Phase compensation of MARSIS subsurface sounding data
and estimation of ionospheric properties: New insights
from SHARAD results
Bruce A. Campbell1 and Thomas R. Watters1
1Center for Earth and Planetary Studies, Smithsonian Institution, Washington, District of Columbia, USA
Abstract Subsurface radar sounding observations by theMars Advanced Radar for Subsurface and Ionospheric
Sounding (MARSIS) and Shallow Radar (SHARAD) instruments are affected by ionospheric phase distortions
that lead to image blurring and delay offsets. Based on experience with SHARAD image correction, we
propose that ionospheric blurring in MARSIS radargrams may be compensated with a model of smoothly
varying quadratic phase errors along the track. This method yields well-focused radargrams for geologic
interpretation and allows analysis of the validity range for models used to derive total electron content (TEC)
from phase distortion terms in previous MARSIS studies. The quadratic term appears to be a good proxy for
TEC at solar zenith angles >65° for MARSIS Band 4 (5MHz) and >75° for Band 3 (4MHz). Comparison of
MARSIS- and SHARAD-derived TEC values from 2007 to 2014 reveals correlations in seasonal behavior and in
the characterization of ionospheric activity due to coronal mass ejections. We also present SHARAD and
MARSIS evidence for a persistent region of anomalous radar scattering south of Arsia Mons. These echoes
have been previously suggested to arise from refraction of the radar signal by electron density variations.
There are no strong signatures, however, in the quadratic image compensation term correlated with the
anomalous scattering, suggesting either that electron density variations responsible for refracted signal
paths occur primarily in regions offset from the spacecraft track or that these density changes have aminimal
impact on the integrated phase distortion of the subspacecraft footprint. We suggest observations and
analyses to better constrain the mechanism and timing of such echoes.
1. Introduction
The ionosphere of Mars exhibits fluctuations in electron content with time and geographic location due to
variations in distance from the Sun, the degree of solar activity, local solar zenith angle, and remnant crustal
magnetic fields. Electron density varies with altitude above the surface, with a scale height between 8 and
30 km and a maximum dayside density at altitudes from about 120 to 150 km [Gurnett et al., 2005; Withers
et al., 2012]. The spatial and temporal characteristics of the electron density are of interest as a measure of
ionospheric activity [e.g., Withers, 2009], and because of their impact on radar-sounding observations of
the surface and subsurface. This work examines current methods for correcting ionospheric effects in orbital
radar sounding data, demonstrates a new approach based on recent studies of spatial variation in the
electron density, and discusses implications for estimating the total electron content (TEC) and understanding
anomalous features in the sounder data.
Two radar-sounding instruments are currently in orbit at Mars. The Mars Express spacecraft carries the Mars
Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) [Picardi et al., 2005; Jordan et al., 2009],
while the Mars Reconnaissance Orbiter carries the Shallow Radar (SHARAD) instrument [Seu et al., 2007].
MARSIS subsurface sounding observations utilize one of four bands with center frequencies, f0, of 5MHz,
4MHz, 3MHz, and 1.8MHz. The bandwidth of the linear frequency-modulated “chirp” signal is 1MHz for each
mode. SHARAD operates at a single center frequency of 20MHz, with a 10MHz chirp bandwidth. The result-
ing free-space, one-way vertical resolution is 150m for MARSIS and 15m for SHARAD, reduced by the root of
the real permittivity, ε′, for propagation in geologic materials (about 80m and 8m, respectively, in water ice,
for which ε′ is about 3.2).
Because the transmitted power is low, the chirp signal allows for recovery of fine time resolution from a pulse
that is 250μs long for MARSIS and 85μs long for SHARAD. The reflected signal is correlated with a model for
the original swept-frequency chirp to achieve a much shorter effective pulse (“range compression”), but the
ionosphere can complicate this process. A radar signal passing through the ionosphere experiences three
CAMPBELL AND WATTERS PHASE COMPENSATION OF MARSIS DATA 180
PUBLICATIONS
Journal of Geophysical Research: Planets
RESEARCH ARTICLE
10.1002/2015JE004917
Key Points:
• SHARAD results can improve ionospheric
compensation of MARSIS sounding data
• Total electron content from both
sensors can be merged for long-term
studies
• Scattering by refraction in the
ionosphere occurs over long periods
in some regions
Correspondence to:
B. A. Campbell,
campbellb@si.edu
Citation:
Campbell, B. A., and T. R. Watters (2016),
Phase compensation of MARSIS subsur-
face sounding data and estimation of
ionospheric properties: New insights
from SHARAD results, J. Geophys. Res.
Planets, 121, 180–193, doi:10.1002/
2015JE004917.
Received 30 JUL 2015
Accepted 6 JAN 2016
Accepted article online 11 JAN 2016
Published online 22 FEB 2016
Published 2016. This article is a U.S.
Government work and is in the public
domain in the USA.
effects: (1) an increased time delay with respect to that determined from the speed of light in vacuum, (2)
distortion of the range-compressed echo due to variations in phase over the frequency range of the chirp,
and (3) attenuation of the reflected signal. The impact of the ionosphere increases for lower frequency radar,
and if the signal approaches the plasma frequency, there is essentially no propagation.
The desire to obtain subsurface sounding data means that many observations from both instruments must be
corrected for the delay and distortion effects—there is no way to recover power lost due to attenuation.
MARSIS began operations in July 2005, and several approaches to ionosphere compensation and TEC estimation
are well documented [Safaeinili et al., 2003, 2007; Mouginot et al., 2008; Zhang et al., 2009; Cartacci et al., 2013].
These studies show that MARSIS observations are affected by the ionosphere to a solar zenith angle (SZA) value
of about 120°, rather far onto the “nightside” of Mars. MARSIS also has an active topside sounding mode (AIS),
used to characterize the upper layers of the ionosphere, and assess the impact of crustal magnetic fields
[Gurnett et al., 2005; Duru et al., 2006]. SHARAD arrived at Mars in 2006, and subsequent work has addressed
the smaller but still important effects of the ionosphere [Campbell et al., 2011, 2014]. SHARAD echoes, due to their
higher frequency, are little impacted beyond SZA values of about 100°.
Recent experience with SHARAD data sheds new light on how the ionosphere of Mars behaves over relatively
short (few tens of kilometers) length scales, and the large number of orbit crossovers at different solar zenith
angles, and thus echo delay, allows for well-calibrated estimates of the total electron content. Taken together,
these findings motivate a new look at the correction of MARSIS data for ionospheric blurring effects, and at
the retrieval of TEC values from these observations. We first provide a synopsis of how the electron density
affects radar signals, and the methods used to date in correcting MARSIS and SHARAD echoes (section 2).
We then compare TEC estimates from the two sensors during periods of overlapping observation, use
SHARAD data to support a new method for representing the along-track changes in MARSIS phase distor-
tion, and demonstrate the utility of this method to improve recovery of the subsurface sounding informa-
tion (section 3). In section 4, we revisit the estimation of TEC from MARSIS based on the information
extracted from the new compensation scheme. In section 5, we use the extended temporal coverage from
the two sounders to study long-lived ionospheric effects south of Arsia Mons. Section 6 summarizes results
and directions for future work.
2. Ionospheric Distortion, Compensation, and TEC Estimation
The electron content of a planetary ionosphere may have a complicated distribution as a function of height
above the surface, with a peak density that can vary in both amplitude and elevation [e.g.,Withers et al., 2012].
Depending on the degree of solar activity, collisional interactions between neutral particles in the atmo-
sphere may also play an important role. Active sounding from high altitude can probe this distribution by
obtaining reflections from regions of enhanced electron content [e.g., Gurnett et al., 2005; Duru et al.,
2006]. Signals from an orbiting subsurface sounder, in contrast, traverse the lower ionosphere, ideally without
undergoing such reflections. The primary goal of ionospheric compensation is thus to obtain a high-quality
radargram for geologic studies, with a secondary goal of retrieving information on the electron content.
The radargrams, two-dimensional representations of echo power with along-track location and signal time
delay, for MARSIS and SHARAD are built up from a series of individual “frames,” each of which represents a
certain number of echo records received in response to transmitted pulses. These batches of echoes are
Doppler processed to narrow the along-track resolution and improve the signal-to-noise performance
through coherent summation of signals from a given point of the surface or subsurface as it passes beneath
the sensor [e.g., Picardi et al., 2004; Seu et al., 2007]. Figure 1 shows representative MARSIS and SHARAD radar-
grams over the south polar layered deposits of Mars, highlighting the differences in depth of penetration and
vertical/horizontal spatial resolution. Our main concern here is with the range compression of signals, rather
than the choice of parameters for Doppler processing. In this section, we review the basic effects of the elec-
tron density on a linear frequency-modulated (chirp) radar signal, and the methods currently used to correct
MARSIS and SHARAD data.
2.1. Phase Effects on a Radar Signal
MARSIS and SHARAD signals can be approximated by a linear frequency ramp over the duration of the chirp. In
reality, the transmitted signal has variations in amplitude (and perhaps phase) due to the imperfect impedance
Journal of Geophysical Research: Planets 10.1002/2015JE004917
CAMPBELL AND WATTERS PHASE COMPENSATION OF MARSIS DATA 181
match between the signal and the dipole antenna and matching network, but neglecting these aspects appears
to still allow stable ionospheric modeling results [e.g., Campbell et al., 2014]. The MARSIS “up-swept” chirp can be
expressed as an instantaneous angular frequency, φ, that varies with time, t, from the start of the pulse:
φ tð Þ ¼ 2π FL þ atð Þ (1)
where FL is the low-frequency end of the signal bandwidth and a is the chirp rate (in Hz/s). The actual phase
function, Φ, applied to the transmitted signal is the integral of φ(t) over time, so the basic form is quadratic:
Φ tð Þ ¼ 2π tFL þ a2 t
2

 
(2)
and the discrete, complex values of the chirp compression function are the following:
Ci ¼ sin Φ tið Þð Þ þ icos Φ tið Þð Þ (3)
For MARSIS, ti is incremented by about 0.714μs for each of 490 complex samples (a 1.4MHz sampling rate)
and a is 4.0 × 109 Hz/s. For SHARAD the time increment between the 3600 real-valued samples is 0.0375μs,
and a is about 7.4 × 1010 Hz/s. In the absence of ionospheric effects, echoes collected by the receiver can
be range compressed to power format by multiplying the frequency domain signal spectrum by the
conjugate of the Fourier transform of the chirp phase function (equation (3)), performing an inverse
Fourier transform, and taking the squared magnitude of the complex signal.
The ionosphere distorts the phase of the radar signal as it transits the column of electrons, with a dependence
on frequency that leads to degradation of the range-compressed surface and subsurface echoes. Mitigating
this distortion in the range compression requires an additional function that modifies either the reflected sig-
nals or the reference chirp. The most common approach to date expresses the necessary correction function
in terms of the constituent frequencies of the chirp and the physical parameters of the ionosphere, primarily
the electron density as a function of altitude, z, above the surface, N(z). Expansion of this function and reten-
tion of only terms up to third order leads to an approximation in inverse powers of the radar frequency, f, and
the moments of the electron density distribution [Safaeinili et al., 2007]:
Δφ fð Þ ¼ 2π
c
8:982
f
∫N zð Þdz þ 8:98
4
3f 3
∫N2 zð Þdz þ 8:98
6
8f 5
∫N3 zð Þdz
 
(4)
Figure 1. Radargrams for both channels (F1 and F2) of MARSIS track 4719, processed using the autofocus algorithm
discussed in this paper. The south polar layered deposits (SPLD) of Mars are at right. Bottom panel is portion of nearby
SHARAD track 16344_01, showing the SPLD layering in more detail, but with almost no reflection from the bright basal
reflector seen by MARSIS. Arrows denote approximately correlated locations in the two data sets.
Journal of Geophysical Research: Planets 10.1002/2015JE004917
CAMPBELL AND WATTERS PHASE COMPENSATION OF MARSIS DATA 182
The first integral is the total electron content, in number per square meter, often normalized by a factor of
1016 to “TEC units” or TECUs. A realistic model of the phase distortion requires a description of the
ionosphere that typically includes a scale height, maximum electron density, and overall shape with altitude
(e.g., Gaussian, quadratic, and triangular). Equation (4) allows for a description of the distortion based on
three parameters (a1, a2, and a3) related to the moments of the electron distribution [Safaeinili et al., 2007;
Mouginot et al., 2008; Cartacci et al., 2013]. Zhang et al. [2009] propose an extension of this function to include
effects due to collisional interactions in the neutral atmosphere, thus adding additional terms.
We can also represent the phase variation without reference to any particular physical model for how it is
generated in the ionosphere. In this view, the chirp is distorted as function of time along the pulse, and
the correction process is the derivation of an optimum “matched filter” for range compression. Starting from
equation (2), the distorted chirp is given, to third order, by
Φ tð Þ ¼ π 2t FL þ αð Þ þ t2 aþ βð Þ þ t3χ
 
(5)
Here α represents a linear term that leads only to a delay (i.e., vertical position) offset in the radargram frames,
and β and χ define the quadratic and cubic errors that cause image distortion. Higher-order distortions are
not expected to play a significant role in the sounder echoes, and even the cubic term may be negligible if
the sounder’s operating band is properly chosen to be well above the plasma frequency. The α term is similar
to the a1 term in common applications of equation (4), while the a2 and a3 terms of those expansions may
mix the quadratic and cubic phase components to some degree [Cartacci et al., 2013].
Schemes for mitigating phase distortion in the range compression, using either of the models above, can be
described as autofocusing—using the echoes themselves as the metric for the compensation algorithm and
optimizing the strength (signal-to-noise ratio, or SNR) of the reflected power. This approach has been proven
successful in imaging radar applications, using a variety of functional representations for the phase errors and
for the search algorithms that optimize the final product. One important note is that autofocus algorithms
generally rely on a degree of redundancy, such as multiple bright scattering features in a scene, to yield a
“true” maximum signal response in the presence of clutter and noise [e.g., Wahl et al., 1994; Fienup and
Miller, 2003].
2.2. MARSIS Processing
MARSIS data in the most frequently used subsurface mode (SS3) are processed on the spacecraft to create
spectra for three Doppler filters (a trailing frequency bin, a center or nadir bin, and a leading frequency
bin), and these spectra are transmitted to the ground without being range compressed [Jordan et al.,
2009]. The spectra are converted to baseband, so FL=0.5MHz (equation (1)) for all operating bands. Each
SS3 record contains two channels, termed F1 and F2, with echoes in frequencies selected from the four pos-
sible based on the solar zenith angle, and thus often switching as the SZA changes along track. Considerable
work has been done in relating the MARSIS range compression to estimates of ionospheric properties while
optimizing the signal-to-noise ratio of the radargrams.
Safaeinili et al. [2007] use the formulation of equation (4), optimizing the an terms by reference to the time
delay between the sensor and the surface at the elevation defined by the Mars Orbital Laser Altimeter
(MOLA), and to a maximum SNR of echoes within each frame. Mouginot et al. [2008] use a Gaussian model
for the electron density profile, and seed each succeeding optimization with the parameters defined from
the previous frame. Both frequency channels of the SS3 mode, F1 and F2, are optimized simultaneously
on the assumption that the chosen ionosphere structure model, which constrains relationships between
the an terms, is appropriate over the range of the MARSIS bands (1.3 MHz to 5.5MHz). The a1 value
(the coefficient on the first-order term of equation (4)) derived from this technique is used to form the
Planetary Data System (PDS) archive of MARSIS TEC estimates. Zhang et al. [2009] propose a more
complex physical ionosphere model that includes neutral collision effects. Finally, Cartacci et al. [2013]
present a study of nightside MARSIS tracks, treating the F1 and F2 channels independently and deriving
a TEC estimate based on the a2 term and the center frequency, f0, of the MARSIS band:
TEC ¼ a2cf
3
0
2π 8:98ð Þ2 (6)
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CAMPBELL AND WATTERS PHASE COMPENSATION OF MARSIS DATA 183
The results of Safaeinili et al. [2007] and Cartacci et al. [2013] demonstrate possible correlations between the
component of the remnant crustal magnetic field perpendicular to the surface and the electron content of
the ionosphere.
As a general observation, the TEC values derived by these methods have significant variability within groups
of frames, and occasional anomalous spikes. The quality of the radargrams is also affected, since the autofo-
cus method has not converged in these frames to the true distortion function. The range of variation, as a
fraction of the mean TEC value, appears to be larger at smaller values of the SZA. We suggest that much of
this behavior stems from application of autofocus techniques to a single echo record, in the presence of
noise, rather than to the groups of observations typical of many SAR focusing studies. There are also ques-
tions about the magnitude of derived TEC values, which are high relative to the AIS measurements under
dayside conditions [Sanchez-Cano et al., 2015].
As both Cartacci et al. [2013] and Sanchez-Cano et al. [2015] note, application of equation (6) is based on
assumptions that may break down at higher electron densities. Cartacci et al. [2013] suggest that their TEC
values are systematically overestimated, with the error increasing to 10% or more at the lowest solar zenith
angles. They thus limit their study of possible magnetic field effects to SZA> 90°. The impact of model
approximations on the TEC results of Mouginot et al. [2008], using the a1 term, is uncertain. Results from
SHARAD suggest that a modified approach to MARSIS processing (section 3) can yield improvements in
radargram image recovery, shed light on where these earlier methods of TEC estimation can yield robust
results, and provide a stable solution for examination of long-term trends in ionospheric behavior.
2.3. SHARAD Processing
SHARAD data offer an advantage in understanding the nature of ionospheric distortion due to their higher
sampling rate relative to the ground speed of the spacecraft and the capability to downlink the full record
of all pulses without onboard processing. The compensation for products delivered by the U.S. instrument
team to the PDS is based on autofocusing, with the “downswept” linear chirp modified by an empirically
derived function given by
Φ tð Þ ¼ E FH  at½ 1:93 (7)
where FH is the maximum chirp frequency (25MHz) and E is a scalar parameter optimized by the autofocus-
ing. The fixed power law exponent means that the coefficients of the quadratic (β) and cubic (χ) phase
distortion terms have a fixed ratio [Campbell et al., 2011], and this approximation appears valid over the
SHARAD frequency band. For groups of observations, typically spanning about 35 km along the track, the
autofocus method optimizes the SNR, and the derived compensation is applied to all radargram frames
within the region. The scalar coefficient, E, has a close correlation with delay offsets at hundreds of orbit
crossover locations observed at different solar zenith angles, showing that a very good approximation for
the TEC is 0.29E [Campbell et al., 2014]. This “calibration” of the TEC values is accurate enough to reduce
the RMS errors in surface echo vertical positioning to just a few range cells (i.e., <50m).
SHARAD results suggest a generally smooth, cosine-like drop in TEC with solar zenith angle, as predicted by
the model of Chapman [1931], with broad fluctuations of 10–20% due to localized nightside effects possibly
linked with remnant crustal magnetic fields [Campbell et al., 2011] and dayside conditions modulated by
these fields and other mechanisms [Withers, 2009]. In thousands of SHARAD tracks processed to date, we also
observe that changes in the total electron content of the ionosphere are smooth down to the scale of the
radargram postings (about 500m). If there were poorly modeled spatial-frequency (few kilometers to
500m) shifts in the phase distortion, we would expect to see badly range-compressed areas within each
35 km region.
2.4. Comparing MARSIS and SHARAD Data
We can illustrate the similarities and differences in sounder estimates of the TEC during a period of overlap,
December 2006 to September 2007, between the PDS-released MARSIS products (Tracks 3748–4808) based
on the method of Mouginot et al. [2008] and the PDS archive of SHARAD observations (Tracks 1689–5522)
based on Campbell et al. [2011, 2014]. Figure 2 shows the average and standard deviation of the TEC derived
from both data sets during this period. It is clear that MARSIS values tend to exceed those from SHARAD, and
the maximum offset between them is about 10%. The standard deviation of the MARSIS estimates rises
Journal of Geophysical Research: Planets 10.1002/2015JE004917
CAMPBELL AND WATTERS PHASE COMPENSATION OF MARSIS DATA 184
steadily onto the dayside, whereas the
higher SHARAD frequency and greater
degree of redundancy for autofocusing
allow a more consistent TEC estimation
performance to SZA values as low as
45°. The typical outcome of the two
approaches is shown by tracks obtained
just a day apart in 2007 (Figure 3); again,
the MARSIS estimates become progres-
sively more widely scattered and larger
than the SHARAD values at smaller SZA.
3. A New Approach to MARSIS
Ionosphere Compensation
Earlier efforts to compensate iono-
spheric effects on the MARSIS echoes
assume that the phase distortion varies
significantly between successive frame
acquisitions and thus that the autofo-
cusing must operate on a single frame
at a time. While the phase effects likely
do vary rapidly, SHARAD results (section 2) support the notion that these changes can bewell modeled by smooth
functions of the along-track location, as expressed here by the frame number within each segment of the track
defined by the use of one of the operating frequency bands. We thus represent the quadratic phase term in
equation (5), β, by a polynomial function of this along-track frame number, n, over each period of a chosen
frequency in the F1 and F2 channels. The two channels are optimized independently as are the individual seg-
ments. We do not index the polynomial to solar zenith angle because for MARSIS polar observations the same
SZA value can occur at two locations along the track. The choice of equation (5) to represent the distortion distances
our approach from any physical description of the electron density distribution, but it does provide significant
insight into limits on assumptions about the linkage of quadratic errors and TEC as a function of solar zenith angle.
For each single-band segment of the F1 and F2 radargrams, we optimize the quadratic error term by refer-
ence to the summed SNR of all constituent frames in the segment. A seventh-order polynomial on the frame
number appears to adequately repre-
sent the along-track fluctuations in β:
β nð Þ ¼
X7
i¼0
Cin
i (8)
with the coefficients, Ci, optimized
through a downhill simplex minimiza-
tion algorithm (IDL’s AMOEBA) using
the summed SNR as a metric. The great
value here is that the autofocusing can
exploit the redundancy in groups of
frames to achieve a robust solution to
the range compression. Figure 4 shows
how the fitting yields a piecewise
solution for the ionospheric behavior
along a MARSIS track. As with most
other methods, we sum the signals from
all three Doppler channels to reduce
speckle in the radargram, though this
may reduce the SNR of extremely smooth
surfaces to some degree (i.e., by adding
MARSIS (thin line) and SHARAD (thick line)
Estimates of Total Electron Content
Average over period from December 6, 2006 to September 30, 2007
Figure 2. Comparison of total electron content unit estimates for the
period from 6 December 2006 to 30 September 2007 from MARSIS
[Mouginot et al., 2008] and SHARAD [Campbell et al., 2011, 2013] data.
Note that MARSIS TECU estimates exceed those from SHARAD by up to
about 10% and exhibit progressively greater variance with smaller
solar zenith angle.
MARSIS Track 4719 (crosses)
SHARAD Track 5226_01 (triangles)
Figure 3. Comparison of estimated total electron content unit values for a
MARSIS track collected 6 September 2007 and a SHARAD track collected 7
September 2007. Note that MARSIS values are typically higher than
those of SHARAD and exhibit far more variance at solar zenith angles less
than about 85°.
Journal of Geophysical Research: Planets 10.1002/2015JE004917
CAMPBELL AND WATTERS PHASE COMPENSATION OF MARSIS DATA 185
off-nadir measurements containing little
of the specular echo).
A MARSIS SS3 observation may have
data from as few as two bands (one
each in the F1 and F2 channels) or
employ up to all four bands if the range
of SZA is large enough to cover both
nightside and dayside conditions. Our
optimization yields an estimate of the
total quadratic phase term, so β is
obtained by subtracting the “ideal”
4.0 × 109 Hz/s chirp rate from the com-
ponent in each frame. Each frame is nor-
malized to the background noise, based
on the lowest echo in batches of 32
averaged range cells. With the image
distortion corrected, we compensate
for variations in the vertical position of
the frames by assigning the MOLA elevation to the earliest echo that meets a specified threshold, which
changes with the peak SNR to allow for robust selection when the sidelobes of the surface reflection rise
above the noise. In general, the optimization process yields good range compression over the length of
the radargram (Figure 5). Poor image quality is associated with some of the lowest frequency (Band 1) data,
which may overlap with the plasma frequency of the ionosphere, and with frames where the time delay
between the pulse transmission and the start of the data recording window (i.e., the range to the surface)
was estimated incorrectly.
4. TEC Estimation
Under certain assumptions about ionospheric properties, equation (6) suggests a linear relationship between
the quadratic image distortion term and the TEC [Cartacci et al., 2013]. A similar assumption appears to hold
for the SHARAD data over a wide range of SZA [Campbell et al., 2013], but at the lower MARSIS frequencies,
there are likely limits on its validity. Cartacci et al. [2013] note mismatches between values for the TEC
estimated from equation (6) with the different MARSIS bands on the dayside and thus limit their analysis
to nightside observations (SZA> 90°). We can use the results of the new autofocus method to examine these
behaviors in more detail.
MARSIS Track 4719
F2: BAND 2
F1: BAND 4
F1 and F2: BAND 3
Figure 4. Plot of quadratic phase error term, β, from autofocus solution for
both channels, F1 and F2, of MARSIS SS3-Mode Track 4719 (Figure 1). Note
that the solutions for Band 3 are nearly continuous across the change
in operation.
Figure 5. Representative MARSIS tracks showing value of ionospheric correction and registration to MOLA datum for
subsurface feature interpretation. Three major landforms are illustrated: the Medusae Fossae Formation and the north
and south polar layered deposits. Image width of each panel is 460 MARSIS frames (about 2600 km), and the vertical scale is
178.5 μs.
Journal of Geophysical Research: Planets 10.1002/2015JE004917
CAMPBELL AND WATTERS PHASE COMPENSATION OF MARSIS DATA 186
Figure 6 shows the average quadratic
phase error in MARSIS bands 2–4 (center
frequencies of 3.0, 4.0, and 5.0MHz) for
the same group of orbit tracks used in
Figure 2 (3748–4808). The angular cov-
erage of Band 2 is much smaller, as day-
side ionospheric effects are expected to
greatly impact this frequency range. As
a tool for understanding the TEC,
equation (6) is based on the assumption
that the dominant component in the
expansion of equation (4) is the 1/f term,
which is modulated only by the first
moment of the electron distribution. If
this is the case, then the quadratic
phase values should be related as the
cube of the ratio of their center frequen-
cies. Applying this scaling to the quadra-
tic phase errors determined from the
new method shows an excellent correlation for solar zenith angle values greater than about 75° (Figure 7).
This supports a similar conclusion about the range of TEC validity by Sanchez-Cano et al. [2015] based on
comparisons of estimates from the various subsurface-mode methods with the AIS data.
A comparison of the corrected quadratic terms to the SHARAD TECU estimates for the two tracks used in
Figure 3 shows a reasonable match for SZA= 65–75° when the MARSIS β values, after normalization to a
5MHz frequency, are multiplied by an ad hoc factor of 0.85 (Figure 8). As expected, the agreement between
MARSIS and SHARAD TECU estimates occurs over the largest range of SZA for the 5MHz (Band 4) data, down
to about 65°. The new method may thus allow for accurate recovery of the TEC somewhat farther into the
dayside than in recent studies, but estimates for SZA less than 65° (Band 4) to 75° (Band 3) will depend upon
analyses that might use the frequency dependence in the quadratic phase (equation (4)) to model the
higher-order moments of the electron density distribution.
We processed MARSIS tracks from the start of the mission to mid-2014 and compared the resulting TEC esti-
mates to those of SHARAD over the period beginning in early 2007. We used only MARSIS Band 3 data for this
test, since it is frequently employed in
the SZA range of 75–85°. For every
MARSIS or SHARAD track during the
time period, we extracted all TECU
estimates within this angular range,
normalized by cos(SZA) to reduce
Chapman-like variations, and averaged
the resulting values. Figure 9 shows
the two data sets with an arbitrary offset
for clarity. Despite gaps in temporal cov-
erage, both TEC estimation methods
appear to follow the expected variation
with heliocentric longitude, reaching a
“local minimum” value at each Mars
aphelion (northern summer solstice).
The short-term, interorbit variance in
TECU values is similar for results from
the two sensors.
Both radar sounders also detect
increases in ionospheric activity, such
a major event in early- to mid-2011.
MARSIS Tracks 3748-4808
BAND 4
BAND 3 BAND 2
Figure 6. Average quadratic phase error derived from the autofocusing
method presented in this paper, plotted as averages in each of three
MARSIS bands for tracks 3748–4808, versus solar zenith angle.
MARSIS Tracks 3748-4808
Normalized to 5 MHz (BAND 4)
Band 2
Band 3
Band 4
Figure 7. Plot of quadratic phase errors presented in Figure 6, with a
scaling factor related to the cube of the MARSIS band center frequency
applied to the Band 3 and Band 2 data. The region of overlap from about a
solar zenith angle of 75° indicates where estimates of ionospheric TEC
would also be in close agreement.
Journal of Geophysical Research: Planets 10.1002/2015JE004917
CAMPBELL AND WATTERS PHASE COMPENSATION OF MARSIS DATA 187
The largest upward excursion in the
MARSIS TECU values occurs in early
2011, but it appears that only the wan-
ing period of this enhancement was
captured by SHARAD due to a gap in
observations. The plot of relative values
of the TECU parameter from MARSIS
and SHARAD shows the potential for
integrating data from the two sounders
to develop a long-term view of the
Martian ionosphere.
5. Persistent Ionospheric
Scattering Behavior
One unexpected aspect of the inter-
action between MARSIS signals and
the ionosphere is the frequent occur-
rence of linear, arcuate, wavy, or
parabolic radar echoes at round-trip
delay times greater than that of the
local surface. In some cases the echo patterns resemble those expected of subsurface scattering fea-
tures, but they may not reappear identically in subsequent MARSIS observations of the same region
[Picardi et al., 2005; Watters et al., 2006]. White et al. [2009] point out a number of such anomalous
echoes in the Ma’adim Vallis region. They suggest that the off-nadir reflections arise due to refraction
of the transmitted signal by passage through regions of varying electron density, with the beam
encountering the surface at normal incidence well away from the nadir point beneath the spacecraft.
In this scenario, multiple reflections represent multiple signal paths through the electron-density distribution.
Kane [2012] models one specific type of parabolic echo pattern, suggesting that these features could occur
where the subspacecraft electron density is much lower than the regional average.
To date, discussions of these scattering
phenomena emphasize their transient
nature, though White et al. [2009] note
several instances near Ma’adim Vallis.
The long-term coverage of both radar
sounders shows that such features are
persistent in a relatively smooth region
just south of Arsia Mons, comprising
the area from about 13°S to 15°S
latitude and about 129°E to 131°E
longitude. In at least eight MARSIS
tracks from October 2007 to February
2012, there are scattering features that
span the range of forms (linear, arcuate,
wavy, convex-upward, and convex-
downward parabolas) observed else-
where in “transient” anomalies (Table 1
and Figure 10). Most remarkable is the
occurrence on track 6202 of a very clear
but quite small, nested-parabola pattern
(Figure 11) that mimics those studied by
Watters et al. [2006] and Kane [2012].
There are five tracks in the period from
MARSIS Track 4719
SHARAD Track 5226_01 (diamonds)
Band 2
Band 4
Band 3
Figure 8. Plot of MARSIS quadratic phase term, β, normalized to 5MHz
frequency, and multiplied by an ad hoc value of 0.85, for Bands 2–4 on
Track 4719. Diamonds show TECU values derived for SHARAD track
5226_01. Note that the highest-frequency MARSIS band provides a
comparable TECU value down to SZA of about 65°, where the lower
frequency Band 3 diverges at about SZA = 75°.
Relative TECU Values for SZA=75-85 deg
SHARAD (20 MHz)
MARSIS BAND 3 (4 MHz)
Aphelion
June 25, 2008
Aphelion
May 13, 2010
Aphelion
March 30, 2012
Aphelion
Feb 15, 2014
Figure 9. Plot of relative values of the TECU parameter from SHARAD
(squares) and MARSIS Band 3 (crosses) data over a time period from
early 2007 to mid-2014. The individual plot symbols correspond to
one track from the sensor, with values normalized to the cosine of
the solar zenith angle and averaged where SZA = 75-85°. The two
data sets are offset by an arbitrary value for easier comparison.
Arrows denote approximate times of greatest Sun-Mars distance
(aphelion).
Journal of Geophysical Research: Planets 10.1002/2015JE004917
CAMPBELL AND WATTERS PHASE COMPENSATION OF MARSIS DATA 188
Table 1. Sounder Observations of the Region South of Arsia Monsa
Track Date SZA(deg) MARSISBands Observations of Ionosphere-Induced Radar Echo Properties
M2778 3/11/2006 109 3, 2 No detection
M3137 6/20/2006 71 4, 3 Strong dayside attenuation
M3908 1/21/2007 111 3, 2 No detection
M4899 10/26/2007 102 3, 2 Wavy reflections
M4910 10/29/2007 101 3, 2 Wavy reflections
M6015 9/7/2008 116 3, 2 Wavy reflections
M6202 10/31/2008 85 4, 3 Nested parabolic pattern
M7084 7/11/2009 93 3, 2 Dual parabolic pattern
M7109 7/18/2009 88 3, 2 Only very weak linear features
S1589701 12/17/2009 47 - Wavy reflections
M8111 5/3/2010 116 2, 1 Complex, wavy features
M8199 5/28/2010 102 3, 2 No detection
M9130 2/23/2011 112 3, 2 Parabolic pattern
M10339 2/11/2012 91 3, 2 Sharp, narrow parabola
M12248 8/20/2013 112 3, 2 No detection except bright feature near Arsia
aMARSIS observations indicated by “M” prefix, and SHARAD observations by “S” prefix. Solar zenith angle (SZA) noted
near the center of the anomalous echo region.
Figure 10. Examples of ionosphere-induced radar scattering features in MARSIS data, highlighted by white arrows, for
three tracks over the region south of Arsia Mons (visible at left in the top two tracks). Each panel is about 1700 km in
width and represents the full delay range of the MARSIS data. North is to the left in all images.
Journal of Geophysical Research: Planets 10.1002/2015JE004917
CAMPBELL AND WATTERS PHASE COMPENSATION OF MARSIS DATA 189
March 2006 to August 2013 where little
or no anomalous behavior is observed.
There are also instances, particularly in
the lower frequency channel of each
SS3 observation, of strong localized
echoes that are more irregular in shape.
Coverage by SHARAD is much more
limited, but on one dayside track
(15897_01, 17 December 2009), a wavy
echo pattern is clearly observed in the
same region (Figure 12). Five other
tracks from SHARAD have no evident
anomalous scattering.
The long-term presence of these fea-
tures over a small region of Mars sug-
gests that some mechanism creates
distortions of the ionospheric electron
density, evidently with different charac-
teristics at different times based on the
wide range of echo forms (Figure 10).
The MARSIS detections occur for solar
zenith angles of 85°–116°, while the
nondetections occur for SZA of 88° to 112°. The SHARAD detection occurs well onto the dayside
(SZA= 46°–49°), but the derived TECU value of 0.57–0.59 is consistent with the average behavior at this geo-
metry (Figure 2). There is some possibility that the MARSIS detections occur preferentially during periods of
higher dayside TEC, but the small sample size does not provide confirmation.
None of the anomalous scattering examples discussed above has a strong associated signature in the
quadratic phase distortion term derived from our focusing process. To the extent that these phase errors
are related to the total electron content of the column between the sensor and the nadir footprint, we
do not see evidence for the “holes” proposed by Kane [2012] to explain radar signal refraction. In the mag-
netic field map derived by Lillis et al. [2008], remnant crustal field patterns are detected south of the Tharsis
Montes volcanic province, though their magnitude is low relative to features farther south in the highlands.
Likewise, the subtle TEC variations relative to a smoothly varying behavior with SZA, noted by Safaeinili
et al. [2007] and Cartacci et al. [2013, Figure 9], do not suggest a unique pattern of behavior south of
Arsia Mons.
To provide some insight into how the refraction occurs, and the potential impact on the TEC measured from
phase distortion of the nadir-location echo, we examine a model for a “slab” of enhanced electron content
that occurs at some altitude and offset from the spacecraft ground track (Figure 13). The edges of this slab
or cloud are treated as a rectangular shape—while a natural feature would have a less regular margin, this
serves to show the general scattering behavior. The index of refraction, η, of the ionosphere is linked with
the electron density, Ne. For units of
electrons per cubic centimeter, this rela-
tionship is given by [Andrews et al., 2013;
Safaeinili et al., 2007]:
η ¼ 1 8980
2Ne
f 2
 1=2
(9)
where f is the frequency of the radar sig-
nal. Because a plasma has η< 1, a ray
that enters a region of higher electron
density bends away from the normal to
the interface. The slab vertical edge
Figure 11. Portion of MARSIS track 6202, with aspect ratio increased two-
fold from the images in Figure 10. Image width is about 600 km, and the
vertical scale is about 163 μs in round-trip delay time. Note the well-
defined nested parabolic echoes, particularly in the Band 3 data.
Figure 12. Portion of SHARAD track 15897_01, showing wavy, ionosphere-
induced radar scattering features south of Arsia Mons. Image width is about
925 km, and the vertical scale is about 76μs in round-trip time.
Journal of Geophysical Research: Planets 10.1002/2015JE004917
CAMPBELL AND WATTERS PHASE COMPENSATION OF MARSIS DATA 190
occurs at some altitude, h, and horizontal
offset, Δx, from the ground track. We
characterize the anomalous MARSIS
echoes by their arrival time, Δt, with
respect to the nadir surface return, and
the spacecraft altitude, H. The slab has a
refractive index of η2, while the subspa-
cecraft region at altitude h is character-
ized by η1.
The signal from the sounder reaches the
vertical edgeof the slab at a local incidence
angle of θ1, which is approximately related
to the slab height and offset (neglecting
the bending of the ray from the spacecraft
by the intervening electrons):
sin θ1 ¼ H hffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Δx2 þ H hð Þ2
q (10)
The horizontal offset term is related to
the delay offset by
Δx ¼ H hþ cΔt
2
	 
2
 H hð Þ2
" #1=2
(11)
where we assume that the vertical
extent of the slab is too small to affect
the travel time of the ray relative to the
background ionosphere. Passing into
the higher-density plasma, the ray
bends toward the surface of Mars, to
an angle θ2 with respect to the normal
to the edge of the slab:
sin θ2 ¼ η1η2
sin θ1 (12)
Finally, the signal enters the background
electron content level, bending to an
angle θ3 that is even closer to the normal
to the Martian surface. Using small-angle
approximations where appropriate:
θ3≈
η2
η1
1 1
2
η1
η2
sin θ1
	 
2" #
(13)
Our requirement for encountering the surface at normal incidence means that θ3 must approach zero,
which occurs when
η1
η2
sin θ1 ¼
ffiffiffi
2
p
(14)
We can thus define the electron content of the slab based on values for the spacecraft altitude, slab edge
location, electron content at the slab altitude along the subspacecraft axis, and the delay offset of the parti-
cular MARSIS echo from the surface return. Note that if an anomalous echo is present in a particular MARSIS
band, we expect little difference in the time delay offset for echoes at lower frequencies, since the ray is
Mars Surface
Sensor
Figure 13. Schematic of radar scattering paths through a slab-like layer
of Mars ionosphere. Signals from the sounder reflect from the surface
directly below the spacecraft, but refraction due to abrupt interfaces in
the electron density can yield additional ray paths that also encounter the
surface at normal incidence. Lower diagram shows geometry of refraction
in the slab, with labeling of angles discussed in text.
Journal of Geophysical Research: Planets 10.1002/2015JE004917
CAMPBELL AND WATTERS PHASE COMPENSATION OF MARSIS DATA 191
simply bent more toward the Mars surface normal by the higher refractive-index contrast induced by the
change in electron density (equation (9)). At some point, however, lower frequency signals may reach the
criterion for total internal reflection and simply bounce off the slab margin.
As an example, consider an anomalous echo that occurs 10μs (about 14 MARSIS range cells) after the surface
return in Band 3 (f=4MHz) for a spacecraft altitude of 350 km. If the slab occurs at an altitude of 130 km, near
the typical peak of the dayside electron density, then the edge of the slab is offset by ~26 km from the space-
craft ground track. If the background density is 1.0 × 105 cm3 at 130 km altitude beneath the spacecraft,
then the slab density must be about 50% higher to produce the necessary refraction path. These geometric
and electron density values are consistent with the results of Kane [2012], though we have allowed the con-
trast to occur due to the off-nadir slab rather than a subspacecraft “hole.” Our model does not at present,
however, capture the azimuthal symmetry in refraction paths required by some of the most complex
observed scattering features.
When anomalous echoes occur, how much of a signature should we expect in the TEC value derived from
autofocusing of reflections from the nadir region of the ground track? These features may have little discern-
ible impact on a TEC value inferred from the quadratic phase distortion or a comparison of delay time to
MOLA data, especially if the enhanced electron content is some distance from the ground track
(Figure 13). In addition, the enhancement in electron content need only occur over a small vertical scale to
create the refraction, so the effect on the integrated column abundance will depend upon the shape of
the full distribution with altitude. A survey of dayside column shape and variability by Withers et al. [2012]
suggests that thin (kilometer-scale) slabs or clouds of higher electron content might be difficult to discern
from the integral over the often complex vertical distribution. It would be interesting to collect subsurface
sounding data over short time periods (days to weeks) across substantial (hundreds of kilometers) regions,
in order to map the complexity of the TEC signature and perhaps find evidence for persistent spatial patterns.
Such experiments are certainly possible with SHARAD.
6. Conclusions
Observations by the MARSIS and SHARAD radar sounders are affected by ionospheric phase distortion for
dayside observations, and to varying degrees in the nightside region. Based on experience with total electron
content estimation and image correction from SHARAD data, we propose that ionospheric blurring of the
MARSIS radargrams may be effectively compensated with a model of smoothly varying quadratic phase
errors along the track. This approach allows analysis of the validity range for models used for TEC estimation
in previous MARSIS studies. We conclude that a linkage between the quadratic phase distortion term and the
TEC can yield robust estimates of the total electron content for solar zenith angles >65° for MARSIS Band 4
and >75° for MARSIS Band 3, consistent with empirical analyses by Sanchez-Cano et al. [2015]. The proposed
methodology yields well-focused radargrams for geologic interpretation and provides a robust and less
locally (i.e., frame to frame) variable solution for the general behavior of the ionosphere along a MARSIS track.
Comparison of the derived MARSIS and SHARAD TEC values from 2007 to 2014 reveals good correlation in
both seasonal behavior and in the characterization of anomalous ionospheric activity due to coronal mass
ejections. Finally, we presented SHARAD and MARSIS evidence for the existence of at least one persistent
region of anomalous ionospheric radar scattering and suggested future observations that might better
constrain the mechanism, extent, and timing of these features. In particular, it may be worthwhile to collect
subsurface sounding data over regions of interest on short enough time scales to map lateral fluctuations in
the ionosphere.
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