Small variations in ice composition and layer thickness explain bright reflections below martian polar cap without liquid water

Abstract

Abnormally bright radar reflections below the Martian south polar layered deposit were originally interpreted as evidence of subglacial liquid water. However, unlike on Earth, conditions beneath the Martian ice are too cold to create or maintain meltwater. In this work, we use radar reflectivity simulations to show that the strong reflections can instead be caused by constructive interference between dusty ice layers that are more closely spaced than the radar resolution. Unlike previous hypotheses, interference does not require anomalous subsurface conditions or exotic materials to be present beneath the ice. In addition, interference between thin layers can explain the variable power of radar returns beneath the entire ice sheet and does not require different mechanisms to be responsible for reflections in different regions.

Simple layers of ice and dust can explain radar reflections previously interpreted as evidence for liquid water on Mars.

INTRODUCTION

Recent radar observations from below the Martian south polar layered deposit (SPLD) have reignited debate about the potential presence of liquid water on modern day Mars (1–5). The SPLD is a formation of nearly pure water ice that can reach more than 3 km thick and is approximately centered over the South Pole (6). Within the SPLD, many ice layers with variable amounts of dust impurities are visible in both optical and radar data (6), although layers in the two datasets have yet to be positively correlated with each other (7). Because of the dome-like structure of the SPLD, the contact between its base and the underlying bedrock is not visible in imagery, but it can be detected by radar (8, 9). Recently, observations by the Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS) on board the Mars Express orbiter have revealed the presence of anomalously bright basal reflections scattered beneath the entire SPLD (10). On Earth, similar radar signatures below ice sheets are often indicative of subglacial lakes or other hydrological features (11, 12), which led to the initial interpretation that the bright MARSIS reflectors were evidence of liquid water (2).

Here, we present evidence for an alternate interpretation. When multiple material interfaces are present at subresolution scales, reflections from each interface can constructively interfere with one another, creating bright reflections. The resulting radar signature becomes a function not only of composition but also of layer thickness (13). Recently, simulations showed that relatively thin layers of CO₂ ice near the base of the SPLD could constructively interfere, resulting in reflections of a similar magnitude to those observed by MARSIS (3). There are doubts, however, surrounding the plausibility of solid CO₂ buried so deep below the water ice (14), and while the stratigraphies simulated in past work produced bright reflections, there was no single layering scenario that was consistent with observations at each MARSIS frequency.

In this work, we close these gaps in the interference hypothesis by modeling realistic MARSIS reflections caused by simple layering scenarios. By modeling the radar return from thousands of semirandom stratigraphies, we show that it is possible for a single set of layers to produce reflections that match the MARSIS observations at each frequency simply by varying the amount of dust or other impurities within each icy layer. Furthermore, we do so without introducing any additional material constituents beyond water ice and dust. We also demonstrate that small changes in layer thickness and dust content may explain the wide distribution of observed reflection powers both within and outside of bright reflectivity regions more easily than other proposed mechanisms.

While multiple hypotheses have been put forward to explain the bright SPLD basal reflections, none have been consistent with all available observations (3–5, 10, 15, 16). Thermal modeling using a realistic range of geothermal heat fluxes indicates that the temperature at the base of the SPLD is not warm enough to melt the overlying ice and create liquid water, even under favorable conditions (15, 16). Brines were suggested as one way to lower the melting point, but even with heavily saturated brines, the melting point remains above the best-case basal temperature (17), and the volume of salts that would need to be concentrated in one area to produce those brines is difficult to reconcile (16). While the initial finding was limited to one small location beneath the SPLD (2), subsequent and more comprehensive radar mapping of the SPLD basal contact has shown that similar bright reflections are somewhat common in both MARSIS (10) and Shallow Radar (SHARAD) data (18) across the entire formation, including in places where the ice thickness is much less than 1 km and thus not amenable to the presence of melt. Such a widespread geographical distribution of strong reflections casts doubt on the hypothesis that extreme but highly localized conditions (such as a recent magma chamber) could be a possible explanation for meltwater at the original discovery site (15). A recent analysis of all MARSIS reflections across the entire surface of the planet also found that approximately 2% of the dry Martian surface produced reflections as bright as those initially identified as liquid water, even after correcting for additional attenuation through dusty ice (19). While the cause of those bright surface reflections remains unclear, their presence does indicate that there must be conditions on Mars capable of producing strong reflections in the absence of liquid water.

In addition to liquid water, the presence of other high-reflectivity materials has been invoked to explain the bright reflections. The most commonly investigated scenarios involve the presence of hydrous clay minerals or saline ice (4, 5). However, saline ice faces similar questions to liquid brines regarding the source, concentration, and emplacement mechanism of the salts, and while initial laboratory experiments with conductive clay minerals were promising (4), further testing at more relevant temperatures has cast doubt on that hypothesis as well (20).

To investigate the constructive interference hypothesis in more detail, we started with a thin layer reflectivity model previously used for radar sounder analysis on Mars (3). The model is capable of calculating the effective reflectivity of a group of subresolution layers with arbitrary thickness and composition. For this work, we generated 10,000 semirandom SPLD basal layering scenarios as input for the model. Each set of layers was limited to 100 m in total thickness (approximate MARSIS vertical resolution). Layers consisted of either pure ice or a mixture of ice and dust. The number of dusty layers along with their thickness, separation, and dust content was randomly generated using constraints from previous studies when possible (Fig. 1 and see Materials and Methods) (7, 13, 21). Specifically, layer thickness was allowed to vary between 1 and 20 m, average separation distance was set to 10 m, and dust content varied between 20 and 100%

Fig. 1. Examples of semirandom basal layering scenarios used as input for reflectivity modeling.

Each scenario shown produced reflections consistent with those in the originally defined bright region (2). Permittivity, shown on the x axis, is positively correlated to dust content.

Once the original set of basal layering scenarios was created, we modeled the effective reflectivity of each scenario, assuming that the layers were situated beneath water ice with a bulk composition consistent with that of the SPLD and above solid, dry bedrock. Following a previously established method (19), we then used the modeled reflectivity to estimate the corresponding normalized basal echo power for the same set of layers beneath approximately 1400 m of SPLD ice, consistent with the original detection of strong reflections (2). We used standard assumptions for SPLD attenuation and surface reflectivity (see Materials and Methods). Converting the effective reflectivity into inferred basal echo power allowed us to compare our model results directly to observations. Last, we repeated the above procedure 1000 times for each original layering scenario, applying meter-scale variations to layer thickness and small changes to dust content (typically less than 10%) for each iteration (Fig. 2 and see Materials and Methods). The result was a separate distribution of normalized basal echo powers for each starting scenario, where each value in the distribution corresponds to a variation on the original set of layers. This step allowed us to investigate the distribution of basal echo powers that would arise from small changes in layer thickness or composition that naturally occur laterally over tens of kilometers, the approximate scale of the initially identified bright region (2). Normalized basal echo power was calculated for each of the three MARSIS frequencies for every modeled scenario.

Fig. 2. Single layering scenario used to generate distributions both inside and outside the bright region.

(Left) Originally generated layering scenario, consistent with reflections in bright area. (Right) Variation on original scenario, consistent with reflections outside bright area.

To determine whether the same stratigraphy could explain MARSIS returns both within the bright region and in the surrounding area, we carried out one final group of simulations. From our initial results, we selected the distributions with basal echo powers consistent with observations inside the bright area, which we defined as median basal power higher than surface power at each frequency, and descending median basal power from 3 to 5 MHz. From each of the distributions matching that criteria, we selected the individual layering scenario variant whose corresponding basal echo power most closely matched the median return outside of the bright area, rather than inside of it (i.e., it was consistent with “normal” dimmer reflections). We then introduced small variations in layer thickness and dust content to that set of layers, following the same process described in the previous paragraph (see Materials and Methods), creating new basal echo power distributions. The end result is two paired normalized basal echo power distributions: one corresponding to MARSIS reflections inside the bright area and the other corresponding to MARSIS reflections outside the bright area using the same basic layer structure (e.g., Figs. 2 and 3). In this way, we simulate a change in the average layer thickness and composition of the same set of layers over a large lateral area (i.e., inside and outside of the bright area) while still including smaller-scale local variability.

Fig. 3. Simulated and observed basal echo power distributions.

(Top row) Distribution of simulated MARSIS normalized basal echo power for a single starting scenario capturing the behavior both inside the bright area (gray histograms) and outside the bright area (red histograms). (Bottom row) Observed normalized basal echo power distributions both inside the initially defined bright area (2) (gray histograms) and the surrounding region (red histograms). Dotted lines indicate the median value of the observed power distributions.

RESULTS AND DISCUSSION

Of the original 10,000 semirandomly generated layering scenarios, 216 produced distributions with median normalized basal echo powers that were consistent with bright MARSIS observations in terms of both reflection strength and the power ratio between frequencies, i.e., the 3-MHz reflection power was the strongest, followed by 4 MHz and then 5 MHz (17). In 99 of those layering scenarios, the echo strength and frequency ratio of the paired distributions were also consistent with observations outside of the bright region (Fig. 3). Inspection of the qualifying layering scenarios does not reveal any obvious patterns or common features besides the inclusion of at least one layer with a permittivity approaching that of pure lithic material (Fig. 1).

The basal echo power distributions produced by applying small changes in layer thickness and composition are qualitatively similar in shape to the observed data (2) but are slightly narrower and feature a tail toward low values (Fig. 3). The interquartile range (IQR) of observed normalized basal echo powers in the bright region is approximately 4.7, 6.2, and 5.6 dB at 3, 4, and 5 MHz, respectively. Outside of the bright region, the observed IQRs for each frequency are 4.9, 4.6, and 4.4 dB. Typical IQRs for our modeled stratigraphies are between 2 and 4 dB in both cases.

The results described above demonstrate that interference between subresolution layers can produce radar reflections consistent with MARSIS observations below the SPLD, including their frequency-dependent behavior and their regional variability. Furthermore, these results were obtained without exotic materials and without invoking extreme environmental conditions. While a relatively small number of our layering scenarios produced bright reflections consistently across frequencies, this is to be expected, as in reality most SPLD basal reflections are not bright (10), and constructive interference requires precise layering. However, the exact fraction of simulated scenarios that produced constructive interference is not particularly meaningful. The layering scenarios were only semirandom, and the initial constraints used in their generation could influence the final results, such that the fraction of consistent scenarios might vary. In addition, real layers are typically deposited by nonrandom processes, which will result in different patterns of variability compared to our randomly generated stratigraphies.

Our results are also consistent with the observation that bright reflections are sparsely distributed across the entire base of the SPLD, with no correlation to subsurface conditions or overlying ice volume (10). In the case that bright reflections are due to liquid water, one might expect a correlation with total SPLD thickness, as thick ice cover is believed to be necessary to create melt conditions (15–17). However, previous work has shown that no such correlation exists, and instead bright reflections are found even near the thin SPLD margins (10, 18). While anomalously high geothermal heating may be able to explain the presence of meltwater in an isolated location (15), it is inconsistent with the widespread nature of observed strong reflections. Similarly, if bright reflections are caused by exotic minerals or other compositional changes, then there must be some explanation for why they are sparse in density, geographically extensive, and do not seem to correlate with surface or bed topography. Interference, on the other hand, is essentially independent of other environmental conditions such as total ice thickness, heat flux, or basal topography. Given the precise layering required to generate constructive interference and the changes in layer thickness expected over kilometer scales, the quasi-random, sparse, widespread pattern of bright reflections is exactly what one would expect. Similar resonant behavior has already been identified in the north polar layered deposits (NPLD) using multiband SHARAD data, with interference patterns changing over distances as small as 1 km, which is less than the MARSIS spatial resolution (22, 23).

Notably, interference also presents the most plausible explanation for the wide range of observed basal echo powers. Previous inversion analysis found that basal permittivity would have to vary by more than two orders of magnitude over kilometer-scale distances to match observations of SPLD basal echo power (2, 24). The brightest reflections would require relative permittivities in excess of 300 (24), which is more than three times greater than pure liquid water. These large changes in composition over relatively small distances are difficult to explain using geologic materials and are not common elsewhere on Mars. In contrast, while our modeling also struggles to match the extremes of the observed power distributions, changes of a few meters in layer thickness and less than 10% dust content over the same kilometer-scale distances produce variability close to that observed by MARSIS (Fig. 3). These small changes in layer thickness could reasonably arise from changes in paleo-accumulation rates and are consistent with measurements of layer thickness variability made at SPLD outcrops (7). No estimates of dust content for individual layers in the SPLD exist, but changes of a similar magnitude are observed in the NPLD (13).

While modeled variability due to changing layer thickness tends to be smaller than observations, our analysis does not include changes to secondary parameters that affect observed reflectivity, such as interface roughness, attenuation, and the bulk dust content of overlying ice, all of which are likely to vary from region to region. Our model also assumes sharp, instantaneous contacts between layers, while contacts between real layers can become sharper or more gradational over large distances. Our chosen value for dust and rock permittivity also remains unchanged between model runs, while in reality it is possible for that value to vary between locations based on the precise composition of the lithic material. Perhaps most importantly, while we were unable to determine the radiometric precision of MARSIS, target precision for SHARAD, a similar Mars radar sounder, was ~2 dB (25), which is comparable to the difference between our modeled variability and the observed variability. We expect that contributions from each of these factors would broaden the modeled distributions shown in Fig. 3, but without better constraints, it is difficult to say by how much.

It is important to be clear that our analysis cannot determine which specific layering scenarios exist at the base of the SPLD. One of the primary results of this work is that the conditions that lead to bright reflections are nonunique and relatively easy to generate, even when accounting for the available constraints on layer thickness and composition. It is likely that none of the randomly generated layering scenarios used in this work represent the true stratigraphy at the base of the SPLD. However, observations of the NPLD and its underlying basal deposit show that layering similar to that generated here is certainly plausible (26). While pure dust or lithic layers are not observed in the upper NPLD, large sand and dust sheets tens of meters thick can be observed in both radar and visible imagery near the base and within the underlying cavi unit (26). It is believed that these sand sheets are paleo-dune fields preserved by later ice deposition (26), and it is plausible that similar features could exist near the base of the SPLD.

While we lack the ability to make specific predictions about basal layering, we can confidently state that the constructive interference hypothesis is compatible with the available observations. The process is consistent with the magnitude and distribution of observed echo powers across frequencies, as well as the geographic distribution of bright echoes. It requires no rare materials to be present and is agnostic of environmental conditions such as geothermal heating. Interference is also known to affect radar reflection power elsewhere on Mars (22, 23). While the diversity of layering scenarios that produce constructive interference is too large to place constraints on the actual basal stratigraphy, we do know that broadly similar layering exists at the base of the NPLD (26) and is thus plausible for the SPLD as well. In contrast, other hypotheses often require anomalous environmental conditions or the presence of uncommon materials and are inconsistent with either the geographic distribution or frequency-dependent behavior of the bright reflections.

MATERIALS AND METHODS

Each individual layering scenario is randomly generated based on five inputs: total stratigraphic thickness, mean separation between dusty layers, maximum dusty layer thickness, and minimum and maximum dust content for dusty layers. For this work, the total stratigraphic thickness was set to 100 m, mean separation was 10 m, maximum layer thickness was 20 m, and dust contents were between 20 and 100%. These values were chosen on the basis of the nominal MARSIS vertical resolution, measurements from SPLD outcrops (7), and the inferred composition of similar NPLD layers (13, 21). Layering scenarios are expressed as two vectors, one containing dielectric permittivity (i.e., composition) and the other containing layer thickness. Scenarios are initially generated meter by meter. For every meter, a random number is drawn and compared to the period defined by the inverse of the mean separation distance. If the random number is less than the mean period, then a new dusty layer is inserted into the stratigraphy. The thickness of the dusty layer is randomly determined from a uniform distribution between 1 m and the maximum possible thickness (20 m). The dust content of the layer is chosen randomly from a uniform distribution with the previously defined minimum and maximum values. That dust content is then inserted into the Maxwell-Garnett mixing formula to calculate the layer’s permittivity, assuming a mixture of pure ice and basaltic dust. Dust permittivity was assumed to be 8.8 – i × 0.17, which differs slightly from the typical Shergottite value used in previous work (3, 13). Our value was chosen such that a mixture of pure ice and 10% dust matches the measured bulk loss tangent of the SPLD (17). Once the cumulative sum of all layer thicknesses exceeds 100 m, the column is normalized such that the total thickness is exactly 100 m. All sections of the stratigraphy other than the defined dusty layers are assigned a permittivity consistent with pure water ice at MARSIS frequencies (27).

To apply small changes to each layering scenario (and thus simulate variability over regional scales), we first determine new layer thicknesses. The new thickness for each layer is drawn randomly from a normal distribution with mean equal to the layer’s original thickness and an SD equal to one-third of that thickness. After new thicknesses are drawn for each layer, the entire set of layers is once again normalized to be 100 m thick in total. Rather than determining a new dust content for each dusty layer, the permittivity is altered directly. For each dusty layer, a value is drawn from a normal distribution with a mean of zero and an SD of 0.25, and that value is then added to or subtracted from the original permittivity. For context, a difference of 0.25 in relative permittivity corresponds to approximately an 8% change in dust content using the Maxwell-Garnett mixing formula.

To model the total effective reflectivity of our randomly generated stratigraphies, we use a standard procedure commonly used to model Martian radar sounder data in the past (3, 4, 13). We will briefly describe the method here. For a full derivation and in-depth analysis of the method, see (28, 29), although note that we use our own implementation of the model, which we have made publicly available. First, a 2 × 2 constitutive matrix (M) is constructed for each intermediate model layer

$$\mathbf{M}=\left[\begin{array}{cc}\text{cos}(i\mathrm{\gamma }d)& \left(\frac{i}{\mathrm{\eta }}\right)\text{sin}(i\mathrm{\gamma }d)\\ i\mathrm{\eta }\text{sin}(i\mathrm{\gamma }d)& \text{cos}(i\mathrm{\gamma }d)\end{array}\right]$$

Here, γ is the propagation constant inside the layer, d is the thickness of the layer, and η is the admittance of the layer. The propagation constant and admittance are each related to the permittivity of the layer and the frequency of the radar. The matrices for each intermediate layer are then multiplied together, producing a final characteristic matrix representing the full set of layers (M_tot)

$${\mathbf{M}}_{\mathbf{\text{tot}}}={\mathbf{M}}_{\mathbf{1}}{\mathbf{M}}_{\mathbf{2}}{\mathbf{M}}_{\mathbf{3}}\dots =\left[\begin{array}{cc}{m}_{11}& m_{12}\\ m_{21}& m_{22}\end{array}\right]$$

The elements of the characteristic matrix are related to the total effective reflectivity by the formula

$$R={\left|\frac{{\mathrm{\eta }}_{\mathrm{f}} (m_{11}+m_{12}{\mathrm{\eta }}_{\mathrm{L}})-(m_{21}+m_{22}{\mathrm{\eta }}_{\mathit{L}})}{{\mathrm{\eta }}_{\mathrm{f}} (m_{11}+m_{12}{\mathrm{\eta }}_{\mathrm{L}})+(m_{21}+m_{22}{\mathrm{\eta }}_{\mathrm{L}})}\right|}^2$$

where η_f and η_L are the admittance of the first model layer (free space) and the last model layer (bedrock).

Because MARSIS transmits with a 1-MHz bandwidth around each center frequency, this process must be repeated for all sampled frequencies within each separate bandwidth. For our modeling, we chose to sample every 1 kHz. The results are then combined into the final effective reflectivity for each operating mode by integrating over the frequency bandwidth, following the method of Lalich et al. (13).

To directly compare our model results to observations, we convert modeled reflectivity into inferred normalized basal echo power. According to Grima et al. (19), normalized basal echo power can be expressed as

$$\frac{P_{\mathrm{ss}}}{P_{\mathrm{s}}}=\frac{R_{\mathrm{ss}}}{R_{\mathrm{s}}}{T}_{\mathrm{s}}^{2}A$$

where P_ss/P_s is the normalized basal echo power, R_ss is the subsurface reflectivity, R_s is the surface reflectivity, T_s is the transmission coefficient through the surface (equal to 1 − R_s), and A is the two-way attenuation through the overlying ice. The attenuation A can be expressed as

$$A=\text{exp}(-2\mathrm{\pi }f\mathrm{\tau } \text{tan}\mathrm{\delta })$$

where f is the radar frequency, τ is the one − way propagation time, and tanδ is the loss tangent through the overlying ice. The surface reflection and transmission coefficients were calculated using the standard Fresnel equations, assuming a surface permittivity consistent with previous measurements of bulk SPLD ice (17). The attenuation was calculated separately for each center frequency, assuming a one-way propagation time of 17 μs (approximately 1400 m in water ice), consistent with measurements in the originally identified bright region (2), and a bulk loss tangent consistent with the most recent measurements in the area (17). The influence of intermediate reflectors was not explicitly considered in our model; however, the derivation of loss tangent in (17) implicitly includes their influence. By inserting our modeled subsurface reflectivity (R_ss) into the above equations, we can produce an inferred normalized basal echo power (P_ss/P_s).