# Understanding the effects of spacecraft trajectories through solar coronal
mass ejection flux ropes using 3DCOREweb

Hannah T. Rüdisser Austrian Space Weather Office, GeoSphere Austria, Graz,
Austria  Institute of Physics, University of Graz, Graz, Austria Hannah T.
Rüdisser<EMAIL_ADDRESS>Andreas J. Weiss NASA Postdoctoral
Program Fellow, NASA Goddard Space Flight Center, Greenbelt, MD, USA  Justin
Le Louëdec Austrian Space Weather Office, GeoSphere Austria, Graz, Austria
Ute V. Amerstorfer Austrian Space Weather Office, GeoSphere Austria, Graz,
Austria  Christian Möstl Austrian Space Weather Office, GeoSphere Austria,
Graz, Austria  Emma E. Davies Austrian Space Weather Office, GeoSphere
Austria, Graz, Austria  Helmut Lammer Space Research Institute, Austrian
Academy of Sciences, Graz, Austria

(Received May 3, 2024; Revised June 7, 2024)

###### Abstract

This study investigates the impact of spacecraft positioning and trajectory on
in situ signatures of coronal mass ejections (CMEs). Employing the 3DCORE
model, a 3D flux rope model that can generate in situ profiles for any given
point in space and time, we conduct forward modeling to analyze such
signatures for various latitudinal and longitudinal positions, with respect to
the flux rope apex, at 0.8 au. Using this approach, we explore the appearance
of the resulting in situ profiles for different flux rope types, with
different handedness and inclination angles, for both high and low twist CMEs.
Our findings reveal that CMEs exhibit distinct differences in signatures
between apex hits and flank encounters, with the latter displaying elongated
profiles with reduced rotation. However, constant, non-rotating in situ
signatures are only observed for flank encounters of low twist CMEs,
suggesting the existence of untwisted magnetic field lines within CME legs.
Additionally, our study confirms the unambiguous appearance of different flux
rope types in in situ signatures, contributing to the broader understanding
and interpretation of observational data. Given the model assumptions, this
may refute trajectory effects to be the cause for mismatching flux rope types
as identified in solar signatures. While acknowledging limitations inherent in
our model, such as the assumption of constant twist and non-deformable torus-
like shape, we still draw relevant conclusions within the context of global
magnetic field structures of CMEs and the potential for distinguishing flux
rope types based on in situ observations.

Solar coronal mass ejections(310) — Heliosphere(711) — Dynamical
evolution(421) — Solar wind(1534)

##  1 Introduction

A major unsolved problem in space weather forecasting is the correct
prediction of the time series of the solar wind magnetic field vector in near-
Earth space. In particular, spacecraft have observed structures in situ in the
solar wind inside interplanetary coronal mass ejections (ICMEs), which lead to
the strongest excursions in the total magnetic field. ICMEs typically comprise
a shock, sheath and magnetic ejecta, where the field vector smoothly rotates
up to 180∘ (Zurbuchen & Richardson, 2006). This is usually interpreted as the
observational signature of a spacecraft passing through a large scale magnetic
flux rope within the magnetic ejecta (Burlaga et al., 1981; Marubashi, 1986;
Burlaga, 1988), in which helical magnetic field lines are wound around a
central axis. This is described by the Lundquist (1950) or Gold & Hoyle (1960)
solutions of the basic equations of magnetohydrodynamics (MHD). This picture
has been generally accepted as the main concept capable of reconstructing the
global structure of CMEs, and towards predicting their in situ magnetic field
structure for space weather forecasting. Many different models have been
developed which are based on the flux rope hypothesis (e.g. Lepping et al.,
1990; Hidalgo & Nieves-Chinchilla, 2012; Isavnin, 2016; Möstl et al., 2018;
Rouillard et al., 2020; Nieves-Chinchilla et al., 2020). However, other
interpretations have been suggested. One such interpretation is spheromaks,
known as possible MHD solutions (Farrugia et al., 1995; Vandas & Romashets,
2017). Another interpretation involves a different kind of rotating magnetic
field that gives similarly rotating signatures emerging from simulations of
erupting flux ropes (Al-Haddad et al., 2013, 2019).

Following Bothmer & Schwenn (1998) and Mulligan et al. (1998), there exists a
comprehensive classification scheme for flux ropes, categorizing them into
eight distinct types based on their chirality and orientation in space. This
arises from a flux rope being characterized by both the poloidal field
wrapping around, and the axial field running parallel to the central axis. Low
inclination flux ropes have their central axis nearly parallel to the ecliptic
plane, which leads to a change of sign in the normal magnetic field component
$B_{n}$ upon crossing. Depending on their handedness and orientation of the
central axis, they can be classified as one of the following: left-handed:
North-West-South (NWS), South-East-North (SEN); right-handed: North-East-South
(NES), South-West-North (SWN). Flux ropes with their axis nearly perpendicular
to the ecliptic plane experience a sign change in the tangential component
$B_{t}$ and are termed high inclination flux ropes. The four different types
are: left-handed: East-North-West (ENW), West-South-East (WSE); right-handed:
East-South-West (ESW), West-North-East (WNE). A graphical representation of
the flux rope types is shown in Figure 1.

Figure 1: Graphic representation of the eight flux rope types: a) low
inclination flux rope types, and b) high inclination flux rope types. A 3DCORE
model is shown at the top for both low and high inclinations, and the
simplified sketches of the flux ropes together with the in situ profiles for
an apex hit for each flux rope type are visualised below. Each flux rope type
is labelled next to the corresponding sketch, along with its handedness (LH:
left-handed, RH: right-handed).

The global structure of CMEs is believed to have both ends of the flux rope
connected to the Sun for a considerable duration during its propagation
through the heliosphere. This is suggested by the presence of bidirectional
electron flows in some CMEs up to 1 au (e.g. Richardson, 1997; Shodhan et al.,
2000). Nevertheless, while Zurbuchen & Richardson (2006) proposed the legs of
a CME to contain highly twisted field lines, Owens (2016) suggested the
existence of “legs” of untwisted magnetic flux. This theory might serve as an
additional explanation for the appearance of ICME signatures that deviate from
the ideal flux rope signatures.

Although relatively rare, measurements of the same ICME by spacecraft at
multiple points over varying heliocentric distances and longitudinal
separations have provided valuable insights into their structural
characteristics. While there is a general consistency with the helical flux
rope (FR) model, it is noteworthy that not all ICMEs exhibit clear FR
structures. Different studies have highlighted significant variations among
individual ICMEs, deviating from overall statistical trends (for overviews see
Kilpua et al., 2009; Good et al., 2018; Lugaz et al., 2018; Salman et al.,
2020; Davies et al., 2022). This variability suggests possible deviations from
the classic flux rope hypothesis. These deviations may result from
interactions with other structures or the background solar wind, and from
different spacecraft measurement points and cuts through the ICME (e.g. Möstl
et al., 2009, 2012). Such factors particularly affect the flattening of the
circular cross section (e.g. Riley & Crooker, 2004; Owens et al., 2006; Savani
et al., 2010; Davies et al., 2021). For an overview on these various processes
CMEs undergo as they propagate away from the Sun, we refer the reader to
Manchester et al. (2017), Luhmann et al. (2020) and Temmer et al. (2023).

Regnault et al. (2023) recently highlighted the scarcity of simultaneous
multipoint measurements of the same ICME, emphasizing the need for more data
to enhance our understanding. Looking ahead, currently operating missions such
as Parker Solar Probe, Solar Orbiter, BepiColombo, Wind, and STEREO-A are
anticipated to contribute significantly to this field by providing additional
multipoint observations (e.g. Möstl et al., 2022; Lugaz et al., 2024). These
missions, currently operational within 1 au, offer opportunities to study a
broader range of ICME events and further refine our understanding of their
complex structures and dynamics.

A subset of magnetic flux ropes that can neither be fitted using the force-
free model (Lepping et al., 1990), nor be reconstructed with the Grad-
Shafranov technique (Hu & Sonnerup, 2002), are known as “magnetic-cloud-like”
(MCL, Lepping et al., 2006) ejecta. One special observational signature within
these that has puzzled researchers for a long time are so-called “back
regions” of ICMEs. These “back regions” follow after the main magnetic field
rotation of the flux rope has passed the observer. In these regions, the field
stays somewhat elevated, but does rotate only very slightly and the field
components remain essentially constant. Two explanations have been put forward
for this behaviour: (1) Ruffenach et al. (2012) show how magnetic reconnection
at the front of a CME is thought to alter the magnetic field signature in the
back of the flux rope. Due to the magnetic field lines of the flux rope
reconnecting with the interplanetary magnetic field at the front, the in situ
signature seems to have a tail or back region with little to no magnetic field
rotation but more or less constant components. Dasso et al. (2006, 2007) show
examples of ICME events exhibiting such tails or back regions interpreted as
results of magnetic reconnection as the CME propagates through the solar wind.
(2) Another explanation is based on the idea that the observer passes through
the flux rope in such a way that the constant field arises for a quasi-
stationary observer purely from a geometrical effect (Möstl et al., 2010) and
is actually part of the flux rope itself. In reality, both processes may
contribute to the ICME signature that is then observed by a spacecraft.

Improving modeling capabilities to account for the high complexity of CME
propagation and evolution has been a key element of studies within the past
years (e.g. Pomoell & Poedts, 2018; Sarkar et al., 2020; Pal et al., 2022; Kay
et al., 2023; Maharana et al., 2023). An investigation of the influence of
initial parameters of a CME MHD simulation on the results at different
latitudinal and longitudinal locations at 1 au has been conducted by Shen et
al. (2021). Their study indicated, that as long as the initial mass of the CME
remains unchanged, the initial geometric thickness will have a different
influence in the latitudinal and longitudinal direction. Scolini et al. (2021)
used a swarm of simulated spacecraft in radial alignment to study the
development of CME magnetic complexity during propagation. They were able to
relate the probability of detecting complexity changes to the interaction with
large-scale solar wind structures. Similarly, a swarm of synthetic spacecraft
at different latitudinal and longitudinal positions was used in Scolini et al.
(2023) to study the coherence of CMEs. Their simulations suggest a CME to
retain a lower complexity and higher coherence along its magnetic axis, while
still requiring crossings along both the axial and perpendicular directions
for a characterization of its global complexity. Additionally, coherence is
found to be lower in the west flank of the structure, due to Parker spiral
effects.

A study comparing stationary spacecraft and trajectories similar to Parker
Solar Probe in an MHD simulation was conducted by Lynch et al. (2022). Finding
in situ flux rope models to be generally applicable for the inference of some
physical properties, such as size and flux content, they conclude shortcomings
in the determination of the flux rope axis orientation.

In this study, we test two hypotheses: (1) Constant, non-rotating (CNR) in
situ signatures can be explained by an effect of the trajectory of an observer
through a 3D expanding magnetic flux rope, without invoking magnetic
reconnection as an explanation for those signatures. (2) Trajectory effects
can lead to a misinterpretation of flux rope types. According to Palmerio et
al. (2018), only about half of the studied events show a match regarding their
flux rope type, when comparing in situ observations to observations from the
Sun. Therefore, we investigate the appearance of different flux rope types for
different trajectories and attempt to validate or refute the second
hypothesis.

To this end, we employ the 3DCORE model, which is a 3D magnetic field model
for ICME flux ropes first presented by Möstl et al. (2018) and significantly
improved by Weiss et al. (2021a, b). We place up to 20 synthetic spacecraft at
0.8 au and analyze how their respective positions influence measured in situ
signatures. Thereby, we attempt to gain insight into how CNRs present in ICME
in situ signatures can be generated.

In Section 2, we give a short summary of the 3DCORE model in general and
report on a new tool called 3DCOREweb, which facilitates its open-source
usability. We additionally outline the general setup of the simulation. In
Section 3, we show the in situ signatures obtained by spacecraft at different
locations, and discuss these in Section 4.

##  2 Method

###  2.1 3DCOREweb

3DCORE is a semi-empirical 3D flux rope model, which is described in detail in
Weiss et al. (2021a, b). In the past, the model has proven successful in
inferring flux rope parameters by fitting in situ magnetic field observations
employing an Approximate Bayesian Computation-Sequential Monte Carlo (ABC-SMC)
method (e.g. Davies et al., 2021; Telloni et al., 2021; Möstl et al., 2022;
Long et al., 2023). In the case of limited longitudinal separations (within
$\sim 5^{\circ}$), even multipoint events have successfully been fitted
simultaneously (e.g. Davies et al., 2021; Weiss et al., 2021b). 3DCORE assumes
a torus-like shape with an embedded Gold-Hoyle-like magnetic field, based on
an analytical solution by Vandas & Romashets (2017). The structure is attached
to the Sun on both ends and expands self-similarly during its propagation. The
ambient solar wind is approximated using a constant solar wind speed as one of
the models input parameters. The interaction with the background solar wind is
considered through a simple drag model (Vršnak et al., 2013), allowing for the
frontal part of the CME to either be accelerated or decelerated, depending on
the relative speed of the ambient solar wind. By including an elliptical
cross-section through variation of the aspect ratio, propagation effects like
flattening of the flux rope in the direction of propagation (also known as
“pancaking”, Riley & Crooker, 2004) are approximated. A more thorough
explanation of the mathematical setup of the model and its 13 input parameters
can be found in Weiss et al. (2021a, b). These 13 parameters are: longitude,
latitude, inclination, diameter at 1 au ($D_{1\mathrm{au}}$), aspect ratio
($\delta$), launch radius ($R_{0}$), launch velocity ($V_{0}$), expansion rate
($n_{a}$), background drag ($\Gamma$), solar wind speed ($V_{sw}$), twist
factor ($T_{f}$), magnetic decay rate ($n_{b}$) and magnetic field strength at
1 au ($B_{1\mathrm{au}}$). The magnetic field within the toroidal structure is
given for custom curvilinear coordinates ($r\in\lceil 0,\infty)$,
$\psi\in\lceil 0,2\pi)$, $\phi\in\lceil 0,2\pi)$) based on the toroidal
coordinate system by

$\displaystyle B_{r}$ $\displaystyle=0$ (1a) $\displaystyle B_{\psi}$
$\displaystyle=\frac{B_{0}}{1+b^{2}r^{2}}$ (1b) $\displaystyle B_{\phi}$
$\displaystyle=\frac{B_{0}br}{(1+b^{2}r^{2})\left(1+r\frac{\rho_{1}}{\rho_{0}}\cos\phi\right)},$
(1c)

following a Gold-Hoyle-like solution described in Vandas & Romashets (2017),
with $B_{0}$ as the magnetic field at the central axis of the toroidal
structure and $b$ as a modified twist parameter defined as

$b=T_{f}\frac{\rho_{1}}{2\pi\rho_{0}}\sin\left(\frac{\psi}{2}\right)^{2}.$ (2)

where $\rho_{0}$ and $\rho_{1}$ define the major and minor radius of the base
torus, while the flux rope structure itself is defined by the implicit volume
$r\leq 1$. As defined in Weiss et al. (2021b), the twist factor $T_{f}$ used
as input parameter relates to the number of twists $\tau$ as
$\tau=T_{f}/E(\delta)$, where $E(\delta)$ is a function for the circumference
of an ellipse with a given aspect ratio $\delta$. The scaling laws are
implemented according to Leitner et al. (2007) as

$\displaystyle D(t)$ $\displaystyle=D_{1au}R_{apex}(t)^{n_{a}}$ (3a)
$\displaystyle B_{0}(t)$ $\displaystyle=B_{1au}R_{apex}(t)^{-n_{b}},$ (3b)

including the time dependency. $R_{apex}$ hereby refers to the distance of the
CME’s apex point to the Sun.

While the model’s simplicity allows for real-time application as well as the
generation of large ensembles, there are some drawbacks which have to be taken
into account. Examples of such drawbacks are the fixed flux rope width of
$180^{\circ}$, as well as the background solar wind speed which is assumed to
be constant throughout the heliosphere. While this implementation still
produces sufficiently reasonable results locally, the application to
multipoint events has shown that the global large-scale structure is not
adequately and realistically enough modelled to overcome large spacecraft
separations (Weiss et al., 2021b; Davies et al., 2024). In the past, this has
been circumvented by fitting both in situ spacecraft observations separately
and retrospectively comparing their results. This approach has yielded
meaningful conclusions, but still has to be considered when analysing and
interpreting model results. Additionally, deformations and deflections aside
from the flattening of the cross section as well as a non constant twist have
not yet been implemented. Nevertheless, these possible improvements are
already subject to further investigation (Weiss et al., 2022).

Recently, we have made an effort to increase the model’s usability through
3DCOREweb111https://github.com/hruedisser/3DCOREweb. A Dash (Plotly
Technologies Inc., 2015) application is available via GitHub and includes a
graphical user interface that can be used without any prior Python knowledge.
An example screenshot of this graphical user interface is shown in Figure 2.

Figure 2: A screenshot of the graphical user interface in 3DCOREweb, as
available via GitHub. This screenshot shows the subpage “Plot”, where the user
is able to create interactive 3D plots inserting the 3DCORE model into the
heliosphere. The panel on the left shows the details of the event, in this
case an ICME measured by Solar Orbiter (SOLO) on 2022-06-22. It also contains
the sliders to adjust the model input parameters. Above the plot, the user can
modify plotting options and visualize the temporal evolution by adjusting the
time slider. Furthermore, the user can visualize generated in situ signatures
of the model, use the ABC-SMC algorithm as introduced in Weiss et al. (2021a),
and analyse the results.

The user can choose to reconstruct ICME signatures from the HELIO4CAST ICME
catalog222https://helioforecast.space/icmecat, an extensive living catalog of
interplanetary coronal mass ejections (Möstl et al., 2020). Alternatively,
they can select a custom event for various spacecraft (e.g. Solar Orbiter,
Parker Solar Probe, STEREO-A) after the data is pre-downloaded from a given
repository. The straightforward implementation of the fitting algorithm as
well as a clear overview of the results facilitate the application of the tool
for the general scientific community. Additionally, we exploited the usage of
3DCORE as a simple forward modeling tool, including a large variety of Python
routines for modeling, analyzing and plotting.

###  2.2 Simulation Setup

Figure 3 presents an overview of the experiment setup for a low inclination
flux rope, placing 20 synthetic spacecraft at a radial distance of 0.8 au from
the Sun. Due to the simplified propagation and lack of interaction within the
model, we focus on a single radial distance in our study. This approach is
supported by Scolini et al. (2023), who reported a lack of increase in the
magnetic complexity of CMEs in the absence of interactions with other large-
scale structures. Furthermore, due to the self-similar expansion of the model,
observations at 0.8 au are representative of those at L1. Placing the
spacecraft at this distance avoids the added complexity of differing arrival
times at various longitudes, which would complicate interpretation of results
for spacecraft positioned at a greater distance from the Sun. While the
intermediate radial distance of 0.8 au is not as close to the Sun as the
perihelia of Solar Orbiter or Parker Solar Probe, it still provides a
realistic setting for typical events measured by spacecraft in the inner
heliosphere. The chosen distance ensures that in situ signatures span a
sufficiently long time period to enable adequate interpretability of results
and comparison between spacecraft. These considerations yield an experimental
setup that effectively balances the need for representative data and
manageable analysis. The respective positions of the spacecraft include five
longitudinal (the central meridian with respect to the CME, $\pm 30^{\circ}$,
$+45^{\circ}$ and $+60^{\circ}$) and four latitudinal planes (at the solar
equatorial plane, $\pm 5^{\circ}$, and $+15^{\circ}$). These are visualized by
different colors representing different latitudinal planes, as well as
different symbols for different longitudinal planes. The asymmetry of the
spacecraft distribution was chosen due to the inherent symmetry of the
structure introducing redundancy in the results.

Figure 4 shows the simulation setup similarly for a high inclination flux
rope, with 16 spacecraft in four longitudinal (the central meridian with
respect to the CME, $\pm 5^{\circ}$ and $+15^{\circ}$) and four latitudinal
planes (at the solar equatorial plane, $\pm 30^{\circ}$, and $+45^{\circ}$),
also at a radial distance of 0.8 au from the Sun. Since the longitudinal
extension of the high inclination flux rope is much smaller than for the low
inclination flux rope, fewer longitudinal planes are included, while the four
latitudinal planes are stretched out to account for the higher latitudinal
extension in this case.

The initial parameters as used for the model in 3DCOREweb are shown in Table
1. While inclination and twist are varied accordingly to produce the eight
different flux rope types (see Table 2), the other parameters are kept to
generic standard values to better compare the influence of the observers’
locations. Due to the model setup, inclination values of $0^{\circ}$ and
$180^{\circ}$ correspond to low inclination flux ropes with their central axis
pointing in opposite directions. Inclination values of $90^{\circ}$ and
$270^{\circ}$ lead to both orientations of high inclination flux ropes. For
the flux rope example in this study, a $T_{f}=50$ corresponds to a high twist
number of $\tau\approx 5$ turns and a $T_{f}=5$ corresponds to a low twist
number of $\tau\approx 0.5$ turns. The twist number $\tau$ is defined as the
total number of twists along the entire torus. These numbers are chosen in
agreement with Kahler et al. (2011), who estimated the number of field line
rotations over the assumed CME full length to be 1–10 turns. A visualization
of a single field line for both low and high twist CME can be seen in Figure
5, where the low twist field line is represented in blue, and the high twist
in red.

Figure 3: Synthetic spacecraft setup for the low inclination flux rope, shown from three different viewing angles: a) top view down from solar equatorial north, b) front view from the apex of the structure along the solar equatorial plane, c) angled view. Spacecraft positions include five longitudinal (the central meridian with respect to the CME, $\pm 30^{\circ}$, $+45^{\circ}$, and $+60^{\circ}$) and four latitudinal planes (at the solar equatorial plane, $\pm 5^{\circ}$, and $+15^{\circ}$) at 0.8 au radial distance from the Sun. Figure 4: Synthetic spacecraft setup for the high inclination flux rope, shown from three different viewing angles: a) top view down from solar equatorial north, b) front view from the apex of the structure along the solar equatorial plane, c) angled view. Spacecraft positions include four longitudinal (the central meridian with respect to the CME, $\pm 5^{\circ}$, and $+15^{\circ}$) and four latitudinal planes (at the solar equatorial plane, $\pm 30^{\circ}$, and $+45^{\circ}$) at 0.8 au radial distance from the Sun. Table 1: Model parameters longitude, latitude, inclination, diameter at 1 au ($D_{1\mathrm{au}}$), aspect ratio ($\delta$), launch radius ($R_{0}$), launch velocity ($V_{0}$), expansion rate ($n_{a}$), background drag ($\Gamma$), solar wind speed ($V_{sw}$), twist factor ($T_{f}$), magnetic decay ($n_{b}$), magnetic field strength at 1 au ($B_{1\mathrm{AU}}$), for low inclination and high inclination flux ropes with low and high $T_{f}$. The longitude and latitude of the flux rope apex are given in HEEQ coordinates. Parameters | Values | Units
---|---|---
Longitude | $0.$ | deg
Latitude | $0.$ | deg
Inclination |  $0.$ / $90.$ / $180.$ / $270.$ | deg
$D_{1\mathrm{AU}}$ | $0.3$ | au
$\delta$ | $2.$ |
$R_{0}$ | $20.$ | solar radii
$V_{0}$ | $600.$ | km/s
$n_{a}$ | $1.14$ |
$\Gamma$ | $1.$ |
$V_{\mathrm{sw}}$ | $500.$ | km/s
$T_{f}$ |  $50.$ / $5.$ / $-5.$ / $-50.$ |
$n_{b}$ | $1.64$ |
$B_{1\mathrm{au}}$ | $25.$ | nT
Table 2: Inclination and $T_{f}$ as set in the 3DCORE model for different flux rope types including both low and high twist values. Flux rope type | Handedness | Inclination [deg] |  $T_{f}$ (high twist) |  $T_{f}$ (low twist)
---|---|---|---|---
SWN | Right-handed | $180.$ | $50.$ | $5.$
NES | Right-handed | $0.$ | $50.$ | $5.$
NWS | Left-handed | $180.$ | $-50.$ | $-5.$
SEN | Left-handed | $0.$ | $-50.$ | $-5.$
WNE | Right-handed | $270.$ | $50.$ | $5.$
ESW | Right-handed | $90.$ | $50.$ | $5.$
ENW | Left-handed | $270.$ | $-50.$ | $-5.$
WSE | Left-handed | $90.$ | $-50.$ | $-5.$
Figure 5: A visualization of two field lines within the CME shape for high
twist of $T_{f}=50$ (red) and low twist of $T_{f}=5$ (blue).

By comparing the resulting in situ profiles, we investigate which
circumstances lead to CNRs. More precisely, we analyse the influence of flux
rope type, twist parameter and observer location on the measured in situ
signatures. Furthermore, we attempt to show whether flux rope types can be
unambiguously distinguished.

##  3 Comparison of Signatures

Figures 6 – 9 show the results. Each figure presents the synthetic in situ
measurements for a specific flux rope type as measured by the observers
described in Section 2.2. Each subplot coincides with one spacecraft, with
each row representing a different latitude and each column representing a
different longitude. The vertical axis shows the magnetic field $B(t)$ in nT
and the horizontal axis indicates the time that has passed since the launch of
the CME in hours. All three magnetic field components (radial $B_{r}$,
tangential $B_{t}$, normal $B_{n}$), as well as the total magnetic field
($B_{tot}$) are shown in RTN coordinates. We have chosen one low inclination
and one high inclination flux rope type, each with low twist and high twist
configurations. The general tendencies of how the signatures change upon
varying longitude and latitude are the same for each low/high flux rope type
and only differ regarding its handedness. Nevertheless, these figures have
been created for all flux rope types for completeness and can be found in the
Appendix.

###  3.1 High Twist Flux Ropes

Figure 6 shows the results for a low inclination and high twist SWN flux rope
type. As expected, the in situ signatures exhibit a bipolar $B_{n}$ component,
changing sign from negative (South) to positive (North), and a unipolar
$B_{t}$ component that stays positive (West).

Varying the spacecraft longitude from $-30^{\circ}$ to $+60^{\circ}$, $B_{r}$
shifts from positive to negative. Similar behaviour can also be observed when
varying latitude, with a negative latitude corresponding to a negative $B_{r}$
component and a positive latitude corresponding to a positive $B_{r}$. The
$B_{r}$ component stays 0 for the apex hit at both longitude and latitude
equal to 0. This pattern is also observed in other classic flux rope models
such as the Lundquist model, where the deviation of $B_{r}$ away from 0 gives
a sense of the distance of the spacecraft from the flux rope axis, otherwise
known as the impact parameter (Good et al., 2018; Lepping et al., 1990, 2006).
Additionally, moving from the apex to the flanks of the CME, the profile gets
stretched in time and the total change of the values in all components becomes
smaller. For the flank encounters, high latitudes do not measure any
signatures as the CME does not hit a synthetic spacecraft at that point, as
expected. Additionally, a larger radial width of the CME is traversed for a
latitude of $0^{\circ}$ compared to high latitudes. The high twist of the flux
rope is reflected in the significant rotation of the magnetic field vector
leading to a variation in all three components for apex hits and still a
considerable variation in $B_{n}$ for flank encounters. However, the overall
profile is notably stretched and flattened, meaning a reduced variation in
each magnetic field component. In future work, this could be investigated more
closely by calculating the difference between the maximum and minimum value of
each component. As this lies beyond the scope of our current study, we
determine the flatness of a profile only through visual inspection. In the
extreme cases of a latitude of $-15^{\circ}$ combined with a longitude of
$30^{\circ}$ or a latitude of $15^{\circ}$ combined with a longitude of
$-30^{\circ}$, $B_{t}$ is observed very close to 0.

Interestingly, the total magnetic field increases significantly for flank
hits. For an apex hit, the maximum $B_{tot}$ is only slightly more than 25 nT,
while for a longitude of $60^{\circ}$, $B_{tot}$ almost reaches 50 nT. The
observed effect arises from the tapering of the torus shape, resulting in an
inverse relationship between the torus radius and magnetic field strength.
Nevertheless, the validity of this assumption may be refined through future
investigations into multipoint events.

Figure 6: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a low inclination and high twist SWN type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots except for a longitude of $60^{\circ}$.

Figure 7 shows a high inclination and high twist WNE flux rope type. The high
inclination of the flux rope can be seen in the bipolarity of $B_{t}$,
changing sign from positive (West) to negative (East), and the unipolarity of
$B_{n}$, staying positive (North).

In the high inclination case in general, high latitudes correspond to flank
encounters, while the spacecraft in the solar equatorial plane experience apex
hits. Keeping this in mind, we observe similar patterns as for the high twist,
low inclination flux rope types (for example Figure 6), with flank encounters
producing considerably flatter in situ profiles compared to the apex hits.

Figure 7: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a high inclination and high twist WNE type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots.

Interestingly, we observe no CNRs for any of the high twist flux rope types,
even for flank hits. While the unipolar components show a less significant
variation for flank hits, the bipolarity of the respective component is
conserved throughout the whole structure. As a result, the components analysed
for the determination of the flux rope types are unambiguous, regardless of
where the CME hits the spacecraft. Nevertheless, we observe some extreme cases
for which the unipolar component is observed very close to 0 which might lead
to a misclassification of the flux rope type. One such example would be the
crossing at a a longitude of $-30^{\circ}$ and a latitude of $15^{\circ}$ for
the SWN type shown in Figure 6. Since the tangential component is very close
to 0, the flux rope might be mistaken as SEN type, as shown in Figure 12 of
the appendix for the crossing at a longitude of $30^{\circ}$ and a latitude of
$15^{\circ}$.

###  3.2 Low Twist Flux Ropes

Figures 8 and 9 show the low twist counterparts to Figures 6 and 7. Figure 8
shows the results for a low inclination and low twist SWN flux rope type. The
low twist of the flux rope leads to a very minor rotation of the magnetic
field. Compared to the pronounced bipolarity of $B_{n}$ for the high twist SWN
flux rope, only a very minor change from slightly negative to slightly
positive can be observed in this plot. Nevertheless, as $B_{t}$ appears very
flat, it is constantly positive and has a greater difference to 0 than for the
high twist counter part.

While apex hits already show very flat signatures, we observe CNRs for flank
hits. In contrast to Figure 6 and 7, that showed significantly higher
$B_{tot}$ values for flank hits compared to the corresponding apex hits, the
maximum total magnetic field is only slightly higher for flank hits compared
to an apex hit in this example.

Figure 8: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a low inclination and low twist SWN type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots except for a longitude of $60^{\circ}$.

Figure 9 shows a high inclination and low twist WNE flux rope type. The high
inclination of the flux rope can once again be identified by the bipolarity of
$B_{t}$, changing sign from positive to negative, and the unipolarity of
$B_{n}$, staying positive. Nevertheless, as for the low twist SWN type (Figure
8), the observed bipolarity is very minor.

Figure 9: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a high inclination and low twist WNE type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots.

As for all low inclination, low twist types, flank encounters produce
considerably flatter in situ profiles compared to the apex hits, leading to
CNR signatures. This makes a distinction of flux rope types based on in situ
signatures difficult, even for perfectly radial encounters. Furthermore, it
can be observed that several cases are almost indistinguishable (for example
Figure 9, latitude $45^{\circ}$, longitude $-15^{\circ}$ and $15^{\circ}$).
When disregarding the duration of the signatures, the difference between cases
is even more negligible. For example in Figure 9, longitudes of $30^{\circ}$,
$45^{\circ}$ and $60^{\circ}$ produce qualitatively equal results only varying
in their temporal extension.

##  4 Discussion and Conclusions

In this study, we investigated the effect of the position of a synthetic
spacecraft and the resulting trajectory at different latitudinal and
longitudinal locations at 0.8 au on the in situ magnetic field signatures
observed using 3DCOREweb. We investigated hypothesis (1), whether trajectory
effects could be a possible explanation for the observation of CNRs. We
discover that for a high twist CME, a flank hit results in a very flat in situ
profile with two out of three components not exhibiting a visible variation
that would indicate a rotation of the magnetic field vector. Nevertheless, the
third component still displays a bipolar signature, although it is much
flatter than observed for an apex hit. To observe a CNR, the CME had to be
initialized with a low twist and a flank hit had to be simulated. Relating our
findings to the general context of whether the legs of a CME might contain
twisted field lines, as studied in Owens (2016), further investigation of
multipoint events will be needed. While our initial findings suggest that
observing a constant field for a flank impact implies minimal twisting within
its legs, confirming this requires simultaneous measurements at the apex. This
would solidify whether the observed CME’s structure has varying levels of
twist throughout, rather than assuming it to be a generally low twist CME.

This also points out an obvious drawback of our model, namely the constant
twist and its non-deformable shape. The opening angle of $180^{\circ}$
prevents the modeling of a trajectory that experiences both an apex hit and a
flank encounter for the same CME. Keeping in mind that CMEs are thought to be
generally deformable structures (e.g. Manchester et al., 2017; Kilpua et al.,
2019; Luhmann et al., 2020), which may deviate strongly from our idealized
shape and thus in reality quite often experience such scenarios, limits the
accuracy of our model. Nevertheless, the separate analysis of flank encounters
and apex hits ties in with the possible explanation of trajectory effects
causing CNR signatures.

In the past, intrinsic flux rope types, as identified in solar signatures,
have often not matched the in situ flux rope types identified as investigated
in e.g. Palmerio et al. (2018). Throughout this work, we compared in situ
results for different flux rope types and investigated hypothesis (2), whether
flux rope types could be misinterpreted due to non-apex hits. For a low twist
CME, it appeared indeed to be challenging to identify the flux rope type, due
to CNRs observed for flank hits. Nevertheless, for high twist CMEs, the flux
rope type could be unambiguously assigned, regardless of where the impact
occurred, unless one of the identified rare cases of an almost zero unipolar
component occurred. While this hints towards the need for alternative
explanations for the mismatching of flux rope types from solar to in situ
observations, we have to consider that our model poses some very general
assumptions. For a deformable CME, as well as non-frontal encounters, this
could nonetheless be explained by trajectories and needs to be further
investigated. For a highly deformed flux rope, a spacecraft could potentially
be impacted by the front part of a CME, followed directly by a flank
encounter. In comparison to that, the self-similar expansion implemented in
our model combined with a stationary spacecraft leads to a highly idealized
frontal encounter with the flux rope, which might only partially model
reality. Especially for spacecraft in close proximity to the Sun, such as
Parker Solar Probe, a rapidly changing spacecraft position may have to be
taken into account when analysing CME encounters. Even though this has been
studied in Möstl et al. (2020) and the effect turned out to be negligible,
this study only looked at one particular type of encounter.

To further corroborate the validity of our results, we are awaiting the
possible occurrence of many more multipoint measurements in the near future.
Especially with Solar Orbiter due to commence probing higher latitudes and the
general increase in spacecraft measuring the solar wind, including the future
operational space weather mission Vigil, planned for launch by ESA in 2031, as
well as the approach of the maximum of solar cycle 25, statistical studies
will hopefully be facilitated.

Throughout this work, we confirm the substantial impact of both latitudinal
and longitudinal positions of spacecraft on the appearance of in situ
signatures. These results could significantly aid in future analysis of in
situ data, particularly in concluding the relative trajectory of the
spacecraft through the CME with respect to its propagation direction. However,
it is crucial to acknowledge the potential challenges in discerning between
similar profiles, especially in real-life scenarios. Our research highlights
that, especially in cases of low twist, distinctions among signatures at
different locations may be subtle, often distinguishable solely by their
duration. Yet, in real-world contexts, the duration could as well be
attributed to the CMEs thickness, complicating the determination of spacecraft
trajectory based solely on in situ profiles. Nonetheless, integrating
additional data sources, such as remote sensing observations or complementary
spacecraft measurements, holds promise for resolving certain ambiguities and
deriving meaningful conclusions regarding spacecraft trajectory.

In summary, our work not only contributes to advancing our understanding of in
situ observations but also underscores the necessity for a comprehensive
approach in interpreting such data, ultimately enhancing our ability to
navigate the complexities of space weather phenomena.

For the development of the 3DCOREweb application, we have benefited from the
availability of SolO, STEREO, Wind, PSP, and BepiColombo data, and thus would
like to thank the instrument teams and data archives for their data
distribution efforts. H.T. R., U.V. A., C. M., and E. D. are funded by the
European Union (ERC, HELIO4CAST, 101042188). Views and opinions expressed are
however those of the author(s) only and do not necessarily reflect those of
the European Union or the European Research Council Executive Agency. Neither
the European Union nor the granting authority can be held responsible for
them. A.J. W. acknowledges the financial support by an appointment to the NASA
Postdoctoral Program at NASA Goddard Space Flight Center, administered by Oak
Ridge Associated Universities through a contract with NASA. J. L. acknowledges
that this research was funded in whole, or in part, by the Austrian Science
Fund (FWF) [P 36093]. For open access purposes, the author has applied a CC BY
public copyright license to any author-accepted manuscript version arising
from this submission. A living version of 3DCOREweb can be found at
https://github.com/hruedisser/3DCOREweb. To allow the community to compare
future studies with our findings, the source code to generate the figures is
available as a Jupyter notebook at
https://github.com/hruedisser/3DCOREweb/blob/main/Signatures_Paper.ipynb and
is preserved on Zenodo at https://doi.org/10.5281/zenodo.11445313. Finally, we
sincerely thank the editor and reviewer for their helpful comments and
suggestions to substantially improve the quality of our research. The second
right-handed low inclination flux rope type NES is shown in Figure 10, for
which $B_{n}$ changes sign from positive to negative and $B_{t}$ remains
negative.

Figure 10: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a low inclination and high twist NES type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots except for a longitude of $60^{\circ}$.

Figures 11 and 12 show the left-handed counterparts NWS and SEN to these,
where the NWS type exhibits $B_{n}$ changing sign from positive to negative
and $B_{t}$ remaining positive, while the SEN type has $B_{n}$ changing sign
from negative to positive and $B_{t}$ remaining negative.

Figure 11: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a low inclination and high twist NWS type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots except for a longitude of $60^{\circ}$.
Figure 12: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a low inclination and high twist SEN type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots except for a longitude of $60^{\circ}$.

The second right-handed high inclination flux rope type is shown in Figure 13,
for which $B_{t}$ changes sign from negative to positive and $B_{n}$ remains
negative.

Figure 13: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a high inclination and high twist ESW type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots.

Figures 14 and 15 show the left-handed counterparts to these, where the ENW
type exhibits $B_{t}$ changing sign from negative to positive and $B_{n}$
remaining positive, while the WSE type has $B_{t}$ changing sign from positive
to negative and $B_{n}$ remaining negative.

Figure 14: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a high inclination and high twist ENW type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots. Figure 15: In situ measurements of the
synthetic spacecraft in different latitudes and longitudes for a high
inclination and high twist WSE type flux rope. For better comparison of the
times of arrival, the x-axis displays the same time range for all subplots.

Figure 16 shows the second right-handed low inclination flux rope type NES
$B_{n}$ changes sign from slightly positive to slightly negative and $B_{t}$
remains negative.

Figure 16: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a low inclination and low twist NES type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots except for a longitude of $60^{\circ}$.

Figures 17 and 18 show the left-handed counterparts to these, where the NWS
type exhibits $B_{n}$ changing sign from slightly positive to slightly
negative and $B_{t}$ remaining positive, while the SEN type has $B_{n}$
changing sign from slightly negative to slightly positive and $B_{t}$
remaining negative.

Figure 17: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a low inclination and low twist NWS type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots except for a longitude of $60^{\circ}$.
Figure 18: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a low inclination and low twist SEN type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots except for a longitude of $60^{\circ}$.

The second right-handed high inclination flux rope type is shown in Figure 19,
for which $B_{t}$ changes sign from slightly negative to slightly positive and
$B_{t}$ remains negative.

Figure 19: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a high inclination and low twist ESW type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots.

Figures 20 and 21 show the left-handed counterparts to these, where the ENW
type exhibits $B_{t}$ changing sign from slightly negative to slightly
positive and $B_{n}$ remaining positive, while the WSE type has $B_{t}$
changing sign from slightly positive to slightly negative and $B_{n}$
remaining negative.

Figure 20: In situ measurements of the synthetic spacecraft in different
latitudes and longitudes for a high inclination and low twist ENW type flux
rope. For better comparison of the times of arrival, the x-axis displays the
same time range for all subplots. Figure 21: In situ measurements of the
synthetic spacecraft in different latitudes and longitudes for a high
inclination and low twist WSE type flux rope. For better comparison of the
times of arrival, the x-axis displays the same time range for all subplots.

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# Generalization of Spoofing Countermeasures: a Case Study with ASVspoof 2015
and BTAS 2016 Corpora

###### Abstract

Voice-based biometric systems are highly prone to spoofing attacks. Recently,
various countermeasures have been developed for detecting different kinds of
attacks such as replay, speech synthesis (SS) and voice conversion (VC). Most
of the existing studies are conducted with a specific training set defined by
the evaluation protocol. However, for realistic scenarios, selecting
appropriate training data is an open challenge for the system administrator.
Motivated by this practical concern, this work investigates the generalization
capability of spoofing countermeasures in restricted training conditions where
speech from a broad attack types are left out in the training database. We
demonstrate that different spoofing types have considerably different
generalization capabilities. For this study, we analyze the performance using
two kinds of features, mel-frequency cepstral coefficients (MFCCs) which are
considered as baseline and recently proposed constant Q cepstral coefficients
(CQCCs). The experiments are conducted with standard Gaussian mixture model -
maximum likelihood (GMM-ML) classifier on two recently released spoofing
corpora: ASVspoof 2015 and BTAS 2016 that includes cross-corpora performance
analysis. Feature-level analysis suggests that static and dynamic coefficients
of spectral features, both are important for detecting spoofing attacks in the
real-life condition.

Index Terms—  Spoofing Attack, Replay Attack, ASVspoof 2015, BTAS 2016,
Generalized countermeasure.

##  1 Introduction

_Spoofing attacks_ imitate a person’s identity in order to gain illegitimate
access to sensitive or protected resources. Nowadays, significant advancement
in speech technology related to SS and VC techniques poses threat to speech-
based biometric systems like _automatic speaker verification_ (ASV) systems
[1]. _Replay attacks_ are another form of spoofing attack, where an adversary
tries to attack a system using pre-recorded speech accumulated from target
speakers [2]. Due to the availability of high-quality, low-cost recording and
playback devices, replay attacks are also a serious threat to the voice
biometric systems. Several replay spoofing detection approaches such as fixed
pass-phrase method, spectral ratio and modulation index were proposed in [3,
4, 5]. A study on cross database evaluation was demonstrated in [6].

To detect SS and VC attacks, diverse range of feature extraction methods such
as _mel-frequency cepstral coefficients_ (MFCCs) cepstral feature [7], phase
features [8, 9, 10], a combination of both amplitude and phase feature [11],
prosodic features [12] were reported. A concise experimental review of
spoofing detection was presented in [13]. While, MFCCs are considered as the
standard feature extraction techniques in speech processing, _constant Q
transform cepstral coefficients_ (CQCCs) have shown best detection
performance, especially for unknown attacks in ASVspoof 2015 corpus [14].
However, it was not implemented for replay attack detection.

Fig. 1: Spectrogram of (a) genuine and replay speech signals for same sentence
“The subject should read the sentences carefully”. The replayed signals are
generated by using techniques based on (b) replay laptop, (c) replay laptop
high quality, (d) replay phone, (e) SS, (f) replay SS, (g) replay SS high
quality, (h) VC, (i) replay VC and (j) replay VC high quality.

Techniques to generate voice converted speech and synthetic speech, made a
rapid progress in recent times. Notable among them are _joint density-Gaussian
mixture model_ (JD-GMM) [15], _line spectrum pairs_ (LSP) [16], MARY _text-to-
speech synthesis_ (MARY-TTS) [17], _hidden Markov model_ (HMM) based TTS [18]
etc. It is not practically possible to anticipate the kind of SS and VC attack
all the time to include those types of speeches in the training database. At
the same time, it is expected that detection performance will degrade if
similar kinds of data are unavailable in the training corpus. The previous
studies on spoofing detection do not focus on _attack dependency_ which is the
central theme of this work. There are some results generated in recent
spoofing challenges with _unknown attack_ types but no exhaustive study is
done that can lead to _generalization_ ability of certain training schemes
over other for a range of unknown attacks.

In this work, we did a systematic study of attack dependency to discover
corresponding generalization ability. We demonstrate the result using
conventional MFCCs and newly proposed CQCCs features on GMM-maximum likelihood
(GMM-ML) framework. It is found that GMM-ML as a classifier is better suited
for spoofing detection task [19]. We have experimented on two recent
databases: ASVspoof 2015, developed as a part of _Automatic Speaker
Verification Spoofing and Countermeasure Challenge_ [20] and BTAS 2016 corpus
in _Speaker Anti-spoofing Competition_ [21]. BTAS 2016 introduces more
realistic replay attacks compared to ASVspoof database. Our study shows the
generalization ability of one countermeasure over the other.

##  2 Generalization Framework

Figure 1 illustrates the spectral characteristics of spoofed signals for
diverse attacks. _Generalized countermeasure_ refers to the ability to
overcome the attack dependency in the detection process. This dependency
signifies the types of attacks that are best represented by a similar pattern
in the attack space. It involves a prior knowledge of attack type, which is
not a realistic assumption in all the cases. Therefore, the countermeasure
system needs to be robust enough to detect an attack even though that type of
attack data is not used for training the model. Fig. 2 describes the
functional block diagram of a generalized countermeasure framework where we
find which kind of training has greater generalization ability.

Fig. 2: A speech-based countermeasure system.

Initially, we train the models using all types of replay (i.e., genuine, SS
and VC samples) and synthetic (SS and VC samples) attacks. Then, we study the
impact when one type of spoofing data is not used for modeling the spoofed
data.

##  3 Experimental Setup

###  3.1 Database Description

ASVspoof 2015: ASVspoof database is created to assess ten different types of
SS and VC synthetic speech samples namely S1 to S10 [20]. It includes both the
known attacks (S1-S5) and the unknown attacks (S6-S10).

BTAS 2016: BTAS database contains genuine and different kinds of replay
attacks where genuine, SS and VC speech samples were played back using high-
quality devices. Two new replay unknown attacks (R9 and R10) are introduced in
the evaluation data to make it more challenging. The statistics regarding
types of attacks and the number of utterances for each dataset are presented
in Table 1.

Table 1: Number of utterances in BTAS 2016 database. LP: laptop, HQ: high quality speaker, PH1: Samsung Galaxy S4 phone, PH2: iPhone 3GS and ‘PH3’ is iPhone 6S. Types | Training | Development | Evaluation
---|---|---|---
Genuine | 4973 | 4995 | 5576
Replay | Replay LP LP | R1 | 700 | 700 | 800
Replay LP HQ LP | R2 | 700 | 700 | 800
Replay PH1 LP | R3 | 700 | 700 | 800
Replay PH2 LP | R4 | 700 | 700 | 800
Replay PH2 PH3 | R9 | - | - | 800
Replay LP PH2 PH3 | R10 | - | - | 800
SS | SS LP LP | R5 | 490 | 490 | 560
SS LP HQ LP | R6 | 490 | 490 | 560
VC | VC LP LP | R7 | 17400 | 17400 | 19500
VC LP HQ LP | R8 | 17400 | 17400 | 19500
Table 2: Performance (in % of EER) for MFCC and CQCC features on BTAS 2016 development data. The corresponding class of attacks that are not considered in the training are highlighted. | Train |  |  |  |  |  |  |  |  |  | Average
---|---|---|---|---|---|---|---|---|---|---|---
Features | Replay | SS | VC | Type | R1 | R2 | R3 | R4 | R5 | R6 | R7 | R8 | Replay | SS | VC | All
|  |  |  | Static | 0.14 | 0.61 | 0.09 | 0.00 | 0.00 | 0.84 | 0.00 | 0.02 | 0.21 | 0.42 | 0.01 | 0.21
|  |  |  |  Static+$\Delta\Delta^{2}$ | 0.34 | 2.74 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 | 0.01 | 0.77 | 0.29 | 0.01 | 0.46
| ✓ | ✓ | ✓ | $\Delta\Delta^{2}$ | 19.50 | 41.35 | 28.62 | 28.67 | 1.33 | 0.86 | 0.00 | 0.01 | 29.54 | 1.10 | 0.01 | 15.04
|  |  |  | Static | 4.91 | 5.92 | 30.33 | 24.56 | 0.00 | 1.07 | 0.01 | 0.01 | 16.43 | 0.54 | 0.01 | 8.35
|  |  |  |  Static+$\Delta\Delta^{2}$ | 4.73 | 6.98 | 30.51 | 26.29 | 0.00 | 0.65 | 0.01 | 0.00 | 17.13 | 0.33 | 0.01 | 8.65
| $\times$ | ✓ | ✓ | $\Delta\Delta^{2}$ | 25.44 | 44.39 | 34.34 | 35.52 | 1.33 | 1.10 | 0.00 | 0.01 | 34.92 | 1.23 | 0.01 | 17.77
|  |  |  | Static | 0.27 | 0.63 | 0.00 | 0.00 | 0.00 | 1.93 | 0.00 | 0.02 | 0.23 | 0.97 | 0.01 | 0.36
|  |  |  |  Static+$\Delta\Delta^{2}$ | 0.31 | 3.50 | 0.00 | 0.00 | 0.00 | 2.07 | 0.00 | 0.01 | 0.95 | 1.04 | 0.01 | 0.74
| ✓ | $\times$ | ✓ | $\Delta\Delta^{2}$ | 19.63 | 40.88 | 27.35 | 27.99 | 2.39 | 1.62 | 0.00 | 0.01 | 28.96 | 2.01 | 0.01 | 14.98
|  |  |  | Static | 0.00 | 0.30 | 0.00 | 0.00 | 0.00 | 0.04 | 0.32 | 2.13 | 0.15 | 0.02 | 1.23 | 0.35
|  |  |  |  Static+$\Delta\Delta^{2}$ | 0.04 | 0.08 | 0.00 | 0.00 | 0.00 | 0.02 | 0.55 | 0.85 | 0.03 | 0.01 | 0.70 | 0.19
MFCC | ✓ | ✓ | $\times$ | $\Delta\Delta^{2}$ | 2.44 | 24.05 | 5.80 | 2.69 | 0.14 | 0.85 | 3.60 | 6.30 | 8.75 | 0.50 | 4.95 | 5.73
|  |  |  | Static | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
|  |  |  |  Static+$\Delta\Delta^{2}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
| ✓ | ✓ | ✓ | $\Delta\Delta^{2}$ | 20.04 | 6.43 | 25.22 | 41.05 | 1.10 | 0.11 | 0.09 | 0.18 | 23.19 | 0.61 | 0.14 | 11.78
|  |  |  | Static | 1.27 | 0.00 | 47.71 | 40.84 | 0.00 | 0.00 | 0.00 | 0.00 | 22.46 | 0.00 | 0.00 | 11.23
|  |  |  |  Static+$\Delta\Delta^{2}$ | 8.25 | 0.00 | 49.18 | 44.75 | 0.00 | 0.00 | 0.00 | 0.00 | 25.55 | 0.00 | 0.00 | 12.77
| $\times$ | ✓ | ✓ | $\Delta\Delta^{2}$ | 25.07 | 9.36 | 33.72 | 43.77 | 1.03 | 0.23 | 0.09 | 0.19 | 27.98 | 0.63 | 0.14 | 14.18
|  |  |  | Static | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
|  |  |  |  Static+$\Delta\Delta^{2}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
| ✓ | $\times$ | ✓ | $\Delta\Delta^{2}$ | 20.31 | 6.48 | 25.54 | 40.93 | 2.26 | 0.20 | 0.08 | 0.18 | 23.32 | 1.23 | 0.13 | 12.00
|  |  |  | Static | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
|  |  |  |  Static+$\Delta\Delta^{2}$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
CQCC | ✓ | ✓ | $\times$ | $\Delta\Delta^{2}$ | 10.52 | 2.71 | 18.08 | 29.93 | 0.41 | 0.30 | 2.46 | 2.89 | 15.31 | 0.36 | 2.68 | 8.37
Table 3: Performance (in % of EER) for MFCC and CQCC (static) features on BTAS 2016 evaluation data. The corresponding class of attacks that are not considered in the training systems are highlighted. | Train |  |  |  |  |  |  |  |  |  |  | Average
---|---|---|---|---|---|---|---|---|---|---|---|---
Features | Replay | SS | VC | R1 | R2 | R3 | R4 | R5 | R6 | R7 | R8 | R9 | R10 | Replay | SS | VC | All
| ✓ | ✓ | ✓ | 1.11 | 8.26 | 0.01 | 0.14 | 0.06 | 3.67 | 0.03 | 1.68 | 17.87 | 10.85 | 6.37 | 1.87 | 0.86 | 4.37
| $\times$ | ✓ | ✓ | 6.61 | 16.12 | 32.89 | 24.38 | 0.14 | 5.34 | 0.06 | 2.88 | 30.50 | 40.89 | 25.23 | 2.74 | 1.47 | 15.98
| ✓ | $\times$ | ✓ | 1.42 | 8.41 | 0.02 | 0.11 | 0.73 | 5.80 | 0.04 | 1.84 | 18.21 | 10.23 | 6.40 | 3.27 | 0.94 | 4.68
MFCC | ✓ | ✓ | $\times$ | 0.22 | 2.31 | 0.00 | 0.00 | 0.00 | 0.16 | 3.06 | 4.90 | 19.47 | 6.59 | 4.77 | 0.08 | 3.98 | 3.67
| ✓ | ✓ | ✓ | 0.00 | 0.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.56 | 0.00 | 1.27 | 0.00 | 0.00 | 0.76
| $\times$ | ✓ | ✓ | 7.20 | 0.43 | 48.79 | 43.96 | 0.00 | 0.00 | 0.00 | 0.01 | 10.02 | 32.76 | 23.86 | 0.00 | 0.10 | 14.32
| ✓ | $\times$ | ✓ | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 | 0.00 | 0.00 | 13.08 | 0.03 | 2.19 | 0.10 | 0.00 | 1.33
CQCC | ✓ | ✓ | $\times$ | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.01 | 12.19 | 0.03 | 2.04 | 0.00 | 0.13 | 1.25

###  3.2 Feature Extraction Techniques

Mel-frequency cepstral coefficients (MFCCs): MFCC [22] feature utilizes mel-
scale based triangular filter bank. The power spectrum is integrated using
overlapping band-pass filters in the triangular filterbank. We use the
configuration reported in [13].

Constant Q cepstral coefficients (CQCCs): The constant Q transform (CQT) gives
a higher frequency resolution in lower frequencies and a greater temporal
resolution in the higher frequency region. A spline interpolation method is
applied to resample the geometric frequency scale into a uniform linear scale
in order to apply linearly spaced DCT coefficients for CQCC cepstral feature
computation [14].

CQCC feature is implemented with maximum frequency $(f_{max}=4Khz)$ and
minimum frequency of $(f_{min}=15Hz)$. The number of bins per octave is
assigned to 96. Speech activity detector (SAD) is not employed as non-speech
frames could be helpful for spoofing detection.

###  3.3 Classifier and Performance Evaluation

We employ GMM-ML classifier for spoofing detection. Two target models
$\boldsymbol{\lambda}_{n}$ and $\boldsymbol{\lambda}_{s}$ are created from
natural and spoofed speech data respectively [23]. The log-likelihood score is
calculated as,
$\Lambda(\mathbf{X})=\mathcal{L}(\textbf{X}|\boldsymbol{\lambda}_{n})-\mathcal{L}(\mathbf{X}|\boldsymbol{\lambda}_{s}),$
where $\mathbf{X}=\\{\mathbf{x}_{1},\ldots,\mathbf{x}_{T}\\}$ is the feature
matrix of the test utterance, $T$ is the number of frames and
$\mathcal{L}(\textbf{X}|\boldsymbol{\lambda})$ is the average log-likelihood
of X given GMM model $\boldsymbol{\lambda}$. We train GMMs with 10 iterations
of expectation-maximization (EM) algorithm and 512 mixture components.

Equal error rate (EER) is used as the performance metric to evaluate spoofing
attack detection. We use BOSARIS toolkit [24] to calculate the EER using
receiver operating characteristics convex hull (ROCCH) method.

Table 4:  Same as Table 2 but for ASVspoof 2015 evaluation. | Train |  |  |  |  |  |  |  |  |  |  |  | Average
---|---|---|---|---|---|---|---|---|---|---|---|---|---
Features | SS | VC | Type | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | S9 | S10 | SS | VC | All
|  |  | Static | 1.54 | 7.54 | 0.00 | 0.00 | 6.80 | 5.33 | 2.25 | 0.04 | 2.12 | 26.66 | 8.89 | 3.66 | 5.23
| ✓ | ✓ | $\Delta\Delta^{2}$ | 0.09 | 1.46 | 0.00 | 0.00 | 0.36 | 0.30 | 0.02 | 0.03 | 0.02 | 19.45 | 6.48 | 0.33 | 2.17
|  |  | Static | 1.64 | 7.35 | 0.32 | 0.35 | 5.93 | 5.07 | 2.47 | 0.07 | 2.67 | 30.68 | 10.45 | 3.60 | 5.66
| $\times$ | ✓ | $\Delta\Delta^{2}$ | 0.00 | 1.07 | 0.30 | 0.28 | 0.25 | 0.25 | 0.01 | 0.17 | 0.01 | 22.08 | 7.55 | 0.25 | 2.44
|  |  | Static | 19.46 | 35.82 | 0.00 | 0.00 | 35.16 | 34.41 | 26.98 | 0.26 | 24.54 | 8.97 | 2.99 | 25.23 | 18.56
MFCC | ✓ | $\times$ | $\Delta\Delta^{2}$ | 40.96 | 29.02 | 0.00 | 0.00 | 11.21 | 11.39 | 2.18 | 0.19 | 2.57 | 26.23 | 8.74 | 13.93 | 12.38
|  |  | Static | 0.02 | 0.44 | 0.00 | 0.00 | 1.54 | 1.04 | 0.09 | 0.15 | 0.13 | 19.11 | 6.37 | 0.49 | 2.25
| ✓ | ✓ | $\Delta\Delta^{2}$ | 0.02 | 0.31 | 0.01 | 0.03 | 0.27 | 0.25 | 0.12 | 2.29 | 0.15 | 0.94 | 0.33 | 0.49 | 0.44
|  |  | Static | 0.03 | 1.43 | 0.10 | 0.07 | 1.43 | 1.19 | 0.08 | 0.59 | 0.14 | 21.77 | 7.31 | 0.70 | 2.68
| $\times$ | ✓ | $\Delta\Delta^{2}$ | 0.01 | 0.08 | 4.17 | 3.86 | 0.08 | 0.12 | 0.07 | 5.93 | 0.12 | 0.72 | 2.92 | 0.92 | 1.52
|  |  | Static | 2.68 | 16.24 | 0.00 | 0.00 | 25.74 | 22.09 | 10.56 | 0.05 | 12.22 | 6.05 | 2.02 | 12.80 | 9.56
CQCC | ✓ | $\times$ | $\Delta\Delta^{2}$ | 26.59 | 7.86 | 0.01 | 0.03 | 7.86 | 7.85 | 1.90 | 2.09 | 2.96 | 35.20 | 11.75 | 8.16 | 9.24
Table 5:  Cross corpora evaluation performance (in % of EER) on BTAS 2016 evaluation data trained using ASVspoof 2015 training dataset. | Train |  |  |  |  |  |  |  |  |  |  |  | Average
---|---|---|---|---|---|---|---|---|---|---|---|---|---
Features | SS | VC | Type | R1 | R2 | R3 | R4 | R5 | R6 | R7 | R8 | R9 | R10 | Replay | SS | VC | All
|  |  | Static | 46.91 | 50.00 | 50.00 | 50.00 | 46.68 | 49.94 | 42.47 | 49.28 | 46.05 | 50.00 | 48.83 | 48.31 | 45.88 | 48.13
| ✓ | ✓ | $\Delta\Delta^{2}$ | 49.93 | 34.39 | 49.88 | 49.82 | 34.31 | 4.92 | 3.97 | 4.80 | 44.62 | 49.87 | 46.42 | 19.62 | 4.39 | 32.65
|  |  | Static | 46.54 | 50.00 | 50.00 | 50.00 | 46.53 | 49.97 | 42.77 | 49.44 | 45.90 | 49.16 | 48.60 | 48.25 | 46.11 | 48.03
| $\times$ | ✓ | $\Delta\Delta^{2}$ | 49.94 | 35.39 | 49.61 | 49.19 | 39.74 | 7.42 | 3.20 | 3.29 | 47.89 | 49.85 | 46.98 | 23.56 | 3.25 | 33.55
|  |  | Static | 50.00 | 49.98 | 43.23 | 47.96 | 50.00 | 49.99 | 50 | 46.14 | 50 | 49.97 | 48.52 | 50 | 48.07 | 48.73
MFCC | ✓ | $\times$ | $\Delta\Delta^{2}$ | 50.00 | 47.42 | 49.97 | 50.00 | 20.03 | 3.26 | 14.32 | 10.67 | 50.00 | 49.98 | 49.56 | 11.65 | 12.50 | 34.57
|  |  | Static | 48.50 | 49.96 | 38.68 | 44.14 | 41.39 | 49.88 | 49.94 | 49.16 | 49.96 | 45.21 | 46.08 | 45.64 | 49.55 | 46.68
| ✓ | ✓ | $\Delta\Delta^{2}$ | 47.67 | 36.43 | 49.68 | 50 | 19.42 | 17.29 | 18.11 | 19.97 | 46.64 | 49.08 | 46.58 | 18.36 | 19.04 | 35.43
|  |  | Static | 48.38 | 49.96 | 42.89 | 45.88 | 41.74 | 49.88 | 49.96 | 49.95 | 49.96 | 45.03 | 47.05 | 45.81 | 49.96 | 47.36
| $\times$ | ✓ | $\Delta\Delta^{2}$ | 47.83 | 40.07 | 49.57 | 49.94 | 30.61 | 31.82 | 27.10 | 28.22 | 42.81 | 48.44 | 46.44 | 31.22 | 27.66 | 39.64
|  |  | Static | 49.99 | 49.92 | 40.11 | 49.99 | 45.22 | 49.96 | 49.99 | 47.36 | 50.00 | 50.00 | 48.34 | 47.59 | 48.68 | 48.25
CQCC | ✓ | $\times$ | $\Delta\Delta^{2}$ | 44.44 | 46.12 | 42.62 | 49.47 | 9.87 | 13.80 | 21.89 | 23.71 | 49.95 | 49.96 | 47.09 | 11.84 | 22.80 | 35.18

##  4 Results and Analysis

###  4.1 BTAS 2016

We first conduct an experiment on BTAS 2016 replay spoofing development
dataset to investigate the effects of different training data. The aim is to
learn the system’s ability to detect spoofed signals generated by various
spoofing algorithms that are not incorporated in the training phase. Overall
performance evaluation results on eight replay attacks (R1-R8), obtained using
conventional MFCC and proposed CQCC feature based countermeasures are reported
in Table 2. Due to attack dependency, the performance degrades drastically
when one attack type is excluded from training the models and when the system
is confronted with the similar type of attack in the system assessment
process. We also observe that including direct replay in training helps for
both SS and VC but not vice versa. This can be justified by the fact that SS
and VC attacks are different whereas replay attacks have high similarity with
genuine speech in terms of frequency components and formant trajectories [1].
Consequently, the replay speech characteristics of natural signal cannot be
captured properly when they are eliminated from training the models.
Interestingly, the static spectral features lead to promising recognition
accuracy as opposed to their dynamic counterparts. This is in contrast to
previous studies [13, 14].

We perform further experiments for only static features on the evaluation
dataset. The overall and individual results are reported in Table 3. CQCC
feature yields superior result in all training conditions. This probably can
be explained by the fact that CQCC feature provides higher resolution in lower
and higher frequency regions that reflects better human perception system.
Thus, they contribute better ability to capture replay characteristics while
the models are trained by entire or a specific type of attacks. Furthermore,
the pattern in EER values represents similar nature when features from unknown
spoofing classes appear in the evaluation phase. It is worthwhile to mention
that overall performance is compromised throughout all generalization systems
for such unknown attacks (R9-R10). Comparing CQCC feature with MFCC feature,
the CQCC feature outperforms other systems reported in [21] with an average
EER of 0.76 %.

###  4.2 ASVspoof 2015

The results of generalized systems on ASVspoof 2015 synthetic spoofing
database are reported in Table 4. We train the countermeasure with both and
either of the SS and VC attacks. In this study, we find that the dynamic
coefficients provide superior performance in detecting synthetic spoofed
signals. The results show a large amount of deterioration in performance when
a particular attack is not considered in training. Although both MFCC and CQCC
features give poor performance, CQCC feature leads to better performance
across all cases of generalization scenarios. It is also interesting that for
a particular case of generalization (where SS type attack is only used for
training), static features give higher recognition accuracy than dynamic
features for S1 and S10 attacks. We also notice that best performance for a
specific attack is obtained if data from the specific attack type is used in
training.

###  4.3 Cross-corpora Evaluation

The goal of this study has been to check cross-corpora vulnerability in a
similar attack dependency framework where ASVspoof 2015 synthetic data is used
to model the countermeasure and system performance is evaluated on BTAS 2016
replay evaluation dataset. The cross-corpora evaluations are shown in Table 5.
The overall performance is poor as SS and VC data of BTAS 2016 test set
consist of replayed version of SS and VC attacks as oppose to the ASVspoof
database. An interesting observation is that although replay attacks show poor
recognition accuracy, dynamic features convey more distinct information in
case of SS and VC attacks. It seems reasonable given that SS and VC based
spoofed data are better modeled through dynamic characteristics. This, in
turn, enhances the recognition accuracy while detecting replay version of VC
and SS spoofed samples. Conventional MFCC feature proves to be more efficient
in cross-corpora evaluation, but the performance of unknown attacks is poor
for both features.

##  5 Conclusions

This work presents first analysis of spoofing countermeasures for attack
dependency and generalization. A detailed study on BTAS 2016 with extensive
experiments reveals that direct replay data have better generalization
capability than SS and VC based replayed data. Results on ASVspoof 2015
demonstrates that VC spoofed data in training can better represent the attack
space. The cross-corpora evaluation performance is very poor due to lack of
suitable data in training. Our study on both the databases also indicates that
both static and dynamic parts of spectral features are useful for detecting
spoofing attacks in generalized sense.

##  6 Acknowledgment

This work is partially supported by Indian Space Research Organization (ISRO),
Government of India. The paper reflects some results from the OCTAVE Project
(#647850), funded by the Research European Agency (REA) of the European
Commission, in its framework programme Horizon 2020. The views expressed in
this paper are those of the authors and do not engage any official position on
the European Commission.

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