High-Resolution Topographic Analyses of Mounds in Southern Acidalia Planitia, Mars: Implications for Possible Mud Volcanism in Submarine and Subaerial Environments

A northern ocean of Mars is still debated and, if it existed, it may have accompanied valley networks and/or outflow channels, which may have led to the emplacement of a large amount of water to the northern lowlands during the Noachian and/or Hesperian times. However, it is unclear how and under what conditions (submarine or subaerial) geologic features such as mounds and giant polygons formed in the northern lowlands. The densely-distributed mounds in Chryse and Acidalia Planitia, >1000 km-wide basins of the northern plains, were suggested to be ancient mud volcanoes formed in an aqueous setting, which is controversial (i.e., mud vs. igneous and submarine vs. subaerial). However, these mounds have not been quantitatively well characterized, particularly with respect to their detailed topography. Here we generated forty digital elevation models (DEMs) with resolution of up to 1 m/pixel from High Resolution Imaging Science Experiment (HiRISE) stereo image pairs, and we accurately measured the morphometric parameters of ~1300 mounds within the southern part of the Acidalia basin. Their heights and diameters resulted in good accordance with those of mud and igneous volcanoes in submarine/subaerial settings on Earth. Maximum depths of their source reservoirs vary from ~30 to ~450 m for a subaqueous setting and from ~110 to ~860 m for a subaerial setting, both of which are consistent with fluid expulsion from the ~100–4500 m-thick flood deposits (Vastitas Borealis Formation, VBF). On the basis of the morphometric values, we estimated rheological properties of materials forming the mounds and found them consistent with a mud flow origin, which does not rule out an igneous origin. The conditions of possible submarine mud or igneous volcanoes may have harbored less hazardous environments for past life on Mars than those on an ocean-free surface.


Introduction
While liquid surface water is physically not stable under the current Martian climate, the former presence of a northern ocean (or northern oceans) has been proposed for the northern lowlands since either the Noachian [1,2] or the Hesperian [2][3][4]. There are two major views: (1) the valley networks, formed by the long-term hydrological cycle of a warm, wet climate during the Noachian, may have been associated with a persistent ocean [1]; (2) the Hesperian-aged cataclysmic floods, suggested by outflow channels debouching into the northern lowlands [5], may have left behind large amounts of water and sediments forming the northern ocean [6]. Observational evidence for their  [18]. Note that all of the named valleys represent circum-Chryse outflow channels.
Although none of these hypotheses have been proven decisively, the mud volcano hypothesis is considered to have one of the highest astrobiological potential among the above hypotheses. This is because terrestrial mud volcanoes commonly emit not only mud and water to the surface but biotic/abiotic, gaseous hydrocarbons (mostly methane), which, if formed on ancient Mars, is of great significance for interpreting regional magmatic and hydrothermal activity, distributions of clay minerals, present-day detection of atmospheric methane, their interaction with faults and fractures, and possible microbial activity [51]. Mud volcanoes on Earth occur both onshore and offshore, mostly along subduction zones (i.e., lateral tectonic compression zones) and/or in high sedimentation rate sites [52]. lowland units [34]. More than 18,000 mounds (>300 m diameter) were identified, and >40,000 mounds were estimated over southern Acidalia and northern Chryse regions [21,35,36]. Since pitted mounds in eastern Acidalia Planitia-Cydonia Mensae region were first recognized from Viking Orbiter images, terrestrial analog features of various origins have been proposed to explain their occurrence in the Acidalia basin, namely (1) rootless cones (or pseudocraters) formed by the emplacement of lava flows over wet ground and the subsequent explosions [37][38][39][40][41], (2) pyroclastic cones or cinder cones as a result of explosive eruptions and resultant depositions of pyroclastic materials [38,39,[42][43][44][45][46], (3) secondary impact craters with inverted relief [38], (4) pingos caused by a volume increase of ground ice doming terrain surface [3,38,47], (5) tuff rings and tuff cones resulted from phreatomagmatic explosions [25,26], (6) spring mounds originated from evaporate deposits around spring vents [25], (7) mud volcanoes defined as surface manifestation of mud from depth [21,23,25,[48][49][50], and a combination of two or more of the processes above.
Although none of these hypotheses have been proven decisively, the mud volcano hypothesis is considered to have one of the highest astrobiological potential among the above hypotheses. This is because terrestrial mud volcanoes commonly emit not only mud and water to the surface but biotic/abiotic, gaseous hydrocarbons (mostly methane), which, if formed on ancient Mars, is of great significance for interpreting regional magmatic and hydrothermal activity, distributions of clay minerals, present-day detection of atmospheric methane, their interaction with faults and fractures, and possible microbial activity [51]. Mud volcanoes on Earth occur both onshore and offshore, mostly along subduction zones (i.e., lateral tectonic compression zones) and/or in high sedimentation rate sites [52].  [2,11]. White-filled numbered rectangles represent the locations of digital elevation models (DEMs) generated in this study (Site 01 to 40, listed in Table 1). (b) Part of a mosaic of Mars Reconnaissance Orbiter (MRO) Context Camera (CTX) images [53], showing the central part of southern Acidalia Planitia. Pitted mounds appear as bright, circular features on the polygonally fractured terrain [17]. Sunlight illuminates the scene from the left.   [2,11]. White-filled numbered rectangles represent the locations of digital elevation models (DEMs) generated in this study (Site 01 to 40, listed in Table 1). (b) Part of a mosaic of Mars Reconnaissance Orbiter (MRO) Context Camera (CTX) images [53], showing the central part of southern Acidalia Planitia. Pitted mounds appear as bright, circular features on the polygonally fractured terrain [17]. Sunlight illuminates the scene from the left. The previous observations in favor of the mud volcano interpretation are the results from geological data. For example, they are spatially related to other flow-related features [32,36]. They exhibit low thermal inertia relative to the surrounding plains measured from Mars Global Surveyor Thermal Emission Spectrometer (TES) [25] and Mars Odyssey Thermal Emission Imaging System (THEMIS) [54] data, which is consistent with finer-grained materials covering the mound surfaces, and the geologic setting of the Chryse-Acidalia Embayment is a depositional basin [16]. High Resolution Imaging Science Experiment (HiRISE) cameras onboard the Mars Reconnaissance Orbiter (MRO) revealed that many of the mounds in southern Acidalia have bright, smooth surface materials outwardly extending from their peripheries over the rough surrounding plains (e.g., Figure 2c,d; [21]), which suggests the expansion of mound materials occurred on the pre-existing surface. Several mounds show distinct flow features emanating from them (e.g., Supplementary Figure S8; [21]), indicating that the materials behaved as fluids during the mound formation. Other common morphologies include summit and flank pits (Figure 2c), concentric crest structures, surrounding moats, smooth surface textures, which are consistent with the mud volcanic features. However, the biggest problem is that all of the above observations do not rule out alternative interpretations (e.g., igneous volcanoes).
It should be noted that most of the mounds are located more than a few hundred meters below the Deuteronilus shoreline level (~−3760 m; Figure 2a [2,11]). On the basis of a close spatial relationship of giant polygons and pitted mounds (Figure 2b; mounds located just inside polygonal troughs in Supplementary Figures S12 and S13) and its analogy to that of kilometer-sized polygons and terrestrial mud volcanoes in marine settings on Earth [55,56], Oehler and Allen [55] hypothesized that their co-occurrence in the Chryse-Acidalia area may have resulted from fluid expulsion processes of sediment-laden flood water. They suggested that late Hesperian deposition from outflow floods caused a rapid deposition of unconsolidated fine-grained sediments in an aqueous basin, which subsequently developed polygonal fracturing. They also characterized the geometries of submarine mounds and polygons on Earth by using high-resolution 3-D seismic data.
Those of the Martian counterparts were, however, not examined because of lacking high-resolution topographic data. The resolution of the global digital elevation models (DEMs) created based on Mars Global Surveyor (MGS) Mars Orbiter Laser Altimeter (MOLA) is 128 pixels/degree or~463 m/pixel. Each spot (~168 m in diameter) of MOLA observation is separated about 300 m along track [57], which is insufficient to determine the shape of these mounds precisely. Thus, although geometric characterization of the Acidalia mounds are critical for quantitatively assessing how they were formed (e.g., modeling of materials for the mounds), the topographic studies of the mounds were limited to Viking image-based (low-resolution), photoclinometric measurements of about 400 mounds (>400 m wide) with unspecified locations in Acidalia and Chryse Planitiae [23,45].
In this study we extracted high-resolution DEMs from HiRISE stereo images of pitted mounds over the entire southern part of Acidalia Planitia (Figure 2a;~32 • -49 • N,~317 • -357 • E). We then analyzed the relationship between their heights (a few meters to tens of meters) and diameters (tens of meters to a few kilometers) for almost 1300 mounds (Section 3), then tested consistency with a submarine (or subaerial) mud volcano hypothesis by estimating mud reservoir depths and by making first-order estimates of the rheological parameters of fluid flows (Section 4). The values of center longitude and latitude of each DEM were used as the central meridian and standard parallel, respectively when DEMs are mapped to an equirectangular projection.

Data and Methods
We extracted forty high-resolution DEMs (1.0, 2.0, or 4.0 m/post) and corresponding orthoimages for the areas of pitted mounds in the southern part of Acidalia Planitia (e.g., Figure 3a; see also Table 1 and Supplementary Figures S1 to S40). In generating stereo image DEMs, we followed, with minor differences, the workflows of [22]. First, we performed radiometric calibration, bundle adjustment, shifting, mosaicking, and map projection of the Experimental Data Records (EDRs; ten or nine HiRISE RED-filtered raw image files) of HiRISE stereo pairs [58,59] using the US Geological Survey's Integrated Software for Imagers and Spectrometers (ISIS) 3.4.6 [60][61][62]. We used HiRISE image pairs that have ideal camera pointing (moderate convergence angle), good image quality (no severe atmospheric hazes or imaging errors), and 1 × 1, 2 × 2 or 4 × 4 pixel binning as stereo pairs. For the application of bundle adjustment to each pair of HiRISE images, we collected hundreds of image control points between image pairs and three or more ground control points from Mars Express's High Resolution Stereo Camera (HRSC) nadir-channel images at spatial resolutions of 12.5 to 50.0 m/pixel [63]. These HRSC images are map-projected beforehand onto THEMIS geodetically controlled mosaic [64] of the southern Acidalia region using the ISIS software. All raw and calibrated image data are available in National Aeronautics and Space Administration (NASA) Planetary Data System (PDS). We then used a control network of these points to update camera pointing and spacecraft position information of each HiRISE stereo pair with the ISIS's module for bundle adjustment, jigsaw [65]. The resultant vertical accuracies are expected to be around several tens of centimeters for ASPderived DEMs. This value is comparable to ASP-derived (non-bundle adjusted) DEMs and BAE Systems' SOCET SET-derived (bundle-adjusted) DEMs (so-called "HiRISE Digital Terrain Model (DTM)"; https://www.uahirise.org/dtm/) with vertical accuracy of ~20 cm [58,59] (published by the HiRISE Science Team and the USGS), root mean square errors of the discrepancies are better than 0.50 m [69,70]. On the basis of viewing geometry and ground pixel scale [71,72], we also calculated the vertical accuracy values, assuming 0.2-pixel matching error [58,59], The resultant vertical accuracies are expected to be around several tens of centimeters for ASP-derived DEMs. This value is comparable to ASP-derived (non-bundle adjusted) DEMs and BAE Systems' SOCET SET-derived (bundle-adjusted) DEMs (so-called "HiRISE Digital Terrain Model (DTM)"; https://www.uahirise.org/dtm/) with vertical accuracy of~20 cm [58,59] (published by the HiRISE Science Team and the USGS), root mean square errors of the discrepancies are better than 0.50 m [69,70]. On the basis of viewing geometry and ground pixel scale [71,72], we also calculated the vertical accuracy values, assuming 0.2-pixel matching error [58,59], where GSD is the ground sample distance which in this case is equivalent to the larger ground pixel size between the two images (mostly spatial resolution of more oblique images), the subscripts 1 and 2 refer to the two images, PX is a parallax in the X direction, PY is a parallax in the Y direction, EA is an emission angle, and SGA is a sub-spacecraft ground azimuth, which can be extracted by using the ISIS campt application. The resultant values are limited to a range of~0.1 to 0.6 meters ( Table 2). We calculated both the height H and basal width W for manually delineated individual mounds (e.g., Figure 3; Supplementary Figures S1 to S40) in each DEM. To provide accurate measurements of each pitted mound, mounds lacking a summit pit, degraded mounds, fully coalesced mounds forming complex topographies, and mounds including invalid DEM pixels have been carefully excluded from our measurements. H is defined as the difference between the maximum summit elevation and average base elevation [73,74] (Figure 3d), and W is the diameter of a circle having the same area as that of an outlined mound area [74,75].
Taking into account the vertical accuracy and post spacing for each DEM, as well as the minor uncertainties in morphometric measurements ascribed to the manual delineations of each mound (Supplementary Figures S1 to S40 Figure S9) with those derived using a HiRISE DTM (Supplementary Figure S41) and confirmed the discrepancies of both values in these two DEMs are within at most 0.6 m ( Table 3). Table 3. Comparisons of morphometric parameters of 21 measured mounds extracted from both our ASP-derived DEM ( Figure S9) and a SOCET SET-derived DEM ( Figure S41).

H (m) Difference (m) Our DEM
Published DEM

Results
Morphometric measurements were performed for 1297 pitted mounds within southern Acidalia Planitia (see Figure 4 and Table S1). The basal diameters W range from 39 to 1406 m, with a mean and median of 367 and 327 m, respectively, and a standard deviation (std. dev.) of 226 m. The mound heights H are in the range of 1.1-69.5 m with a mean (median) and a std. dev. of 15.2 (12.6) ± 10.8 m.
The data indicate no substantial dependence on latitude, longitude, or elevation. Previous studies, such as the photoclinometric analysis of over 400 pitted mounds within Cydonia Mensae, part of the Acidalia basin, and Chryse Planitia [23,45] and mound heights derived from three MOLA track data in Acidalia [25], are fairly comparable to our results. The exception being that a 3D photogrammetric analysis of HiRISE stereo pairs involving two pitted mounds by Oehler and Allen [21] (the same two mounds in Site 03) resulted in heights of up to 180 m, which are an order of magnitude larger than those of our results (30.8 and 31.6 m in height). This difference is hard to interpret because the past analysis was not described in detail. The ranges of H and W values and height-to-diameter ratios (H/W) of terrestrial and Martian analogous features for comparison with the mounds measured in this study are summarized in Figure 4 and Table 4. analysis was not described in detail. The ranges of H and W values and height-to-diameter ratios (H/W) of terrestrial and Martian analogous features for comparison with the mounds measured in this study are summarized in Figure 4 and Table 4.  Table S1) and analogous features on Earth and Mars [22,76]. The dashed lines represent the best-fit power regression. Table 4. A summary of morphometric parameters of the mounds shown in Figure 4.   Table S1) and analogous features on Earth and Mars [22,76]. The dashed lines represent the best-fit power regression.

Comparison of Morphometric Parameters among Possible Origins
As shown in Figure 4 and Table 4, some features on Earth and Mars show morphometric parameters similar to those of the mounds measured in this study and the others do not, which may give some clues as to what types of features are less or more likely origins of the mounds in Acidalia. Rootless cones (Earth), maars (Earth), pingos (Earth), subaerial/subaqueous mud volcanoes (Earth), and Martian mud volcanoes (Terra Sirenum) have the ranges of all three parameters relatively consistent with those of the mounds measured in this study. Regarding the ranges of the H values, submarine igneous volcanoes and Martian scoria cones are about one order of magnitude larger than the mounds measured in this study. As for the ranges of the W values, submarine igneous volcanoes, Martian scoria cones, and Martian tuff rings/cones show one or more orders of magnitude larger values than those measured in this study. With regard to the H/W ratio ranges (and average values), terrestrial lava domes show values more than two times higher than those of the other features. It should be noted that different environments (gravity, atmosphere, rock types, compositions, etc.) may have affected the mound formation processes. As suggested by Brož et al. [77], the thin atmosphere and low gravity on Mars are expected to cause far-reaching ballistic emplacement of scoria, creating wider and lower volcanic cones than those on Earth. This does not affect the interpretation that submarine igneous volcanoes, scoria cones and tuff rings/cones on Mars are less likely origins because Martian counterparts are much larger than the Acidalia mounds. However, Wilson and Head [46] proposed that the low gravity of Mars causes cooling-limited lava flows to be~6 times longer on Earth, which decreases their H/W ratios significantly. That is why lava domes cannot be ruled out in the context of the morphometric parameters. Relative to igneous volcanism, mud volcanism is generally not such an explosive or high temperature process. Hence, the morphometric parameters of mud volcanoes on Mars are expected to be similar to those of terrestrial mud volcanoes, which are consistent with Table 4. However, another potentially serious caveat of the above discussion is that, after formation of the mounds, erosional or alteration processes could have deformed their topography to date and the observed topography can be quite different from the original one, which complicates the comparisons to newly formed analogs on Earth. If the mud volcanoes formed in a subaqueous setting (or under an ocean) 3.6 Gyr ago, several possibilities of significantly altering their topography should be considered: e.g., submarine landslide, wave erosion, outflow channel floods, periglacial deformation, wind erosion, multiple eruptions, dust cover, etc. Estimating to what extent each of these processes contribute to the deformation is hard to determine due to large uncertainties. Therefore, although the comparison of morphometric parameters provides helpful information for distinguishing the possible origins, we cannot fully rely on the results and the interpretation of this analysis.

Depths of the Sources in Subaqueous or Subaerial Conditions
Oehler and Allen [55] suggested that part of Chryse-Acialia Planitiae hosted oceans and associated marine sediments to cause fluid expulsion producing submarine mud volcanoes during late Hesperian [2,78]. However, subaerial mud volcanism has not been well discussed and ruled out. Here we will assess under which conditions (submarine, subaerial, or both) fluid expulsion caused mud eruptions by using a simple mud eruption model.
In order to operate, mud volcanism would have required subsurface mud reservoirs prior to mud eruptions, and they should have been composed of water-enriched, fine-grained sediments. On Earth, the upwelling of fluidized mud primarily requires the presence of conduits connecting the reservoirs and the surface, and a bulk density inversion between mud reservoirs and overlying materials. As for the former, on Mars, polygonal fractures (or giant polygons) underlying the mounds appear to have acted as the conduits [55,56]. If the other processes that increase the pore pressure of mud reservoirs, such as horizontal compressional forces and additional groundwater, are negligible, an isostatic compensation model to relate the height of a mud volcano (H) to the depth of a putative mud source (D) can be developed ( Figure 5). The balance between the weight of the sediment column with ambient materials (air/water) and that of the mud volcano column constrains the depth to the top of the mud source: where ρ m is the bulk density of mud, ρ s is the bulk density of the surface layers which overlies the mud sources, ρ a is the bulk density of ambient materials during the eruption (1.0 kg/m 3 for liquid water and 0.020 kg/m 3 for air). This buoyancy-driven model has been applied to igneous volcanoes [79][80][81] and submarine mud volcanoes [82,83] on Earth for the first-order analyses. Although variations in gas and fluid content can create large density differences in the mud, we assume ρ m = 1400-2100 kg/m 3 to be a plausible range of bulk mud densities because it is comparable to that measured at most submarine and subaerial mud volcanoes on Earth (the density values of 1400 kg/m 3 and 2100 kg/m 3 correspond to those of clast-free, mousse-like silty clays and clast-bearing mud breccia, respectively) [83][84][85][86][87][88].
reservoirs and the surface, and a bulk density inversion between mud reservoirs and overlying materials. As for the former, on Mars, polygonal fractures (or giant polygons) underlying the mounds appear to have acted as the conduits [55,56]. If the other processes that increase the pore pressure of mud reservoirs, such as horizontal compressional forces and additional groundwater, are negligible, an isostatic compensation model to relate the height of a mud volcano (H) to the depth of a putative mud source (D) can be developed ( Figure 5). The balance between the weight of the sediment column with ambient materials (air/water) and that of the mud volcano column constrains the depth to the top of the mud source: where ρm is the bulk density of mud, ρs is the bulk density of the surface layers which overlies the mud sources, ρa is the bulk density of ambient materials during the eruption (1.0 kg/m 3 for liquid water and 0.020 kg/m 3 for air). This buoyancy-driven model has been applied to igneous volcanoes [79][80][81] and submarine mud volcanoes [82,83] on Earth for the first-order analyses. Although variations in gas and fluid content can create large density differences in the mud, we assume ρm = 1400-2100 kg/m 3 to be a plausible range of bulk mud densities because it is comparable to that measured at most submarine and subaerial mud volcanoes on Earth (the density values of 1400 kg/m 3 and 2100 kg/m 3 correspond to those of clast-free, mousse-like silty clays and clast-bearing mud breccia, respectively) [83][84][85][86][87][88]. The bulk density of surface materials (ρs) overlying mud source reservoirs within the southern Acidalia region is not readily determined because northern lowlands may consist of stratigraphic layers with different compositions (e.g., aeolian, ejecta, volcanic ash, ice-rich material), and their porosities could be a function of depth [2]. Thus, we assume that a real part of bulk dielectric permittivity (ε′) is a function of the depth-averaged bulk density (ρb) of the dry geologic materials [89]: Using a value of ε′ associated with the Vastitas Borealis interior unit [27] (~4.6 [90]), which includes the southern Acidalia region to a depth of 60-80 m [91], we can obtain ρs = 2270 kg/m 3 , which is also consistent with bulk densities of modeled country rock with a porosity of 25% at depths of 1 to 2 km [46]. If a subaqueous setting existed during mud eruptions, then source depths D are estimated at 0.   [83]. D: isostatic compensation depth to the top of the mud source (i.e., thickness of overburden above mud source), ρ m : bulk density of erupted mud through conduit, ρ s : bulk density of overlying materials, ρ a : bulk density of ambient materials.
The bulk density of surface materials (ρ s ) overlying mud source reservoirs within the southern Acidalia region is not readily determined because northern lowlands may consist of stratigraphic layers with different compositions (e.g., aeolian, ejecta, volcanic ash, ice-rich material), and their porosities could be a function of depth [2]. Thus, we assume that a real part of bulk dielectric permittivity (ε ) is a function of the depth-averaged bulk density (ρ b ) of the dry geologic materials [89]: Using a value of ε associated with the Vastitas Borealis interior unit [27] (~4.6 [90]), which includes the southern Acidalia region to a depth of 60-80 m [91], we can obtain ρ s = 2270 kg/m 3 , which is also consistent with bulk densities of modeled country rock with a porosity of 25% at depths of 1 to 2 km [46]. for ρ m = 1400 to 2100 kg/m 3 . While the thickness of the circum-Chryse outflow sediments forming the present VBF surface is uncertain, its thickness estimates range from~100 m [9] to~4500 m [92] (summarized in the discussion of [55]). Therefore, in either case, the estimated depths of the mud columns can be explained by fluid expulsions from the at most~4.5 km-thick VBF sediments. Due to the above reasons, we conclude that, if the Acidalia mounds have been formed by the fluid expulsion from the late Hesperian-aged flood deposits, either subaqueous or subaerial setting may have existed during the mud eruption.

Testing the Rheology of Fluid Flows
As previously proposed by Oehler and Allen [21], appearances of smooth surface flows at their peripheries (e.g., Supplementary Figure S8), together with upward doming topographic profiles (Figure 3c), strongly suggest (1) they were formed by emplacement of the fluids with finite yield strengths and plastic viscosities and (2) they are formed through single events (or the final shapes represent the bulk rheological properties throughout their formational events). However, the proposed mud flows creating the mounds have not been quantitatively examined in the context of rheological parameters. In this section, we test this idea by applying their morphometric parameters to fluid flow models and comparing the resultant rheological parameters with those measured at terrestrial mud volcanoes.
A slurry (a high concentration of cohesive clay particles in water) are commonly approximated as Bingham plastic fluids [93]. When a Bingham fluid slowly spreads over a plane it retains a convex-upward geometry in cross-section with its maximum height proportional to the square root of the yield strength multiplied by its basal width (i.e., a parabolic cross-section) [81,[94][95][96][97]. Assuming that each singular flow of a uniform Bingham fluid formed each of the mounds, and the thickness of the center of this fluid can be approximately equal to the mound height H regardless of a summit depression, the yield strength τ y of materials forming each mound can be described as, where ρ is the bulk density of a fluid and g is the surface gravity on present Mars (~3.71 m/s 2 ). Here we take ρ = 2000 kg/m 3 , which was chosen as a typical value within the value range used in Section 4.1.
Substituting the H and W values measured from the mounds into Equation (7), we obtain that the Bingham yield strengths for the fluids were in the range of 4.8 × 10 1 Pa to 4.4 × 10 4 Pa with a mean (median) value of 5.6 (3.8) × 10 3 Pa, as listed in Supplementary Table S2. These yield strength estimates are of similar magnitude to those of samples from submarine mud volcanoes (10 3 -10 4 Pa [83,98]) and subaerial mud volcanoes (10 1 -10 5 Pa [87,99]). Thus, pitted mounds may be formed by a mixture of liquid water and loosely cemented, fine-grained sediments (e.g., mud slurries), which may explain the observed high albedo and low thermal inertia rather than the surrounding plains [25,54]. Cross-sectional profiles of pitted mounds in Acidalia (e.g., Figure 3c) are similar in morphology to those of typical mud volcanoes on Earth [100], which can also support the hypothesized mud flows.
If this modeling is acceptable, mud viscosity, a significant factor to constrain flow rate, can be roughly estimated. Both yield strengths (τ y ) and viscosities (η) in fine-grained slurries are known to be functions of volumetric sediment concentrations (C v ), where α 1 , α 2 , β 1 , and β 2 are empirical constants that vary with the ratio of silt-and-clay (<63 µm grain size) to sand (>63 µm grain size) in slurries [101,102]. Inserting the expression for C v from Equation (8) into Equation (9), we obtain an equation regarding the viscosity as: The four empirical constants in Equation (10) were assumed to be comparable to the values of the slurries which have a silt-and-clay to sand ratio of 11:1 (α 1 = 3.79 × 10 −6 Pa, α 2 = 6.76 × 10 −17 Pa s, β 1 = 33.07, β 2 = 73.54 [102]), because several mud samples from different terrestrial mud volcanoes are composed of silt and clay with 1-25% sand [85,87,99,103]. By substituting the results from Equation (6) into Equation (9), the resulting viscosities (η) range from 4.2 × 10 −1 Pa s to 1.6 × 10 6 Pa s with a mean (median) value of 4.3 × 10 4 Pa s (6.9 × 10 3 Pa s) (Supplementary Table S2). These values are consistent with the mud viscosities of several mud volcano samples (0.8-1.5 Pa s [86], 100-10 3 Pa s [99], 10 5 Pa s [104], and 10 6 Pa s [88]), which come from different bulk densities and/or water contents at different times in different places on Earth. Perhaps a variation of the estimated η values may also represent the temporal and spatial variability of bulk physical properties of muds erupted from different reservoirs on ancient Mars.

Geological Context of the Mounds in Acidalia Basin
The morphology, topography, morphometry, and modeled rheological properties of the mounds, as stated above, are consistent with both a mud volcano and an igneous volcano origins; though, low or moderate regional gravity data of GSFC Gravity Model (GGM1025) [105,106], relative to Tharsis and Elysium regions, (see Figure 14 of [21]) strongly suggest the absence of high-density igneous bodies (i.e., magma sources) below the Acidalia surface. Moreover, according to Salvatore and Christensen [54], the analyses of THEMIS-derived thermal inertia map revealed that the materials forming the Acidalia mounds and the VBF marginal unit [27] clearly exhibit lower thermal inertia relative to the surrounding terrain (the VBF interior unit [27]), which indicates that the Acidalia mounds were composed of fine-grained sedimentary materials, produced by the expulsion of mud from the shallow subsurface. As a consequence, in the context of non-volcanic geological setting and thermophysical characteristics, we propose that a mud volcano hypothesis is favored over a magmatic hypothesis for the case of the mounds in Acidalia basin.

Conclusions
We created high-resolution digital elevation models, measured the accurate morphometry of nearly 1300 mounds in the Acidalia basin of Martian northern lowlands, and quantitatively assessed the possibility of subaerial/subaqueous mud volcanism by using simple mound formation models. In either case, maximum depth estimates of source reservoirs (less than~860 or~450 m) are consistent with mud eruptions caused by fluid expulsions of the at most~4.5-km-thick Hesperian flood deposits (the present-day VBF surface). In a submarine setting, the Noachian-aged valley networks or the Hesperian-aged outflow channels may have provided a vast amount of water and sediments forming the northern ocean, and during this period, a rapid sedimentation could have triggered fluid expulsion processes creating mud volcanoes (e.g., scenario A of [29]). Alternatively, subsequent sublimation of the surface water could have provided ocean-free surfaces during the late Hesperian or the Amazonian period. Perhaps circum-Chryse outflow events were episodically active, which may have never produced the northern oceans. This subaerial setting may have experienced impact-induced seismic shaking and associated fluidization of subsurface reservoirs may have caused mud volcanism (e.g., scenario E of [29]).
Observational evidence, morphometric measurements, and the estimated rheological estimates of mound-forming materials altogether strongly suggest that the mounds were formed by mud volcanism, which does rule out igneous volcanism. However, on the basis of the absence of a subsurface magma source and the mounds having lower thermal inertia relative to the surrounding plains, we propose the mud volcanism is more plausible hypothesis than igneous volcanism. Similar mud volcanism may have occurred in other areas within northern lowlands, such as Utopia and Isidis basins, where both circular mounds and fractures over the Hesperian-aged VBF(-like) surfaces have been observed [32,[107][108][109]. Unlike the potential hazards of terrestrial mud volcano fields in onshore (e.g., LUSI mud volcano, East Java, Indonesia, trigged by drilling operations [110]) and offshore settings [111], the potential oceans and associated mud volcanoes on ancient Mars may have provided the inventory of a significant amount of liquid water and dissolved gasses, which is also the case for submarine igneous volcanism (e.g., a seamount of Izu-Bonin Arc [112]). In a submarine setting, ocean(s) may have provided more habitable environments for a relatively long period of time than those in a subaerial setting because a large standing body of water possibly protects life against various threats, such as cosmic ray irradiation [113] and UV radiation [114]. Because terrestrial mud volcanic provinces generally provide favorable environments of methane emission and microbial life [115], sediments beneath mud volcano features on Mars may preserve extant aquifers and/or gas hydrate systems, and perhaps traces of past life, which can be one of the most suitable sites for future Mars landing missions.
Supplementary Materials: The following are available online at http://www.mdpi.com/2076-3263/8/5/152/s1, Figures S1-S40: Color-coded, high-resolution DEM draped over a contrast-enhanced grayscale orthoimage for Site 01 to Site 40, Figure S41: a published HiRISE DTM used for the comparison of morphometric parameters of mounds, Table S1: Morphometric parameters of the 1297 pitted mounds at 40 study sites, Table S2: Estimated yield strengths and reservoir depths for all the mounds.