh on the ears.

##  4 Discussion

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 5 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 5
(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; Johnson-Groh, 2019; European Space Agency, 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 and DeWitt, 2021; Archer,
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 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.

## Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any
commercial or financial relationships that could be construed as a potential
conflict of interest.

## Author Contributions

MOA and MDH conceived of the study and supervised the project. MC, XS, SC, and
EDH contributed to the sonification method design and software development.
MOA, MDH, XS, MFJF, and EVM contributed to the survey design. MOA and MFJF
performed the analysis. MOA wrote the manuscript. All authors contributed to
manuscript revision, read, and approved the submitted version.

## Funding

MOA holds a UKRI (STFC / EPSRC) Stephen Hawking Fellowship EP/T01735X/1. MC
was funded by The Ogden Trust physics education grant PEGSU21\101 through
Imperial College London’s Undergraduate Research Opportunity Programme. MDH
was supported by NASA grant 80NSSC21K0796 and NASA grant 80NSSC19K0907. XS is
supported by NASA award 80NSSC19K0907.

## Acknowledgments

MOA would like to thank Sophia Laouici, Takudzwa Makoni, and Nivraj Chana,
whose preliminary work through undergraduate summer internships funded by The
Ogden Trust ultimately helped guide this study. We acknowledge NASA contract
NAS5-02099 and V. Angelopoulos for use of data from the THEMIS Mission.
Specifically: C. W. Carlson and J. P. McFadden for use of ESA data; K. H.
Glassmeier, U. Auster and W. Baumjohann for the use of FGM data provided under
the lead of the Technical University of Braunschweig and with financial
support through the German Ministry for Economy and Technology and the German
Center for Aviation and Space (DLR) under contract 50 OC 0302.

## Supplementary Material

Supplementary Table 1 The survey questions.

Supplementary Figure 1 Examples demonstrating the degree of reversibility of
TSM methods in practice.

Supplementary Figure 2 Venn diagram of survey participants’ self-identified
expertise.

## Data Availability Statement

The THEMIS data was obtained and processed using the software developed in
this study, which is available at https://github.com/Shirling-
VT/HARP_sonification. The survey and its embedded audio clips can be previewed
at
https://imperial.eu.qualtrics.com/jfe/preview/SV_295iuL4yxfaQ0Qu?Q_CHL=preview&Q_SurveyVersionID=current.
All other data used is available in Archer et al. (2022).

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> radiation belt.  _J. Geophys. Res._ 114, A10204.  doi:10.1029/2009JA014393
>
> ## Tables
>
> Question subject(s) | Theme | Codes
> ---|---|---
> TSM method & noise spectrum | Timbre | Positive
> Neutral
> Negative
> Signal-to-noise | Positive
> Neutral
> Negative
> TSM method | Artifacts
> Synonymous sounds
> TSM factor | Detail
> Boredom
> Context
> Table 1: Themes and codes from the qualitative data. Sonification choice | Recommendation
> ---|---
> TSM method | Wavelet phase vocoder
> TSM factor | $6\times$
> Noise spectrum | Equal-loudness contour
> Audio sampling rate | 44,100 Hz
> Waveform amplitude | Normalisation per interval
> Table 2: Final recommendations on ULF wave sonification.
>
> ## Figure captions
>
> Figure 1: Relationship between spacecraft time and frequency to audio time
> and frequency in audification for different ratios of sampling rates. ULF
> wave bands are also highlighted.
>
> Figure 2: Flow chart of the sonification processes used.
>
> Figure 3: Illustration of the Waveform Similarity and Overlap Add (WSOLA)
> method.
>
> Figure 4: Illustration of the Phase Vocoder method.
>
> Figure 5: Illustration of the PaulStretch method.
>
> Figure 6: Illustration of the Wavelet phase vocoder method. Note the shorter
> time range presented due to the different method.
>
> Figure 7: The three example THEMIS ULF wave events used in the survey. Top
> panels show the azimuthal component of the magnetic field with bottom panels
> showing its Short Time Fourier Transform spectrograms with a logarithmic
> colour scale, where the background has been spectrally whitened.
>
> Figure 8: Quantitative results of the survey. Stacked bars show the
> proportions of each ranking from least liked (dark red, far left) to most
> liked (dark blue, far right). The score for each audio clip is indicated by
> the grey bars, with the overall score across all 3 clips for each group
> shown as the black marker along with its 95% confidence interval. Note that
> for TSM methods and TSM factors there were four possible options, and thus
> also four possible ranks, while for noise spectrum there were only two.