# Phase Shifts Measured in Evanescent Acoustic Waves above the Solar
Photosphere and Their Possible Impacts to Local Helioseismology

Junwei Zhao W. W. Hansen Experimental Physics Laboratory, Stanford University,
Stanford, CA 94305-4085, USA  S. P. Rajaguru Indian Institute of Astrophysics,
Bangalore-34, India  Ruizhu Chen W. W. Hansen Experimental Physics Laboratory,
Stanford University, Stanford, CA 94305-4085, USA

###### Abstract

A set of 464-min high-resolution high-cadence observations were acquired for a
region near the Sun’s disk center using the Interferometric BI-dimensional
Spectrometer (IBIS) installed at the Dunn Solar Telescope. Ten sets of
Dopplergrams are derived from the bisector of the spectral line corresponding
approximately to different atmospheric heights, and two sets of Dopplergrams
are derived using MDI-like algorithm and center-of-gravity method. These data
are then filtered to keep only acoustic modes, and phase shifts are calculated
between Doppler velocities of different atmospheric heights as a function of
acoustic frequency. The analysis of the frequency- and height-dependent phase
shifts shows that for evanescent acoustic waves, oscillations in the higher
atmosphere lead those in the lower atmosphere by an order of 1 s when their
frequencies are below about 3.0 mHz, and lags behind by about 1 s when their
frequencies are above 3.0 mHz. Non-negligible phase shifts are also found in
areas with systematic upward or downward flows. All these frequency-dependent
phase shifts cannot be explained by vertical flows or convective blueshifts,
but are likely due to complicated hydrodynamics and radiative transfer in the
non-adiabatic atmosphere in and above the photosphere. These phase shifts in
the evanescent waves pose great challenges to the interpretation of some local
helioseismic measurements that involve data acquired at different atmospheric
heights or in regions with systematic vertical flows. More quantitative
characterization of these phase shifts is needed so that they can either be
removed during measuring processes or be accounted for in helioseismic
inversions.

helioseismology — Sun: oscillations — Sun: photosphere — Sun: atmosphere —
Sun: interior

##  1 Introduction

Helioseismology investigates the Sun’s interior structure and dynamics through
analyzing the oscillation signals observed in either Doppler velocities or
intensities in or above the Sun’s photosphere (Christensen-Dalsgaard, 2002).
Despite great advances and breakthroughs obtained in the last few decades
using both global and local helioseismological analysis methods,
helioseismology still faces challenges of some systematic effects, whose
presence in either data or analysis methods often complicates the
interpretation of measurements or hinders a reliable inference of the Sun’s
interior properties. For instance, the helioseismic center-to-limb effect
(Zhao et al., 2012) is an order of magnitude larger than the meridional-
circulation-induced signals for certain travel distances (Zhao et al., 2013;
Kholikov et al., 2014; Rajaguru & Antia, 2015; Chen & Zhao, 2018), posing a
great challenge to our inferences of the Sun’s deep meridional circulation.
Another systematic effect occurs in and near magnetic regions. As demonstrated
by Gizon et al. (2009), the inferences of subsurface sound-speed perturbations
using different helioseismic analysis techniques gave sharply different
results, implying a systematic effect in such regions. To reduce this effect,
Liang & Chou (2015) and Chen & Zhao (2017) excluded all the magnetic regions
with a strength above a certain threshold.

What causes the center-to-limb effect and the magnetic effect in the
helioseismic analysis is not exactly known, but recently Zhao & Chen (2020)
suggested that the center-to-limb effect and part of the magnetic effect might
have a similar cause: the helioseismic signals used in the analysis,
particularly those pairs of signals used to compute the cross-correlation
functions in time–distance helioseismology, are not observed in the same
atmospheric heights. This height difference may introduce unexpected phase
shifts in acoustic waves. Actually, the possibility that the helioseismic
center-to-limb effect may be related to different heights where oscillatory
signals are taken has already been explored by various authors. In the
photosphere, convective blueshifts in granules dominate in areas over
redshifts, systematically shifting the phases of acoustic waves and causing
the observed center-to-limb effect according to Baldner & Schou (2012); but
the shift caused by this process is not expected to be frequency dependent and
the values of shifts are expected be small. Through coupling the Doppler and
intensity observations, Schou (2015) demonstrated how granulation can change
the observed amplitude and phases of the oscillatory signals. However, how the
phases of the oscillatory signals vary with atmospheric height and acoustic
frequency has not been well studied, although a detailed analysis of the
behaviors of these waves above the photosphere is expected to offer a key
insight of the physical causes of the observed effect.

Meanwhile, we have to recognize that most of the helioseismic waves that we
observe are evanescent waves. Although helioseismic waves are observed between
approximately 2.0 and 8.0 mHz, the photospheric cutoff frequency of the waves
is believed near about 5.0 mHz (Jiménez et al., 2011), meaning that waves with
frequencies below 5.0 mHz, including the strongest oscillatory power near 3.0
mHz, are evanescent waves, and those with frequencies above 5.0 mHz are
propagating waves. While it is often expected that phases of evanescent waves
no longer change with height in the atmosphere unless perturbed by flows or
other physical factors, whether this is exactly the case in observed
intensities and Doppler velocities remains to be examined. Despite the early
effort examining how phases change with height (Lites & Chipman, 1979),
similar efforts with a higher precision that meets the current helioseismic
measurement requirements have not been done, likely due to the scarcity of
high-quality simultaneous observations covering multiple atmospheric heights.

In this article, through analyzing a set of well-observed long-duration data
with high spatial and spectral resolutions, we study how the phases of both
evanescent and propagating waves change with atmospheric height. We believe
that our results have a profound impact on the interpretation and inversion of
many local and global helioseismic measurements, which may challenge us to
design new methods removing these systematic phase shifts. This article is
organized as follows: we introduce our data acquisition and reduction in
Section 2, present our measurements of various types of phase shifts in
Section 3. We then discuss our results in Section 4, and give conclusions in
Section 5.

##  2 Observation and Data Reduction

Figure 1: (a) A continuum image showing the field of view of the observation
with a sunspot at the center of the field. (b) A sample image of Doppler
velocities $V_{\mathrm{40}}$, with blue representing blueshift and red
representing redshift. The area between the two dashed circles in both panels
is used as quiet-Sun region in this study.

The data used in this study were previously acquired and used for different
studies (Rajaguru et al., 2010; Couvidat et al., 2012). These imaging
spectropolarimetry data were obtained on 2007 June 8 using the Interferometric
BI-dimensional Spectrometer (IBIS; Cavallini, 2006) installed at the Dunn
Solar Telescope at Sacramento Peak, New Mexico. These observations have a
spectral resolution of 25 mÅ, with all the Stokes parameters ($I,Q,U,V$) taken
at 23 line positions along the spectral line Fe I 6173.3 Å. The spatial
resolution of this set of observations is $0\farcs 330$ (or $0\farcs 165$
pixel-1), and the circular field of view has a diameter of $80\arcsec$. The
observed region is close to the disk center at S07W17, with a medium-size
sunspot of NOAA AR 10960 near the center of the field (see Figure 1a). The
temporal cadence of the observation is 47.5 s, and a total of 586 time steps
were taken with a duration of approximately 464 min. The Fe I 6173.3 Å line,
which is also used by the Helioseismic and Magnetic Imager onboard Solar
Dynamics Observatory (SDO/HMI; Scherrer et al., 2012; Schou et al., 2012) and
by the Polarimetric and Helioseismic Imager onboard Solar Orbiter (Solanki et
al., 2020), is believed to form between $\sim$100–270 km above the photosphere
according to various authors (Norton et al., 2006; Fleck et al., 2011;
Kitiashvili et al., 2015). The spectral images were then dark subtracted,
flat-fielded, and re-registered to remove the atmospheric distortions that
were derived from the white-light images recorded simultaneously (Rajaguru et
al., 2010).

In this study, we first derive line-of-sight Doppler velocities from the
spectral-line profiles by use of three methods: bisector, MDI-like algorithm,
and center-of-gravity method, and then compare velocities from various heights
and methods for their relative phase shifts in oscillations. For the bisector
method, we extract Doppler velocities of plasma motions within the line-
forming layers from the line bisectors, in a similar way used in previous
studies (Rajaguru et al., 2007, 2010). For the spectral-line profile acquired
at each spatial location, we use 10 bisector levels with equal spacing in line
intensity to derive 10 Doppler velocities, corresponding to
$0\%,10\%,\ldots,90\%$ intensity levels and relative to the line-core
wavelength 6173.34 Å in the rest frame of reference (see Figure 2a). The
Doppler velocities derived from different intensity levels form at different
optical depths, which correspond to, approximately, different atmospheric
heights, with $90\%$-intensity level slightly above the line’s continuum
formation height of 100 km, and $0\%$-intensity level corresponding to line-
core formation height at $\sim$270 km. The intensity levels in between are
approximately formed evenly between these heights; however, one needs to be
cautioned that the line-formation heights vary depending on solar structures.
In this study, for the relative phase shifts measured in Section 3, we only
use Doppler velocities derived for the $80\%,60\%,40\%$, and $20\%$-intensity
levels, denoted hereafter from the lower to higher atmosphere as
$V_{\mathrm{80}}$, $V_{\mathrm{60}}$, $V_{\mathrm{40}}$, and
$V_{\mathrm{20}}$, respectively. Figure 1b displays a sample image of
$V_{\mathrm{40}}$, and Figure 3a shows a comparison of these four velocity
curves at a random location with a 100-min duration. The comparison (Figure
3a) shows that the amplitudes of the Doppler velocities derived for different
atmospheric heights are quite different, larger in higher atmosphere and
smaller in lower, but the oscillations at different heights show clear
similarities with little visual difference.

Figure 2: Methods of deriving Doppler velocities from the observed spectral-
line profiles: (a) Bisector method. The dark curve shows the line profile
observed at a random location, and the vertical dashed line indicates the
wavelength in the rest frame of reference. The magenta line shows the
calculated bisector of the line, and the $20\%,40\%,60\%$, and $80\%$ lines
indicate the intensity levels from which $V_{\mathrm{20}}$, $V_{\mathrm{40}}$,
$V_{\mathrm{60}}$, and $V_{\mathrm{80}}$ are inferred. (b) MDI-like algorithm.
The Gaussian curves, displayed in different colors, represent the filter
sensitivities corresponding to SDO/HMI’s six line positions, and are used to
convert the IBIS-observed line profiles into HMI-like observations. (c)
Center-of-gravity method. The $10\%$ and $90\%$ intensity lines indicate
within which intensity levels the center-of-gravity is calculated, and the red
star indicates the location of the center of gravity, from which Doppler
velocity is calculated relative to the rest frame of reference (the vertical
dashed line). Figure 3: (a) Comparison of Doppler velocities derived from
different intensity levels using the bisector method, taken at a random
location for a random 100-min period. (b) Comparison of Doppler velocities
$V_{\mathrm{40}}$, $V^{\mathrm{HMI}}_{\mathrm{like}}$, and
$V_{\mathrm{CofG}}$, taken from the same location and time period as the
velocities in Panel (a).

The second Doppler-velocity derivation method, MDI-like algorithm, is the
method that was previously used for the data taken by Michelson Doppler Imager
onboard Solar and Heliospheric Observatory (SOHO/MDI; Scherrer et al., 1995)
and is also currently used in the SDO/HMI’s routine production pipeline of
Doppler velocities. Because SDO/HMI only takes observations at 6 line
positions while the IBIS observations cover the full line profile, we can
determine Doppler velocities in the same way as done for SDO/HMI. As shown in
Figure 2b, we first multiply the IBIS-observed line profiles with the six
SDO/HMI filter transmission profiles to match SDO/HMI’s 6-point intensities.
We then follow the procedure prescribed by Couvidat et al. (2012) to derive
the HMI-like Doppler velocities (hereafter,
$V^{\mathrm{HMI}}_{\mathrm{like}}$):

$V^{\mathrm{HMI}}_{\mathrm{like}}=\frac{\mathrm{d}V}{\mathrm{d}\lambda}\frac{T}{2\pi}\mathrm{atan}\left(\frac{b_{1}}{a_{1}}\right),$
(1)

where $\mathrm{d}V/\mathrm{d}\lambda=48,562.4$ m s-1 Å-1, $T$ is the observed
wavelength span equal to $412.8$ mÅ in this case, and $a_{1}$ and $b_{1}$ are
the first Fourier components:

$a_{1}=\frac{2}{T}\int^{+\frac{T}{2}}_{-\frac{T}{2}}I(\lambda)\cos\left(2\pi\frac{\lambda}{T}\right)\mathrm{d}\lambda,$
(2)
$b_{1}=\frac{2}{T}\int^{+\frac{T}{2}}_{-\frac{T}{2}}I(\lambda)\sin\left(2\pi\frac{\lambda}{T}\right)\mathrm{d}\lambda.$
(3)

The third Doppler-velocity derivation method, center-of-gravity method (see
Figure 2c), computes the Doppler shift corresponding to the intensity-weighted
average of the whole line profile following the formula:

$\Delta\lambda=\frac{\sum I_{j}\lambda_{j}}{\sum I_{j}}-\lambda_{0},$ (4)

where $I_{j}$ represents the intensity at the $j$-th line position with a
wavelength of $\lambda_{j}$, and $\lambda_{0}$ is the line-core wavelength in
the rest frame of reference. The center-of-gravity Doppler velocity
($V_{\mathrm{CofG}}$) is then derived from $\Delta\lambda$.

Figure 3b displays a comparison of $V_{\mathrm{40}}$,
$V^{\mathrm{HMI}}_{\mathrm{like}}$, and $V_{\mathrm{CofG}}$ at a random
location for a 100-min duration. The comparison shows that the Doppler
velocities derived from the MDI-like algorithm are similar to
$V_{\mathrm{40}}$, and the velocities from the center-of-gravity method are
similar to the $V_{\mathrm{60}}$ from the bisector method. This implies that
the atmospheric height corresponding to the SDO/HMI Doppler velocities is at
about the 40%-intensity level of the Fe I line. Despite being obtained from
very different methods, the oscillation patterns in these three velocities
show remarkable similarities although the following analysis will disclose
their small phase differences.

For all the above three Doppler-velocity derivation methods, at each location
we first use both the left ($I-V$) and right ($I+V$) circular polarization
profiles to derive two Doppler velocities separately, and then average the two
as the final velocity to be used in the follow-up analyses. This is
essentially consistent with the standard SDO/HMI Doppler-velocity derivation
procedure, in which two sets of Doppler velocities from the left and right
circular polarization are averaged. After all the Doppler velocities are
derived at each location, we then rebin the data by 2$\times$2 in space to
enhance the signal-to-noise ratio before carrying out our phase measurements.

##  3 Data Analysis

One main objective of this study is to investigate the relative phase shifts
between acoustic waves observed at different atmospheric heights, particularly
for the waves with frequencies below the cutoff frequency, i.e., evanescent
waves. It is understandable that in sunspot regions, due to the complicated
interaction between helioseismic waves and magnetic field as well as the
substantial reduction of the cutoff frequency, the results from sunspot
regions will differ significantly from quiet-Sun regions (see Rajaguru et al.,
2010). Therefore, in this study, we limit our analysis to the quiet-Sun
region, delimited by the two dashed circles in Figure 1b, and focus only on
the phase shifts in evanescent waves between different heights.

###  3.1 Cross Spectrum

We first examine the phase-shift diagrams between oscillatory signals observed
at different atmospheric heights, i.e., phase shifts in higher atmosphere of
$V_{\mathrm{20}}$, $V_{\mathrm{40}}$, and $V_{\mathrm{60}}$ relative to the
lower atmosphere of $V_{\mathrm{80}}$. The phase-shift diagram as a two-
dimensional function of harmonic degree $\ell$ and frequency $\nu$ can be
calculated following

$\delta\phi_{\mathrm{n}}(\ell,\nu)=\arg\left[\widehat{V_{\mathrm{n}}}(\ell_{x},\ell_{y},\nu)\widehat{V_{\mathrm{80}}}^{\dagger}(\ell_{x},\ell_{y},\nu)\right],$
(5)

where $\widehat{V_{\mathrm{80}}}(\ell_{x},\ell_{y},\nu)$ represents three-
dimensional Fourier transform of $V_{\mathrm{80}}(x,y,t)$, $\ell_{x}$ and
$\ell_{y}$ are horizontal components of $\ell$ ($\ell=\sqrt{\ell_{x}^{2}
+\ell_{y}^{2}}$), ${\dagger}$ represents the conjugate of the Fourier
transform, $\arg$ represents the argument of a complex numbers, i.e., relative
phase, and $\mathrm{n}$ represents one of the three numbers: 20, 40, and 60.

Figure 4: (a) Power diagram of the cross spectrum between $V_{\mathrm{20}}$
and $V_{\mathrm{80}}$, computed using the entire field of view (including the
sunspot) shown in Figure 1. The power diagrams for other cross-spectra,
calculated between other pairs of Doppler velocities, are very similar, thus
not shown. (b) – (d) Phase diagrams of the cross-spectra between
$V_{\mathrm{60}}$ and $V_{\mathrm{80}}$, $V_{\mathrm{40}}$ and
$V_{\mathrm{80}}$, and $V_{\mathrm{20}}$ and $V_{\mathrm{80}}$, respectively.
The phase diagrams are computed using only the quiet-Sun region shown in
Figure 1, and this explains why the area of $\ell<500$ is not shown. The color
bar on the right represents the relative phases, with positive (negative)
values indicating oscillations in the higher atmosphere leading (lagging
behind) those in $V_{\mathrm{80}}$. The dashed curves in all panels represent
the line separating the $f$\- and $p_{1}$-ridges, below which signals are not
used in the phase-shift analyses that follow.

Figure 4a shows the power diagram of the cross-spectrum between
$V_{\mathrm{20}}$ and $V_{\mathrm{80}}$, so that the relative locations of
acoustic modes (or $p$-modes), $f$-mode, convection, and internal gravity
waves can be easily identified. Figure 4b-d show the phase diagrams of the
three higher-atmosphere velocities relative to $V_{\mathrm{80}}$, calculated
using only the quiet-Sun signals. As can be seen, positive phase shifts
(seemingly downward propagating) dominate the areas beneath the $f$-mode
ridge, between $\ell$ of $500-5000$ and $\nu$ of $0-3$ mHz. These are believed
to mostly correspond to internal gravity waves, consistent with the results
reported by Straus et al. (2008). For acoustic modes above the dashed curve,
the phase shifts clearly show negative signs (seemingly upward propagating) in
higher frequencies and positive signs (seemingly downward propagating) in
lower frequencies. It is not very clear in these plots at what frequency the
phase shifts switch the sign from positive to negative.

###  3.2 Relative Phase Shifts between Different Heights

To more accurately measure how phases change in both evanescent and
propagating waves above the photosphere, we measure the phase shifts
$\delta\phi$ at each spatial location between the Doppler oscillations
obtained at higher atmospheric levels and those at $V_{\mathrm{80}}$ following
the formula:

$\delta\phi_{\mathrm{n}}(x,y,\nu)=\arg\left[\widehat{V_{\mathrm{n}}}(x,y,\nu)\widehat{V_{\mathrm{80}}}^{{\dagger}}(x,y,\nu)\right],$
(6)

where $\widehat{V_{\mathrm{n}}}(x,y,\nu)$ represents the one-dimensional
Fourier transform of $V_{\mathrm{n}}(x,y,t)$, and $\mathrm{n}$ represents one
of the three numbers: 20, 40, and 60. Because we are only interested in
studying the behaviors of acoustic waves, all signals corresponding to the
$f$-mode, convection, and internal gravity waves are filtered out, and only
signals above the dashed curves in Figure 4 are kept. Then a two-dimensional
Gaussian smoothing is applied on the $x$-$y$ space to further enhance the
signal-to-noise ratio. The FWHM of the Gaussian function is $1\farcs 5$ for
the results presented in this article; however, different values of FWHM are
tested and the analysis results remain largely unchanged. After the data are
filtered and smoothed, for each of the three higher atmospheric levels, the
$\delta\phi_{\mathrm{n}}(x,y,\nu)$ is measured at each quiet-Sun location, and
then all the $\delta\phi\mathrm{(}x,y,\nu)$ are averaged in $x$-$y$ space for
$\delta\phi\mathrm{(}\nu)$.

Figure 5: (a) Phase shifts $\delta\phi$ measured from $V_{\mathrm{20}}$,
$V_{\mathrm{40}}$, $V_{\mathrm{60}}$, and $V_{\mathrm{80}}$ relative to
$V_{\mathrm{80}}$, displayed as functions of frequency $\nu$. For clarity,
standard errors are displayed only for selected points in one of these curves,
and the errors for other points in this curve and in other curves are similar.
(b) Same as Panel (a) but relative time shifts $\delta\tau$ are displayed.

Figure 5 shows the relative phase shifts $\delta\phi$ and travel-time shifts
$\delta\tau$ measured for all atmospheric levels as functions of $\nu$,
averaged from the entire quiet-Sun region where the net vertical flow is
presumed to be close to 0. The $\delta\tau$ is computed from $\delta\phi$
following $\delta\tau(\nu)=\delta\phi(\nu)/2\pi\nu$. It can be seen that the
$\delta\phi$, albeit very small between 1.5 and 4.0 mHz, show positive values
below $\sim$3.0 mHz and negative values above $\sim$3.0 mHz, indicating that
even for evanescent waves in a region with no or little net vertical flows,
the measured phases continue to change with height. The positive values
indicate that the phases in the higher atmosphere lead those in the lower
atmosphere, as if the waves propagate downward. Negative phase shifts persist
from 3.0 mHz to 7.0 mHz and continue to grow in values with frequency. It is
not surprising for the phases of $\nu>$ 5.0 mHz waves to grow because these
waves are generally believed to be propagating waves, but it is a bit
surprising that the magnitude of $\delta\phi$ drops beyond $\sim$6.0 mHz. This
may be due to the increased observational noises with the increase of acoustic
frequency, or due to the acoustic halos (e.g., Rajaguru et al., 2013; Rijs et
al., 2016) outside of the sunspot where the data are taken for these analyses.
However, whether the measured values match the expected values above 5.0 mHz
and how to explain the phase behaviors above 6.0 mHz are beyond the scope of
this article. Figure 5b shows that even for the relatively small
$\delta\phi$’s, the corresponding $\delta\tau$’s can be around 1 s or larger,
implying that these small phase changes can cause substantial errors for some
local helioseismic measurements, particularly when travel-time shifts caused
by very weak flows are measured, such as meridional circulation in the Sun’s
deep interior or vertical flows beneath supergranules (see discussions in
Section 4.1).

Figure 6: (a) Relative phases shifts $\delta\phi$, displayed as functions of
intensity level for different frequency bands. (b) Same as Panel (a) but
relative time shifts $\delta\tau$ are displayed. (c) Differences of
$\delta\tau$ between one atmospheric level and its higher level, displayed as
functions of height for different frequencies. For clarity, results for
frequency bands of 6.0 and 7.0 mHz are not displayed.

Figure 5 also shows that $\delta\phi$ ($\delta\tau$, too) are not just
functions of $\nu$, but also functions of height: while the positive
$\delta\phi$ remain largely unchanged with height, the negative $\delta\phi$
grow substantially. Figure 6 shows both $\delta\phi$ and $\delta\tau$ as well
as the change rate of $\delta\tau$ as functions of intensity level (or
approximately, atmospheric height), obtained for a few 1.0-mHz-wide frequency
bands with their middle frequencies marked in the figure. In most atmospheric
layers, the $\delta\phi$ around 2.0 mHz remain largely flat and positive, and
the corresponding $\delta\tau$ are around 1 s. The $\delta\phi$ around 3.0 mHz
also remain mostly flat, close to 0 across all layers. For all the other
frequency bands above 3.0 mHz, the $\delta\phi$ are negative and have a trend
of growth with height, and the $\delta\tau$ values are of an order of 1–2 s.
Figure 6c shows the phase changing rate, i.e., how rapid phase changes with
height, is mostly similar for a same frequency in different heights, except a
few notable points.

Figure 7: (a) Relative phase shifts $\delta\phi$ measured between
$V_{\mathrm{60}}$ and $V_{\mathrm{80}}$ inside the regions with strong
downward and upward flows, as well as the differences between the two
$\delta\phi$ curves. For clarity, error bars are only displayed in selected
points in one curve. The errors are similar for other points of this curve and
for other curves. (b) Same as Panel (a) but relative time shifts $\delta\tau$
are displayed.

To investigate behaviors of acoustic waves in areas with persistent upward and
downward flows, we select areas with the top 10% of upflow speeds and the top
10% of downflow speeds for further analysis. After removing a uniform
background velocity, i.e., caused by rotation, the selected upflow (downflow)
region has an average speed of $-190$ ($+190$) m s-1 during the observation
period. Figure 7 shows that the $\delta\phi$ and $\delta\tau$, measured from
$V_{\mathrm{60}}$ relative to $V_{\mathrm{80}}$, exhibit a frequency-dependent
variation trend similar to those measured in the entire quiet region (Figure
5). It is also clear that the $\delta\tau$ measured in the upflow region is
systematically above the $\delta\tau$ measured in the downflow region, with
the differences around 0.5 s. Note that this difference between the two
$\delta\tau$ can be seemingly explained by the upward (downward) flows that
speed up (slow down) both evanescent and propagating waves, but as a matter of
fact, the measured values are too large to be explained this way. Given that
the sound speed is much greater than 10 km s-1 above the photosphere and the
total distance between these two layers is $<$50 km, a flow speed difference
of 380 m s-1 cannot cause a $\delta\tau$ that matches the measured values.
Measurements between $V_{\mathrm{80}}$ and other higher atmospheres give
similar values below 3.0 mHz and considerably larger values above that.

###  3.3 Relative Phase Shifts between Doppler Velocities from Different
Methods

Figure 8: (a) Phase shifts $\delta\phi$ measured from $V_{\mathrm{80}}$,
$V_{\mathrm{60}}$, $V_{\mathrm{40}}$, and $V_{\mathrm{20}}$ relative to
$V^{\mathrm{HMI}}_{\mathrm{like}}$, displayed as a function of frequency
$\nu$. For clarity, standard errors are displayed only for selected points in
one of these curves, and the errors for other points of this curve and for
other curves are similar. (b) Same as Panel (a) but relative time shifts
$\delta\tau$ are displayed.

As noted in Section 2, in addition to the bisector method, the MDI-like
algorithm and the center-of-gravity method are also used to derive Doppler
velocities from the observed spectral-line profiles. It is also of interest to
examine relative phase shifts in the Doppler velocities derived from these
different methods. Figure 8 shows $\delta\phi$ of the four bisector Doppler
velocities relative to $V^{\mathrm{HMI}}_{\mathrm{like}}$ as functions of
$\nu$. It can be found that the phases of $V^{\mathrm{HMI}}_{\mathrm{like}}$
are relatively close to the phases of the bisector velocities below $\sim$3.0
mHz, but beyond that their phases show substantial differences. The
$\delta\phi$ of the bisector Doppler velocities relative to the
$V_{\mathrm{CofG}}$ (plots not shown in this article) give similar results.

Figure 9: (a) Phase shifts $\delta\phi$ measured from $V_{\mathrm{40}}$
relative to $V^{\mathrm{HMI}}_{\mathrm{like}}$, $V_{\mathrm{40}}$ relative to
$V_{\mathrm{CofG}}$, and $V_{\mathrm{CofG}}$ relative to
$V^{\mathrm{HMI}}_{\mathrm{like}}$. Error bars are similar to those shown in
Figure 8a thus not plotted here. (b) Same as Panel (a) but relative time
shifts $\delta\tau$ are displayed.

As demonstrated in Figure 3b, both the $V^{\mathrm{HMI}}_{\mathrm{like}}$ and
$V_{\mathrm{CofG}}$ show similar magnitudes and variation patterns to
$V_{\mathrm{40}}$, indicating that these two Doppler velocities correspond
best with the bisector velocity inferred for the 40%-intensity level. Figure 9
shows $\delta\phi$ and $\delta\tau$ between these three Doppler velocities.
None of the pairs fully agree with each other in the frequency-dependent
$\delta\phi$, indicating that all the Doppler-deriving methods show a
different amount of combination of information from various atmospheric
heights, and these combinations seem to be frequency dependent as well.

###  3.4 Comparing IBIS and SDO/HMI Results

We have by now examined the relative phase shifts in Doppler velocities
obtained at different atmospheric heights and from different velocity-
derivation methods. It would be interesting to examine how the oscillatory
phases observed in intensities change with height, and how the measured
results from IBIS observations compare with those from SDO/HMI. Unfortunately,
for both IBIS and SDO/HMI, intensities can only be reliably inferred at line
core and continuum of the spectral line but not for other optical depths; IBIS
data were acquired long before SDO was launched, thus simultaneous comparison
of IBIS and SDO/HMI data is not possible; and, SDO/HMI does not have multiple
Doppler velocities available like those used in Sections 3.2 and 3.3. Double-
height Doppler-velocity proxies were attempted previously using SDO/HMI’s
6-position data (Nagashima et al., 2014), but the accuracy of those data
cannot meet the high-precision requirements of this study. Therefore, in this
study for both IBIS data and one selected dataset from SDO/HMI, we compute
relative phase shifts $\delta\phi(I_{\mathrm{lc}}-I_{\mathrm{c}})$ between
line-core intensity ($I_{\mathrm{lc}}$) and continuum intensity
($I_{\mathrm{c}}$), which are then compared. For both sets of data, we also
compute the relative phase shifts, $\delta\phi(V-I_{\mathrm{lc}})$ and
$\delta\phi(V-I_{\mathrm{c}})$, between Doppler velocities $V$, derived using
the MDI-like algorithm for both IBIS and SDO/HMI data, and their corresponding
$I_{\mathrm{lc}}$ and $I_{\mathrm{c}}$, respectively. However, meanwhile, one
needs to keep in mind that the velocity and intensity data show different
senses of mode asymmetries (Duvall et al., 1993a), and discussions related to
this are in Section 4.3.

Figure 10: (a) Phase shifts measured from line-core intensities relative to
continuum intensities, for both the IBIS and SDO/HMI observations. (b) Phase
shifts measured from Doppler velocities, which are derived using MDI-like
algorithm, relative to line-core and continuum intensities, respectively, for
both the IBIS and SDO/HMI observations.

In this study, $I_{\mathrm{c}}$, $I_{\mathrm{lc}}$, and $V$ data are taken
from 2011 January 1 SDO/HMI observations near the disk center, with a duration
of 464 min (same as the IBIS data duration) and covering an area of
$256\arcsec\times 256\arcsec$ with a 45-sec cadence. The SDO/HMI spatial
resolution is $1.0\arcsec$ (or $0.5\arcsec$ pixel-1), much coarser than the
IBIS data; but the field of view of this selected dataset is nearly as 10
times large as the IBIS data. Figure 10a shows
$\delta\phi(I_{\mathrm{lc}}-I_{\mathrm{c}})$ for both datasets, in which it
can be seen that the trends of the curves are similar, with oscillations in
the higher atmosphere lead those in the lower atmosphere substantially between
about $2.0-5.5$ mHz, although the sign-reversal frequency differs in these two
curves. However, it is also clear that the
$\delta\phi(I_{\mathrm{lc}}-I_{\mathrm{c}})$ values from SDO/HMI are
substantially larger than (about twice of) those from IBIS.

Figure 10b shows $\delta\phi(V-I_{\mathrm{lc}})$ and
$\delta\phi(V-I_{\mathrm{c}})$ for both sets of observations, in which $V$
leads both $I_{\mathrm{c}}$ and $I_{\mathrm{lc}}$ substantially in phases.
Again, the variation trends for both $\delta\phi(V-I_{\mathrm{lc}})$ and
$\delta\phi(V-I_{\mathrm{c}})$ curves show many similarities in the IBIS and
SDO/HMI results; however, the $\delta\phi$ measured from the SDO/HMI data are
about as twice large as those measured from the IBIS data.

Figure 11: (a) Power diagram for the cross spectrum between the SDO/HMI-
observed line-core intensity and continuum intensity. (b) Phase diagram for
the same cross spectrum, with the logarithm of the power overplotted as
contours to show relative locations of the power ridges. (c) Phase diagram for
the cross spectrum between the IBIS-observed line-core intensity and continuum
intensity. Same as Figure 4b-d, the low-$\ell$ area is left blank in the plot.
The color bar on the right shows color scales of relative phases in both
panels (b) and (c). The magenta dashed lines in panels (b) and (c) indicate
the middle line separating $f$ and $p_{1}$ ridges, below which signals are
filtered out in the phase-shift analyses presented in Section 3.4.

To understand the differences in the IBIS and SDO/HMI results, we compute
phase diagrams of the cross-spectra between $I_{\mathrm{c}}$ and
$I_{\mathrm{lc}}$ for both datasets (Figure 11b and 11c). Understandably,
because of its higher spatial resolution and smaller field-of-view, the IBIS
data has poorer wavenumber (or harmonic degree $\ell$) resolution relative to
the HMI data. Both of the phase diagrams show similar and clear frequency
dependency that is also seen in Figure 10: large positive $\delta\phi$ in the
range of about $2.0-5.5$ mHz and small negative $\delta\phi$ above about 5.5
mHz. Figure 11b also shows at least two $\delta\phi$-variation trends: (1) The
$\delta\phi$ show alternating positive and negative signs on either side of
the $p$-mode power ridges, with positive values overlapping more with the
power ridges, which results in giving a net positive sign in phase-shift
analysis shown in Figure 10a; (2) Despite the alternating signs of
$\delta\phi$, there is a general trend of decreasing positive values and
increasing negative values with the increase of $\ell$. The trend (2)
explains, we tend to believe, why the values of $\delta\phi$ measured from
IBIS and SDO/HMI differ substantially (Figure 10): the IBIS data are more
sensitive to the higher-$\ell$ wave signals, getting more contributions from
the low-$\delta\phi$ portion to the measured $\delta\phi$ than the SDO/HMI
data.

##  4 Discussion

###  4.1 Impacts to Local Helioseismology Studies

In this study, we have analyzed relative phase shifts, $\delta\phi$, between
oscillatory signals observed in Doppler velocities of different optical depths
(approximately, different atmospheric heights), derived using a set of long-
duration IBIS observations with full spectral-line profiles, high spatial and
spectral resolutions, and a high temporal cadence. Due to the scarcity of
high-quality simultaneous Doppler observations of multiple atmospheric
heights, similar types of analysis were rare in the past. We believe that the
$\delta\phi$, as a function of frequency and atmospheric height, reported in
this article have profound impacts to local helioseismology studies, including
time–distance helioseismology (Duvall et al., 1993b) among others.

As introduced in Section 1, the Sun’s acoustic cutoff frequency
($\nu_{\mathrm{ac}}$) in the photosphere is around 5.0 mHz (e.g., Deubner &
Gough, 1984; Jiménez et al., 2011), thus our observed waves consist of both
evanescent and propagating waves. It is often presumed that the phases of
evanescent waves remain unchanged with height unless the waves are perturbed
by vertical flows or other dynamic parameters; or if perturbed, local
helioseismic inversions are expected capable of recovering these
perturbations. However, our analysis shows that for the acoustic-mode
oscillations inferred from the Fe I 6173.3 Å line in a quiet-Sun region, where
the net vertical flow is expected to be close to 0 (for discussions of the
role of convective blueshift, please refer to Section 4.3): relative to lower-
atmosphere oscillations, higher-atmosphere oscillations lead in phases while
$\nu$ $<$ 3.0 mHz and lag behind while $\nu$ $>$ 3.0 mHz (for discussions of
evanescent waves, please refer to Section 4.2). These measured $\delta\phi$
are not consistent with the general presumption of the stationary phases in
evanescent waves, nor can be simply explained by vertical flows. The long-term
(around 7 hrs in this study) average of the vertical flows, if not exactly net
0, is not expected to exceed an order of 100 m s-1, which, to the waves with a
phase speed $>$10 km s-1 within a travel interval of $<$200 km, can hardly
cause phase (or travel-time) shifts that match the measured values in Figures
5 & 6. Equally importantly, vertical flows cannot explain the measured
frequency dependency of $\delta\tau$, either.

What possibly causes these observed phase shifts will be discussed in Section
4.3, and here we focus on how these results impact local helioseismic studies.
Let us take time–distance helioseismology as example, which measures (see
Figure 12) travel time $\tau_{\mathrm{AB}}$ of acoustic waves traveling from
one surface location $A$ to another surface location $B$ through the solar
interior, and measures travel time $\tau_{\mathrm{BA}}$ along the opposite
direction. Suppose the Doppler observation at location $A$ forms at one
atmospheric level, and the Doppler observation at location $B$ forms at a
slightly higher level — location $B^{\prime}$. Based on our earlier analysis,
there is a travel-time shift $\tau_{\mathrm{BB^{\prime}}}$ between positions
$B$ and $B^{\prime}$; therefore, the presumed $\tau_{\mathrm{AB}}$ measurement
becomes $\tau_{\mathrm{AB^{\prime}}}$, which is equal to $\tau_{\mathrm{AB}}$
\+ $\tau_{\mathrm{BB^{\prime}}}$, and the presumed $\tau_{\mathrm{BA}}$
measurement now becomes $\tau_{\mathrm{B^{\prime}A}}$, which is equal to
$\tau_{\mathrm{BA}}$$-$ $\tau_{\mathrm{BB^{\prime}}}$. The travel-time
difference, $\delta\tau_{\mathrm{AB}}$$\equiv$ $\tau_{\mathrm{AB}}$$-$
$\tau_{\mathrm{BA}}$, which is often interpreted as caused by the plasma flows
along the subsurface travel path, becomes $\delta\tau_{\mathrm{AB}}$ \+
2$\tau_{\mathrm{BB^{\prime}}}$. A measurement error of
2$\tau_{\mathrm{BB^{\prime}}}$ is thus introduced, which will be mistakenly
interpreted as interior flows in the inversions. Based on our analysis shown
in Section 3.2, this $\tau_{\mathrm{BB^{\prime}}}$ can be around $+1$ s
between 1.5 – 3.0 mHz and around $-1$ s between 3.0 – 5.5 mHz, approximately
the same order of magnitude as caused by the near-surface meridional flow,
thus non-negligible. Actually, this model is not strictly accurate because
oscillations at location $B$ and $B^{\prime}$ consist of all types of wave
modes, while waves traveling from $A$ to $B$ consist of only a few modes. So
the $\tau_{\mathrm{BB^{\prime}}}$ measured locally may not be identical to the
$\tau_{\mathrm{BB^{\prime}}}$ in the waves traveling to here from $A$.
Nevertheless, it is still reasonable to believe, although the values may
slightly differ, using oscillatory signals observed at different atmospheric
heights to measure $\delta\phi$ (or $\delta\tau$) can introduce non-negligible
errors.

Figure 12: Schematic plot showing a subsurface ray path connecting two surface
locations $A$ and $B$, along which waves travel between these two locations.
Signals presumably observed at location $B$ are actually observed at a
slightly higher location $B^{\prime}$. Plots are not to scale.

As a matter of fact, it is not rare that observed oscillatory signals form at
different atmospheric heights on and above the Sun’s photosphere, albeit most
times with only small height differences. For instance, due to the limb-
darkening effect, the formation heights of most spectral lines gradually
increase with the distance to the disk center; and in fact, this is believed
to be directly linked to the helioseismic center-to-limb effect (Chen & Zhao,
2018). Due to Wilson Depression, the observed sunspot umbra, penumbra, and
quiet-Sun regions can differ in heights by $\sim$500 km, likely causing a few
seconds of $\delta\tau$ measured between them, which are not due to any flows
but were mistakenly ascribed to flows in some past helioseismic inversions
(e.g., Zhao & Kosovichev, 2003). Another example is supergranules, which are
often thought of as quiet-Sun regions but their central areas may be slightly
warmer, thus spectral lines there form slightly higher, than their boundary
areas. For a long-time (a few hours) analysis typically required by
time–distance helioseismology, the $\delta\tau$ measured between supergranular
centers and boundaries will likely carry a systematic shift that is unrelated
to the supergranules’ subsurface structure or flows, but such a systematic
shift is not accounted for in the time–distance analysis (e.g., Duvall &
Hanasoge, 2013).

Another important implication to the time–distance helioseismic measurements
is in the areas with systematic long-term (an order of a few hours) up- or
down-flows. As illustrated in Figure 7, the measured travel-time shifts in the
areas with up- or down-flows cannot be accounted for by the vertical flows
inferred from Doppler shifts, and some other factors must play a role in
causing these measured shifts. Therefore, if one end of the acoustic waves
used for time–distance measurements (say, location $A$ or $B$ in Figure 12) is
inside a region with systematic vertical flows, one needs to be cautious in
interpreting the measured $\delta\tau$. There is no shortage of such locations
on the solar surface, e.g., again, the boundaries (central areas) of
supergranules are usually associated with downward (upward) flows. This
vertical-flow-related effect may either be just another manifestation of the
effect caused by the different line-formation heights that is discussed above,
because supergranular upflow (downflow) areas are often associated with hotter
(cooler) areas, or it is an independent effect in addition to the line-
formation height.

It is now clear that the unaccounted-for phase shifts in evanescent waves
impact significantly how we interpret local helioseismic measurements, but it
is not immediately clear how this observational fact impacts global
helioseismology. Intuitively, the systematic change of oscillatory phases with
distance to the disk center, i.e., the center-to-limb effect, albeit small,
can systematically change the ridge location $(\ell,\nu)$ in the power
spectrum, hence change the inversion for sound-speed structures inside the
Sun. The effect on the inference of the internal rotation by global
helioseismology should be negligible, because the effect from both sides of
the central meridian can cancel each other. In addition, our observations can
only identify non-zero phase shifts in evanescent waves in and above the
photosphere, but unable to investigate how phases change beneath the
photosphere. For example, let us consider 3.0 mHz waves, which become
evanescent a few hundred km beneath the photosphere: are extra phase shifts
introduced before they are observed at the surface? A tiny change of their
phases in this depth interval that are unrelated to flows will greatly
challenge our interpretation of both global and local helioseismic
measurements.

Our analysis also shows that the Doppler velocities derived from the MDI-like
algorithm and the center-of-gravity method both show small yet non-negligible
phase shifts relative to the velocities that are derived from the bisector
method and match those two methods best. This does not imply that any of these
Doppler-velocity derivation methods introduce extra phase shifts, but caution
us that it may not be appropriate to measure relative phase shifts between
velocities derived using different methods.

###  4.2 Evanescent Waves

Our analysis on this specific set of IBIS observations shows that for most
atmospheric heights, the $\delta\phi$ of the acoustic waves switches from
positive to negative at around 3.0 mHz, where a mixture of both evanescent and
propagating waves is expected. However, what frequency separates evanescent
waves from propagating waves is not very clear in this set of observations.

Studying the helioseismic center-to-limb effect as a function of acoustic
frequency, Chen & Zhao (2018) pointed out that the sign reversal of the
center-to-limb effect occurs at about 5.5 mHz, which is close to the cutoff
frequency, in most regions on the solar disk, and this sign-reversal frequency
decreases with distance to the disk center. If the center-to-limb effect is
indeed, most likely it is, connected to the spectral-line’s formation height,
we would expect the observed sign reversal in our present analysis to occur
around 5.5 mHz instead of near 3.0 mHz, because the analyzed region is very
close to the disk center and both this analysis and their analysis (Chen &
Zhao, 2018) used observations from the same spectral line Fe I 6173.3 Å. A few
factors may play a role in causing this apparent discrepancy: first, in this
study the IBIS-observed region is in the vicinity of a sunspot, with visible
pores in our “quiet-Sun” region. The presence of magnetic regions, though
sparse, and the systematic moat flows around the sunspot, will undoubtedly
affect our results while the magnitude of the influence is difficult to
assess. Second, the sign reversal near 3.0 mHz seen in this analysis is from
the bisector-derived Doppler data, and it is difficult to estimate how the
MDI-like algorithm-derived Doppler velocities would behave as a function of
frequency and height, thus it is difficult to compare these results directly
against the SDO/HMI results. Third, it is possible that different instruments
with different spatial resolutions and modulation transfer functions, despite
using the same spectral line, can cause systematic differences in the measured
results. All these above factors are for Doppler velocities, but the results
obtained from intensity data, presented in Section 3.4, may help shed light on
understanding more of the sign-reversal frequency.

The comparison of measurements, made using IBIS and SDO/HMI line-core and
continuum intensities, show similar frequency-dependent trends of $\delta\phi$
but with substantially different values. The phase diagrams of the cross-
spectra between the two intensities from both datasets help to explain the
discrepancies in the $\delta\phi$ values: the $\delta\phi$ are not just a
function of frequency and height, but also a function of wavenumber. With a
higher spatial resolution, the IBIS $\delta\phi$ measurements are constituted
more of low phase shifts than the SDO/HMI observations, causing the
discrepancies in the measured values. Although this conclusion is only for
intensity data, we speculate the similar thing for the Doppler data. It would
be reasonable to speculate that the $\delta\phi$ in SDO/HMI-observed Doppler
data will show a frequency- and height-dependency similar to those measured
from IBIS data, but likely with higher values and a higher sign-reversal
frequency.

Overall, although it is unclear at what frequency the acoustic waves become
evanescent and whether the phase-shift sign reversal is directly related to
the cutoff frequency, it is quite clear that the phases of the evanescent
waves continue to change, albeit rather small, with the atmospheric height.
The sign and amount of the phase shifts seem to depend upon acoustic
frequency, as well as spectral lines, telescopes, and instruments that are
used for observations in addition to vertical flows.

###  4.3 Physical Causes of Phase Shifts

Our analysis has shown that above the Sun’s photosphere, the measured phases
of evanescent acoustic waves continue to shift, and this frequency-dependent
shift cannot be explained by vertical flows in the region. What causes such
phase shifts?

For an enclosed ideal and adiabatic gas that is experiencing a periodic
variation, the velocity change is expected to lead the temperature change in
phase; however, the Sun’s atmosphere is neither enclosed nor adiabatic. For an
evanescent wave, even if the phases of oscillatory signals in velocities do
not change or only change subtly with atmospheric height, the temperature
responses to them, thus the observed intensity changes, at different heights
may not be simultaneous, but likely with a gradual height-dependent time delay
due to the non-adiabaticity of the atmosphere. That is, intensities at
different heights do not respond simultaneously to a same velocity
perturbation. As clearly shown in Figure 5a and Figure 11a, oscillatory
signals show small phase changes with height when observed in Doppler
velocities, but show substantial, an order of magnitude larger, phase changes
with height when observed in intensities. Now, we need to remind ourselves
that all Doppler velocities are inferred from spectral-line intensities, and a
small leakage from the large height- and frequency-dependent phase shifts in
intensities can result in non-negligible phase shifts in Doppler velocities,
even when local velocities do not carry such phase shifts intrinsically.
Indeed, Fe I 6173.3 Å line is not perfectly symmetric, and its asymmetry gets
enhanced by convective blueshifts (e.g., Löhner-Böttcher et al., 2018; Stief
et al., 2019). And, it is also well known that the red wing of spectral lines
oscillates with larger amplitudes, thus carrying stronger oscillatory power,
than the blue wing (Cavallini et al., 1985; Bertello & Caccin, 1990).
Therefore, the Doppler velocities derived from this asymmetric line profile,
with unbalanced oscillatory power in both of its wings, may carry a height-
dependent phase shift leaked in from intensities. That is, a combination of
the atmosphere’s non-adiabaticity and the spectral line’s properties can cause
height- and frequency-dependent phase shifts in Doppler velocities. This is a
scenario that we speculate can explain most of the observed phase shifts while
the rest can be explained by the scenarios discussed below; meanwhile, we also
recognize that this scenario needs to be confirmed using numerical simulations
(e.g., Kitiashvili et al., 2015), and perhaps, more disk-location-dependent
observations with the full spectral-line profiles are needed for a more
systematic analysis.

Other factors may also play a role in the measured phase shifts. To explain
the helioseismic center-to-limb effect, which is probably a manifestation of
the frequency- and height-dependent $\delta\phi$ reported in this work,
Baldner & Schou (2012) tried to explain that the ubiquitous convective
blueshift above the photosphere likely caused negative phase shifts in both
the evanescent and propagating waves. (Note that the role of convective
blueshift here is to shift phases of acoustic waves, different from its role
in causing the spectral-line asymmetry mentioned above.) This effect
undoubtedly plays a role in causing some phase shifts, but the amount of the
shifts estimated from numerical models are about one order of magnitude
smaller than the observed values, indicating that other factors may play a
leading role. In addition, this mechanism cannot explain the observed
frequency dependence of the phase shifts.

Another cause of the observed $\delta\phi$ may be related to the line-
asymmetry (Duvall et al., 1993a) across the oscillation power ridges. (Note
that the line asymmetry here is across acoustic power ridges, different from
the optical spectral-line asymmetry mentioned above.) It appears (see Figure
11b) that the $\delta\phi$ observed in intensities show opposite signs on
either side of the power spectrum ridges, and the line asymmetry can cause
unequal contributions to the $\delta\phi$ in our $\delta\phi$ or $\delta\tau$
measurements. If the observed line asymmetry across the acoustic power ridges
is caused by correlated noise in observations (Nigam et al., 1998), then it is
possible that such correlated noise is an indirect cause of part of the
observed phase shifts, although the magnitude and the detailed frequency
dependence that this mechanism can incur remain to be investigated.

##  5 Conclusion

Through analyzing oscillatory signals observed at different optical depths,
which roughly correspond to different atmospheric heights, we have found that
the phases of evanescent acoustic waves continue to change with height,
increasing for lower-frequency waves and decreasing for higher-frequency
waves, and the changes are not accounted for by vertical flows. We also found
that in areas with systematic upward or downward flows, the phase shifts
measured in the acoustic waves are more substantial than those expectantly
caused by flows. These pose great challenges to some helioseismic analyses
that involve measurements using observations obtained at different atmospheric
heights or in areas with systematic vertical flows. The comparison of the
phases measured from IBIS and SDO/HMI intensity data shows significant
differences in magnitude, but these differences are likely owing to the
different sensitivities of the instruments to high-$\ell$ waves. We speculate
that our measured frequency- and height-dependent phase changes in acoustic
waves are probably due to the non-adiabaticity of the Sun’s atmosphere with a
combination of the asymmetry in the spectral line used in observations. More
investigations are needed to better quantify the phase changes as functions of
height and frequency, so that this systematic effect can be either removed in
helioseismic measuring processes or can be accounted for in helioseismic
inversions.

We thank the anonymous referee for valuable comments that help improve the
quality of this paper. At the time the IBIS observation was acquired, Dunn
Solar Telescope at Sacramento Peak, New Mexico was operated by National Solar
Observatory (NSO). NSO is operated by the Association of Universities for
Research in Astronomy (AURA) Inc. under a cooperative agreement with the
National Science Foundation. SDO is a NASA mission, and HMI is an instrument
developed by Stanford University under a NASA contract. We thank Dr. M.
Waidele for carefully reading through the manuscript and providing useful
comments. J.Z. was partly supported by a NASA grant 80NSSC19K0857. S.P.R.
acknowledges support from the Science and Engineering Research Board (SERB,
Govt of India) grant CRG/2019/003786.

## References

  * Baldner & Schou (2012) Baldner, C. S., & Schou, J. 2012, ApJ, 760, L1
  * Bertello & Caccin (1990) Bertello, L., & Caccin, B. 1990, A&A, 231, 509
  * Cavallini (2006) Cavallini, F. 2006, Sol. Phys., 236, 415
  * Cavallini et al. (1985) Cavallini, F., Ceppatelli, G., & Righini, A. 1985, A&A, 150, 256
  * Chen & Zhao (2017) Chen, R., & Zhao, J. 2017, ApJ, 849, 144
  * Chen & Zhao (2018) Chen, R., & Zhao, J. 2018, ApJ, 853, 161
  * Christensen-Dalsgaard (2002) Christensen-Dalsgaard, J. 2002, Rev Modern Phys 74, 1073
  * Couvidat et al. (2012) Couvidat, S., Rajaguru, S. P., Wachter, R., Sankarasubramanian, K., Schou, J., & Scherrer, P. H. 2012, Sol. Phys., 278, 217
  * Duvall & Hanasoge (2013) Duvall, T. L., Jr., & Hanasoge, S. M. 2013, Sol. Phys., 287, 71
  * Duvall et al. (1993a) Duvall, T. L., Jr., Jefferies, S. M., Harvey, J. W., Osaki, Y., & Pomerantz, M. A. 1993a, ApJ, 410, 829
  * Duvall et al. (1993b) Duvall, T. L., Jr., Jefferies, S. M., Harvey, J. W., & Pomerantz, M. A. 1993b, Nature, 362, 430
  * Deubner & Gough (1984) Deubner, F. L., & Gough, D. 1984, ARA&A, 22, 593
  * Fleck et al. (2011) Fleck, B., Couvidat, S., & Straus, T. 2011, Sol. Phys., 271, 27
  * Gizon et al. (2009) Gizon, L., Schunker, H., Baldner, C. S., et al. 2009, Space Sci. Rev., 144, 249
  * Jiménez et al. (2011) Jiménez, A., García, R. A., & Pallé, P. L. 2011, ApJ, 743, 99
  * Kholikov et al. (2014) Kholikov, S., Serebryanskiy, A., Jackiewicz, J. 2014, ApJ, 784, 145
  * Kitiashvili et al. (2015) Kitiashvili, I. N., Couvidat, S., & Lagg, A. 2015, ApJ, 808, 59
  * Liang & Chou (2015) Liang, Z.-C., & Chou, D.-Y. 2015, ApJ, 805, 165
  * Lites & Chipman (1979) Lites, B. W., & Chipman, E. G. 1979, ApJ, 231, 570
  * Löhner-Böttcher et al. (2018) Löhner-Böttcher, J., Schmidt, W., Stief, F., Steinmetz, T., & Holzwarth, R. 2018, A&A, 611, A4
  * Nagashima et al. (2014) Nagashima, K., Löptien, B., Gizon, L., Birch, A. C., Cameron, R., Couvidat, S., Danilovic, S., Fleck, B., & Stein, R. 2014, Sol. Phys., 289, 3457
  * Nigam et al. (1998) Nigam, R., Kosovichev, A. G., Scherrer, P. H., & Schou, J. 1998, ApJ, 495, L115
  * Norton et al. (2006) Norton, A. A., Graham, J. P., Ulrich, R. K., et al. 2006, Sol. Phys., 239, 69
  * Rajaguru & Antia (2015) Rajaguru, S. P., & Antia, H. M. 2015, ApJ, 813, 114
  * Rajaguru et al. (2013) Rajaguru, S. P., Couvidat, S., Sun, X., Hayashi, K., & Schunker, H. 2013, Sol. Phys., 287, 107
  * Rajaguru et al. (2007) Rajaguru, S. P., Sankarasubramanian, K., Wachter, R., & Scherrer, P. H., 2007, ApJ, 654, L175
  * Rajaguru et al. (2010) Rajaguru, S. P., Wachter, R., Sankarasubramanian, K., & Couvidat, S. 2010, ApJ, 721, L86
  * Rijs et al. (2016) Rijs, C., Rajaguru, S. P., Przybylski, D., Moradi, H., Cally, P. S., & Shelyag, S. 2016, ApJ, 817, 45
  * Scherrer et al. (1995) Scherrer, P. H., Bogart, R. S., Bush, R. I., et al. 1995, Sol. Phys., 162, 129
  * Scherrer et al. (2012) Scherrer, P. H., Schou, J., Bush, R. I., et al. 2012, Sol. Phys., 275, 207
  * Schou (2015) Schou, J. 2015, A&A, 580, L11
  * Schou et al. (2012) Schou, J., Scherrer, P. H., Bush, R. I., et al. 2012, Sol. Phys., 275, 229
  * Solanki et al. (2020) Solanki, S. K., del Toro Iniesta, J. C., Woch, J., et al. 2020, A&A, 642, A11
  * Stief et al. (2019) Stief, F., Löhner-Böttcher, J.,Schmidt, W., Steinmetz, T., & Holzwarth, R. 2019, A&A, 622, A34
  * Straus et al. (2008) Straus, T., Fleck, B., Jefferies, S. M., Cauzzi, G., McIntosh, S. W., Reardon, K., Severino, G., & Steffen, M. 2008, ApJ, 681, L125
  * Zhao & Chen (2020) Zhao, J., & Chen, R. 2020, Astrophys Space Sci Lib, 57, 123
  * Zhao & Kosovichev (2003) Zhao, J., & Kosovichev, A. G. 2003, ApJ, 591, 446
  * Zhao et al. (2013) Zhao, J., Bogart, R. S., Kosovichev, A. G., Duvall, T. L., Jr., Hartlep, T. 2013, ApJ, 774, L29
  * Zhao et al. (2012) Zhao, J., Nagashima, K., Bogart, R. S., Kosovichev, A. G., & Duvall, T. L., Jr. 2012, ApJ, 749, L5


# Rethinking Wireless Communication Security in Semantic Internet of Things

Hongyang Du, Jiacheng Wang, Dusit Niyato, , Jiawen Kang, Zehui Xiong, Mohsen
Guizani, , and Dong In Kim H. Du, J. Wang and D. Niyato are with the School of
Computer Science and Engineering, Nanyang Technological University, Singapore
(e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>dniyato@ntu.edu.sg).J. Kang is with the School of Automation, Guangdong
University of Technology, China. (e-mail: kavinkang@gdut.edu.cn).Z. Xiong is
with the Pillar of Information Systems Technology and Design, Singapore
University of Technology and Design, Singapore (e-mail:
zehui_xiong@sutd.edu.sg).M. Guizani is with Machine Learning Department,
Mohamed Bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE
(e-mail: mguizani@ieee.org).D. I. Kim is with the Department of Electrical and
Computer Engineering, Sungkyunkwan University, South Korea (e-mail:
dikim@skku.ac.kr).

###### Abstract

Semantic communication is an important participant in the next generation of
wireless communications. Enabled by this novel paradigm, the conventional
Internet-of-Things (IoT) is evolving toward the semantic IoT (SIoT) to achieve
significant system performance improvements. However, traditional wireless
communication security techniques for bit transmission cannot be applied
directly to the SIoT that focuses on semantic information transmission. One
key reason is the lack of new security performance indicators. Thus, we have
to rethink the wireless communication security in the SIoT. As such, in the
paper, we analyze and compare classical security techniques, i.e., physical
layer security, covert communications, and encryption, from the perspective of
semantic information security. We highlight the differences among these
security techniques when applied to the SIoT. Novel performance indicators
such as semantic secrecy outage probability (for physical layer security
techniques) and detection failure probability (for covert communication
techniques) are proposed. Considering that semantic communications can raise
new security issues, we then review attack and defense methods at the semantic
level. Finally, we present several promising directions for future secure SIoT
research.

###### Index Terms:

Semantic communications, internet-of-things, semantic noise, physical layer
security, covert communications

##  I Introduction

The advancement of semantic communications technique has brought about
significant changes to nearly all aspects of wireless communication networks.
As a new communication paradigm, semantic communications no longer focus on
the accurate transmission of bits, but on the transmission of task-related
semantic information [1]. As semantic models become lightweight, deploying
semantic encoders and decoders in network edge devices is also practical.
Thus, the conventional Internet-of-Things (IoT) is evolving toward the
semantic IoT (SIoT), enabling more efficient and energy-saving information
interaction [2].

Data security is an enduring topic in wireless communication networks. When
network devices transmit sensitive data, there is a high risk of eavesdropping
or jamming/interference attacks by malicious third parties. A straightforward
approach is to encrypt the data by using complex algorithms. Although various
encryption algorithms have been proposed, the effectiveness of encryption and
the complexity of computation are positively correlated. To improve the
security of communication networks, high complexity in encryption put much
pressure on network edge devices with insufficient computing power.
Fortunately, besides traditional encryption methods, the physical layer
security (PLS) technique is considered to be an essential driver enhancing 6G
security [3]. Without requiring actual key distribution, PLS can achieve high-
quality network security performance with low computational complexity. A
common disadvantage of encryption and PLS is that they can only guarantee that
the information will not be decrypted. However, a malicious third party can
still use the detected wireless signals to locate the transmitter in the
network and thus perform jamming. To solve this problem, the covert
communications technique is proposed as a more demanding PLS technique. In
order not to be detected by malicious nodes in the act of transmitting data,
transmitters can hide the transmitting activities by designing a suitable
power allocation scheme or by using friendly jammers. A comparison of the
aforementioned wireless communication security techniques is presented in Fig.
1.

Figure 1: Comparison of physical layer security, covert communications, and
encryption techniques, and our proposed new performance indicators for the
SIoT.

However, current research on PLS, covert communications, and encryption is
mainly carried out in the conventional IoT without considering the new
features of SIoT. Moreover, the study of the security of semantic
communications techniques is still in its infancy [4, 5, 6]. The application
of classical wireless communication security techniques in SIoT has not been
clearly discussed. Specifically, the following questions have not been
answered:

  1. Q1)

How do wireless communication security techniques differ in the SIoT compared
to those in the conventional IoT?

  2. Q2)

What are the security performance indicators in SIoT?

  3. Q3)

What new security issues does semantic communication technology bring while
improving the efficiency of the network?

As such, we revisit classical communication security techniques from the
perspective of semantic networks, and discuss the novel attack and defense
methods brought about by the semantic communications techniques. Our
contributions are summarized as follows:

  1. 1.

We revisit three security techniques, i.e., PLS, covert communications, and
encryption. For each technique, we discuss its new features in SIoT (For Q1).

  2. 2.

To quantify the new characteristics brought by the SIoT to PLS and covert
communications, we propose two new performance indicators, i.e., semantic
secrecy outage probability (semantic SOP) and detection failure probability
(DFP), respectively (For Q2).

  3. 3.

We discuss the semantic attack schemes caused by semantic communications
technique, which can be divided into targeted and untargeted semantic attacks
(For Q3). Furthermore, we propose training-based and training-free defense
schemes.

##  II Revisiting Conventional Security Techniques

In this section, we revisit wireless communication security techniques,
including PLS, covert communications, and encryption techniques. We present
the definitions, features, and common security performance indicators. We then
discuss the differences between these techniques when applied in the SIoT and
in the conventional IoT, and propose novel performance indicators.

###  II-A Physical Layer Security

####  II-A1 Definition

The PLS is built upon the information theory, which aims to protect wireless
communications against eavesdropping by exploring and utilizing the inherent
features of the physical medium [3]. Unlike the encrypt method, PLS is
independent of device computing capability, which not only enables it to
achieve effective security but also gives it a natural advantage in saving
resources. Moreover, such a technique is able to adjust transmission
strategies according to the physical layer characteristics to adapt to the
wireless channel changes. According to the working principles of PLS methods,
the security performance indicators mainly include secrecy outage probability
(SOP), the probability of non-zero secrecy capacity (PNZ), and the average
secrecy capacity (ASC) [7].

  * •

Average Secrecy Capacity: The secrecy capacity can be obtained by calculating
the difference between the main channel capacity and wiretap channel capacity.
For a given constraint of perfect secrecy, the average secrecy capacity
provides a criterion for capacity limit from a mathematical point of view. For
instance, if the legitimate user is able to obtain the perfect channel state
information (CSI) of the eavesdropper’s channel, then the coding scheme can be
flexibly adjusted to adapt to different fading coefficients. In principle,
therefore, one can realize any average secure communication rate, which is
below the average secrecy capacity of the channel.

  * •

Secrecy Outage Probability: The SOP is defined as the probability that the
instantaneous secrecy capacity falls less than the target secrecy rate [7].
The SOP first provides the conditions that the wireless channel needs to meet
to support the specified secure rate. Second, it gives a security measure for
cases where legitimate users have no CSI about the eavesdropper. Therefore, as
long as the secrecy capacity is larger than the target secrecy rate, the
eavesdropper’s channel is worse than legitimate users’ estimation and the
secrecy of the network is ensured.

  * •

Probability of Non-Zero Secrecy Capacity: If the main channel capacity is
larger than that of the eavesdropper’s channel, the eavesdroppers are unable
to successfully decode the transmitted information. Here, the occurrence
probability of such an event is defined as the PNZ. On this basis, according
to the definition, the PNZ equals the probability that the instantaneously
received signal-to-noise ratio (SNR) of the legitimate user is greater than
that of the eavesdropper.

####  II-A2 Physical Layer Security in SIoT Network

Figure 2: Rethinking physical layer security technique in the semantic
Internet of Things. A novel security performance indicator, i.e., semantic
secrecy outage probability, is proposed.

In a conventional IoT, an eavesdropper is considered to be successful in
eavesdropping if it can obtain the source message sent by the transmitter.
However, in the SIoT, semantic information is transmitted in the wireless
channel and decoding is required to obtain the original source message, as
shown in Fig. 2 (Part A). Therefore, even if the eavesdropper intercepts the
semantic information sent by the transmitter, it may still not obtain the
required information, as shown in Fig. 2 (Part B). According to the
characteristics of semantic communication, we discuss the possible scenarios
in which the eavesdropper succeeds in eavesdropping on information but fails
in decoding it as follows:

  1. a)

Semantic decoding failure caused by background knowledge difference between
the eavesdropper and the legitimate receiver. In the SIoT, legitimate
communication participants will share the background knowledge for semantic
encoding and decoding. The eavesdropper might not have the same background
knowledge to decode the intercepted semantic information. For example, the
semantic information “Mouse” could be decoded as an animal or a computer
device, in which the eavesdropper may not be able to decode this meaning
correctly. Moreover, the dataset used for semantic encoder and decoder
training can be also regarded as the shared background knowledge that is
unavailable to the eavesdropper.

  2. b)

The eavesdropper’s task objectives are different from those of the legitimate
receiver, resulting in the eavesdropper’s inability to obtain the desired
information. For example, the transmitter is a camera in the SIoT that
captures street view photos. With the help of semantic communication
technology, the camera acts as a transmitter to send these photos to a
legitimate receiver for storage. The owner of the legitimate receiver is a
vehicle company interested in the number and type of cars on the street, while
an eavesdropper wants to steal pedestrians’ information on the road from
images. However, the transmitter, through the semantic encoder, transmits only
the semantic information that satisfies the task of the legitimate receiver,
e.g., image segmentation of vehicles. Therefore, even if the eavesdropper has
perfect access to the images transmitted in the wireless environment, its task
requirement is not met.

  3. c)

Semantic decoding failure caused by the encryption mechanism of the semantic
encoding model itself. Due to the fact that the semantic communication
technique requires only partial data to be transmitted and the decoding of
semantic information relies on the receiver’s decoder design, it has also been
regarded as a potential method for secure communications, the eavesdroppers
are unable to decode successfully. The reason is that the eavesdropper might
not have the semantic decoder that is jointly trained with the semantic
encoder to recover the original source message.

Based on the above discussion, one can conclude that the metrics reflecting
the security performance of the SIoT are not only SOP at the communication
level but also the semantic decoding error probability (SDEP) at the semantic
level. Here SDEP describes the probability that the eavesdropper can
successfully decode the information that it needs from the intercepted
semantic information. For example, in a semantic communications system with
visual question answering (VQA) task [8], SDEP can be the probability that the
eavesdropper uses the eavesdropped semantic information model to obtain the
correct answers to its own questions. To measure the security performance in a
comprehensive manner, we propose a new security performance metric for
physical later security technique in the SIoT, which is named semantic SOP.

######  Remark 1.

As shown in Fig. 2 (Part C), semantic SOP describes the probability that the
eavesdropper in the SIoT successfully eavesdrops on the semantic information
sent by the transmitter and successfully performs the semantic decoding.
Therefore, semantic SOP is defined as the product of SOP and one minus SDEP.

Note that when the task or interest of the eavesdropper is unknown to the
system designer, semantic SOP cannot be calculated accurately by the SIoT
designer. However, our proposed semantic SOP can still be used for theoretical
upper bound performance analysis, to verify the robustness of the proposed
system design. Another feasible research direction is to use statistical
methods to estimate the semantic information that eavesdroppers may wish to
obtain. Thus, the system designer can estimate SDEP to aid in secure SIoT
design, with the help of our proposed semantic SOP metric.

Figure 3: The SOP and the semantic SOP versus the signal-to-noise ratio of the
transmitter-receiver link with different values of SDEP. The distance between
the transmitter and the receiver is $15$ ${\rm{m}}$, the distance between the
transmitter and the eavesdropper is $18$ ${\rm{m}}$, the signal-to-noise ratio
of the transmitter-eavesdropper link is $0$ ${\rm{dB}}$, the target secrecy
rate threshold is $1$, the number of antennas for the transmitter, receiver,
and eavesdropper are all $3$, and the path loss exponent is $2$.

Figure 3 shows the SOP and the semantic SOP versus the signal-to-noise ratio
of the transmitter-receiver link with different values of SDEP. We can observe
that the probability that the eavesdropper fails to decode the semantic
information reduces the semantic SOP. Specifically, when an eavesdropper in
the semantic IoT has a $30\%$ probability of not being able to decode
successfully semantic information, i.e., SDEP = $30\%$, the transmitter can
use an SNR roughly 1 ${\rm{dB}}$ lower to achieve the same SSOP as the SOP in
a conventional IoT. Moreover, if a better pair of semantic encoder and decoder
can be designed to increase further the error probability of the eavesdropper
in decoding the semantic information, e.g., SDEP = $70\%$, we can observe that
the transmitter can use an SNR 5.5 ${\rm{dB}}$ lower to achieve the same SSOP
as the SOP in a conventional IoT.

An important inspiration for secure SIoT research is to perform cross-layer
co-design. Although semantic communications can enhance the system security
and reduce the transmit power required to achieve a certain SSOP, the encoding
and decoding of semantic information consume computational resources of the
network. Therefore, the tradeoff between SIoT performance and security should
be considered. By jointly designing the transmit and jamming power allocation
schemes in the physical layer and the semantic encoding/decoding scheme in the
semantic layer, a more secure and more efficient IoT can be achieved.

###  II-B Covert Communications

####  II-B1 Definition

So far, the PLS has been applied at large to boost wireless transmission
security. Despite its effectiveness, PLS still has certain limitations in
other aspects. By analyzing the wireless signal, for instance, the user’s
location may be exposed, which poses threat to user privacy. Such problems
cannot be solved by PLS techniques, triggering the proposal of covert
communications. Also known as low probability of detection communications,
covert communications aim to deliver information to a legitimate user without
being caught by the warden, who attempt to detect such transmission [9]. The
covert communications can include two major aspects. The first one mainly
focuses on analyzing and exploiting the uncertainty of the average power of
malicious wardens. Another one is to send the signal covered by high-power
signals, so as to improve covertness. It is not difficult to see that covert
communication never relies on the adversary’s competence, indicating that
transmission security can be perfectly guaranteed even if the attacker has a
strong processing capability. According to the above discussion, the covert
rate and DEP, which are detailed as follows, are used to characterize the
performance of covert communications.

  * •

Detection Error Probability: The warden needs to make a binary choice between
silent and transmitting via hypothesis testing. Therefore, the detection error
probability (DEP) is defined as the likelihood of the warden making a wrong
decision, which contains two cases. The first one is that the warden chooses
non-null-decision (transmitting) while the null hypothesis (silent) is true,
which is called false alarm. Another one is that warden sides with a null
hypothesis when the non-null hypothesis is true, which is known as miss
detection. The value of DEP is the sum of the probabilities of making the
above two wrong decisions.

  * •

Covert Rate: Besides DEP, covert rate, which describes the data transmission
rate when the DEP of the warden is close to one, is also vital. The covert
rate of any user can be calculated based on the well-known Shannon–Hartley
theorem [10].

####  II-B2 Covert Communications in SIoT Network

Figure 4: Rethinking covert communications technique in the semantic Internet
of Things. A novel security performance indicator, i.e., detection failure
probability, is proposed.

In a covert communication system, the objective of the warden is to detect
whether the transmission is taking place or not, without caring what data is
being transmitted. Therefore, encoding the source message to be transmitted
into semantic information will not improve the DEP of the warden. If the
warden successfully detects that wireless communication is taking place, it
can analyze and obtain the transmitter’s information such as the location, and
then apply interference to block the semantic communications. To make the DEP
converge to 1 arbitrarily, the solutions are to design a reasonable
transmitting power allocation scheme and/or to use a friendly jammer or a
reconfigurable intelligent surface, as in the conventional IoT. The covert
rate in the semantic IoT is the same as that in the conventional IoT.

However, because the warden can perform multiple detections during the data
transmission process, a failure of one detection does not mean that the warden
cannot discover the transmitting activity. Although the DEP can be arbitrarily
close to 1 with covert communication techniques, the DEP is typically set as
90% to 95% in practical communication systems [11]. Even if we consider that
the DEP is $99\%$, the probability that a warden who can detect the wireless
environment $5$ times per second finds a transmitting activity that lasts $10$
seconds is $1-99\%^{50}=39.5\%$. We can conclude that, when transmitting the
same amount of data, e.g., 1 article of 1000 words, with the same warden DEP,
the probability of the wireless transmission being successfully detected by
the warden is lower in the SIoT than that in the conventional IoT. The reason
is that in the SIoT, the transmitter can encode articles into semantic
information without affecting task completion, e.g., knowledge graphs, which
have fewer bits than the original article. Therefore, with the same covert
rate, transmitters in the SIoT can complete information transmission faster,
as shown in Fig. 4. Because there is an upper limit to the frequency of the
warden’s detection of the wireless environment, the shorter the transmission
time is, the lower the probability that the transmitting activity will be
detected.

However, there is no suitable performance indicator to describe the difference
in covert communication security performance that is caused by the data amount
difference. This research gap exists because all source messages are encoded
in the conventional IoT and there are no differences in the amount of data. To
fill this gap, we propose a new performance indicator for covert
communications, i.e., detection failure probability (DFP), as follows:

######  Remark 2.

DFP describes the probability that no transmitting activity is detected by the
warden’s multiple detections during the transmission time of the data.
Therefore, as shown in Fig. 4, DFP can be defined as a power function of DEP,
where the power is the number of detections. Considering that the warden
performs $f$ detections per unit time due to energy constraints, the number of
detections can be calculated as the data amount divided by covert rate and
then multiplied by $f$.

Figure 5: The detection failure probability versus the ratio of the data
volume of semantic information to that of the source message, in the SIoT and
conventional IoT, respectively. The DEP is $95\%$, the covert rate is $20$
${\rm bit/s/Hz}$, the bandwidth is $5$ ${\rm MHz}$, and the warden detects the
wireless environment at a frequency of twice per second.

Figure 5 illustrates the detection failure probability versus the ratio of the
data volume of semantic information to that of the source message. We can
observe that although the warden’s DEP is the same in both the SIoT and
conventional IoT, i.e., 90% as is set in much of the literature [11], a great
gap exists in the achievable DFP. For example, if the semantic encoder can
reduce the number of bits of the source message by half to obtain the semantic
information, the DFP can be improved by $69\%$.

An interesting insight is that there is a tradeoff between the semantic
encoder computing resource and the physical layer transmit power resource.
However, unlike the tradeoff we discussed in Section II-A2, for the semantic
encoder in the covert communication-aided SIoT, what matters is how much the
encoder reduces the number of semantic information bits. For the semantic
encoder in the PLS-aided SIoT, what matters is how low the probability is that
the semantic information is decoded successfully by an illegal eavesdropper.

###  II-C Encryption

####  II-C1 Definition

Encryption is one of the most classical techniques to ensure secure
transmission, which operates in the upper layers of the communication system.
For encryption techniques, there are comprehensive metrics for performance
evaluation, including but not limited to crack time, the throughput of
encryption/decryption, and power consumption. The crack time and the
computational resources to be used by the eavesdropper are positively related
to the key size.

####  II-C2 Encryption in SIoT Network

In the SIoT, encryption techniques can be seen as a “second layer” of
protection for the transmitted data. The reason is that the input of the
encryption algorithm can be semantic information obtained through semantic
coding, and semantic information itself has encryption properties. Even if the
eavesdropper succeeds in breaking the encryption, it may not succeed in
decoding the semantic information to obtain the source message, as we discuss
in Section II-A2.

A general design is to integrate cryptography as an option with semantic
communication systems [4]. In SIoT, if the transmitter and receiver want to
hide the information from a potential eavesdropper, the goal is to minimize
the error between the transmitter and receiver while maximizing the error
between the transmitter and eavesdropper. Following this idea, an encrypted
semantic communication system is designed in [4]. However, the authors in [4]
only considered symmetric encryption, and related work is still in the vacant
stage. More cryptography-assisted semantic communication systems can be
designed to further improve the security of SIoT.

##  III New Security Issues

In this section, we discuss the new security issues arising from the
introduction of semantic communication techniques in the IoT.

###  III-A Semantic Attack in SIoT Network

Unlike the bit streams transmitted in conventional IoT, the semantic
information in SIoT is largely task-related and dependent on the design of the
semantic encoder and decoder. However, a variety of error-correcting coding
methods have been designed to correct bit errors, but methods that can reduce
semantic noise have rarely been investigated. The semantic noise can have a
small or large impact on system performance. For example, because of the small
deviation of the text semantic vectors, the receiver decodes “bike” into
“bicycle” when recovering the text message. The receiver’s judgment will not
be affected. However, the disturbance of some semantic information may
seriously affect the communication system. For example, if the images are
incorrectly semantic encoded and uploaded to a dataset, the quality of the
artificial intelligence model trained by the dataset may be affected.

The mismatch between the original source message and the obtained semantic
information by semantic encoding is called semantic noise [5], which is
considered as a special type of noise present in semantic communication
systems. In the SIoT, some semantic noise is naturally present, e.g.,
different users have different interpretations of the same word, and require
better semantic encoding and decoding design to overcome. However, some
semantic noise is generated by attackers with the aim of disrupting the
semantic communication system. For source messages in text form, synonym
substitution or reversing the order of certain letters may cause the deep
learning-based semantic model to misinterpret the semantics of the sentence.
For source messages in image form, only by changing some pixels in an image,
the semantic information extracted by a well-pre-trained semantic encoder can
be completely inconsistent with the real content of the image [12]. Regardless
of the modality of the source message, the goal of the semantic attack can
vary and corresponds to different loss function optimization.

Figure 6: The targeted semantic attack approach. The experimental platform for
running the attack algorithm is built on a generic Ubuntu 20.04 system with an
AMD Ryzen Threadripper PRO 3975WX 32-Cores CPU and an NVIDIA RTX A5000 GPU.

  * •

Targeted Semantic Attack: The goal is to generate semantic tampered source
messages with a given target semantic information. Here, the target semantic
information is the semantic information that the receiver in the SIoT wants to
receive. For example, a digital twin service provider wants to collect some
images with snowy mountain as semantic information to build a virtual object.
The attacker can change some pixels in an irrelevant image to make the
semantic information of the irrelevant image very close to snowy mountain.
Therefore, the loss function could be the cosine similarity of the semantic
vectors of the irrelevant pictures and the snowy mountain pictures. As shown
in Fig. 6, as the number of iterations increases, the semantic similarity of
the two images gradually increases. If the digital twin service provider
cannot correctly detect the semantic tampered images, its database will be
contaminated. Therefore, this type of attack can be called semantic data
poisoning attack. Such a semantic tampering approach can also be used for man-
in-the-middle attacks. A malicious intermediate node capable of intercepting
the wireless communication channel can replace the images to be transmitted,
without affecting the semantic information.

  * •

Untargeted Semantic Attack: Similar to the approach of the target semantic
attack but with a different objective function, the aim of the untargeted
semantic attack is to minimize the similarity between the semantic information
of the tampered source message and its true semantic information. In this
case, the devices in the SIoT are unable to perform properly the semantic
encoding of the maliciously tampered source message. For example, the semantic
feature of the attack image in Fig. 6 is not iterating to be closer to the
“snowy mountain”, but as far from the “baseball player” as possible.

###  III-B Defense Methods

####  III-B1 Training-based Defense

By considering that a large part of the semantic communication encoders and
decoders are functioned by deep learning methods, a feasible solution to
reduce semantic noise is to improve the robustness of semantic models during
the training process. Specifically, there have been some training-based
methods, e.g., defensive distillation [13], weight perturbation [14], and
adversarial training [15].

Although there have been several approaches to improve model robustness using
adversarial samples in the fields of natural language and image processing
[15], semantic noise-resistant models in wireless communication have not been
sufficiently studied. Fortunately, researchers can draw inspiration from
existing adversarial training methods and consider the impact of wireless
channels and transmission overhead in the SIoT. Most recently, to reduce the
impact of semantic noise on the system, a masked vector quantized-variational
autoencoder (VQ-VAE) is developed as the architecture of the robust semantic
communication system [5]. To improve the system robustness, a feature
importance module is proposed to suppress noise-related and task-independent
features. It is shown that the proposed masked VQ-VAE requires $0.36\%$
transmitted symbols of the conventional “joint photographic experts group
(JPEG) + low-density parity-check coding” method [5], while effectively
improving the system robustness by reducing the impacts of semantic noise.

####  III-B2 Training-free Defense

Research on training-free defense methods remains to be developed. There may
be different defense methods for data with different modalities. Taking image
data as an example, a possible defense solution is to use the visual
invariance of the semantic tampered images for correct semantic extraction. As
shown in Fig. 6, although the semantic similarity between the two images is
high for a semantic encoder, the human eye can easily see the difference
between them. The reason is that only some pixels in the attack image have
been adjusted. Inspired by this, we try to blur both images by using Gaussian
method, and find that the semantic similarity between them can be reduced from
$0.987$ to $0.78$, without retraining the semantic model. More pre-processing
solutions could be investigated to defend against this kind of semantic attack
as a future research direction.

##  IV Future Direction

###  IV-A Explainable AI-aided Semantic Communications

The past few years have witnessed the rapid development of machine learning
(ML) technologies, especially deep learning, which has shown significant
advantages in a variety of applications. Most of them, however, are often
unable to explain their decisions and actions during the operation process,
triggering the research on explainable artificial intelligence (XAI). The XAI
aims to provide users with detailed explanations of how the decision is made
or the result is obtained. For semantic communications, which rely on ML, the
XAI can make the training of transceiver pairs change from black box to white
box, driving the training process clearer and easier to understand. Such
improvement not only allows semantic communication system designers to
identify and fix potential vulnerabilities or threats but also helps users
understand and trust these semantic communications better. Therefore, studying
explainable AI-aided semantic communications is an indispensable step to
improve its security.

###  IV-B Blockchain-aided Semantic Internet of Things Network

The blockchain is a chain of blocks that store all committed transactions in a
decentralized and distributed network. Unlike the conventional ways, the
blockchain realizes the peer-to-peer digital assets transfer without any
intermediaries, and the features of decentralization, immutability, audit-
ability and transparency drive the transactions’ security. Considering the
above advantages, the stored and shared transaction information in the
blockchain can be replaced with semantic information that needs to be
transmitted. In this way, not only the storage consumption of the blockchain
is reduced, but also, the decentralized blockchain verification mechanism
would further improve the security of semantic content. Therefore, how to
better integrate blockchain and the SIoT is also worthy of further study.

###  IV-C Secure Semantic Communications for Metaverse

As a novel type of Internet application and social form, the Metaverse has
received more and more attention in recent years. To provide an ideal
immersive experience for users, the data that describes the user and physical
world must be transmitted to the virtual world quickly and accurately, during
this process effective tracking and accurate prediction are critical. Thereby,
semantic communication is one of the best-suited techniques for this task.
Considering the characteristics of data and the requirements of applications,
it is vital to study the security of semantic communication under the
framework of the Metaverse. This not only affects the user experience but is
also directly related to the user’s security and privacy in the physical
world.

##  V Conclusion

Considering the new features of the SIoT compared to the conventional IoT, we
rethought three wireless communication security techniques, i.e, PLS, covert
communications, and encryption. We discussed the characteristics of each
technology when applied in SIoT. Specifically, because of the encryption
characteristics of semantic information itself, the security enhancement that
PLS can bring to the network is further improved. In addition, since semantic
information that has fewer bits can be transmitted faster than the original
source message, the difficulty of achieving covert communications is reduced.
To show these two new characteristics, we proposed two new indicators, i.e.,
semantic SOP and DFP. Finally, we discussed new attacks and defense schemes
that have emerged at the semantic level. We foresee that the combination of
semantic communications and classical security techniques will revolutionize
the architecture of communication networks, bringing new inspiration to the
two most important dimensions of performance and security.

## References

  * [1] W. Xu, Z. Yang, D. W. K. Ng, M. Levorato, Y. C. Eldar _et al._ , “Edge learning for B5G networks with distributed signal processing: Semantic communication, edge computing, and wireless sensing,” _arXiv preprint arXiv:2206.00422_ , 2022.
  * [2] Z. Yang, M. Chen, W. Saad, W. Xu, M. Shikh-Bahaei, H. V. Poor, and S. Cui, “Energy-efficient wireless communications with distributed reconfigurable intelligent surfaces,” _IEEE Trans. Wireless Commun._ , vol. 21, no. 1, pp. 665–679, Jan. 2021.
  * [3] A. Chorti, A. N. Barreto, S. Köpsell, M. Zoli, M. Chafii, P. Sehier, G. Fettweis, and H. V. Poor, “Context-aware security for 6G wireless: The role of physical layer security,” _IEEE Commun. Stand. Mag._ , vol. 6, no. 1, pp. 102–108, Jan 2022.
  * [4] X. Luo, Z. Chen, M. Tao, and F. Yang, “Encrypted semantic communication using adversarial training for privacy preserving,” _arXiv preprint arXiv:2209.09008_ , 2022.
  * [5] Q. Hu, G. Zhang, Z. Qin, Y. Cai, G. Yu, and G. Y. Li, “Robust semantic communications with masked VQ-VAE enabled codebook,” _arXiv preprint arXiv:2206.04011_ , 2022.
  * [6] W. Yang, H. Du, Z. Liew, W. Y. B. Lim, Z. Xiong, D. Niyato, X. Chi, X. S. Shen, and C. Miao, “Semantic communications for 6G future internet: Fundamentals, applications, and challenges,” _arXiv preprint arXiv:2207.00427_ , 2022.
  * [7] A. Mukherjee, S. A. A. Fakoorian, J. Huang, and A. L. Swindlehurst, “Principles of physical layer security in multiuser wireless networks: A survey,” _IEEE Commun. Surv. Tut._ , vol. 16, no. 3, pp. 1550–1573, Mar. 2014.
  * [8] H. Xie, Z. Qin, and G. Y. Li, “Task-oriented multi-user semantic communications for VQA,” _IEEE Wireless Commun. Lett._ , vol. 11, no. 3, pp. 553–557, Mar. 2021.
  * [9] I. Makhdoom, M. Abolhasan, and J. Lipman, “A comprehensive survey of covert communication techniques, limitations and future challenges,” _Comput. Secur._ , p. 102784, 2022.
  * [10] O. Rioul and J. C. Magossi, “On shannon’s formula and hartley’s rule: Beyond the mathematical coincidence,” _Entropy_ , vol. 16, no. 9, pp. 4892–4910, Sept. 2014.
  * [11] T.-X. Zheng, Z. Yang, C. Wang, Z. Li, J. Yuan, and X. Guan, “Wireless covert communications aided by distributed cooperative jamming over slow fading channels,” _IEEE Trans. Wireless Commun._ , vol. 20, no. 11, pp. 7026–7039, Nov. 2021.
  * [12] C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” in _Proc. Int. Conf. Learn. Represent._ , 2014.
  * [13] N. Papernot, P. McDaniel, X. Wu, S. Jha, and A. Swami, “Distillation as a defense to adversarial perturbations against deep neural networks,” in _Proc. IEEE Symp. Secur. Priv._ , 2016, pp. 582–597.
  * [14] D. Wu, S.-T. Xia, and Y. Wang, “Adversarial weight perturbation helps robust generalization,” _Proc. Adv. Neural Inf. Process. Syst._ , vol. 33, pp. 2958–2969, 2020.
  * [15] Y. Bai, Y. Zeng, Y. Jiang, S.-T. Xia, X. Ma, and Y. Wang, “Improving adversarial robustness via channel-wise activation suppressing,” _arXiv preprint arXiv:2103.08307_ , 2021.