Quantitative Analysis of the Sloping Terrain on Al-Biruni’s Floor and Implications for the Cratering Process

Abstract

Surface unloading due to impact cratering results in lava filling the crater floor. Elevation differences in the crater floor, a common geological phenomenon on the Moon, represent direct evidence of cratering processes. However, few studies have been conducted on mare-filled craters on the Moon. Al-Biruni (81 km) is a farside impact crater with an inclined topographic profile on its floor. We quantitatively measure the morphology of Al-Biruni and model the basaltic lava emplacement to depict the cratering process. Differential subsidence due to melt cooling, wall collapse, impact conditions and structural failure were assessed as potential factors influencing the formation of the elevation differences on the floor. The results suggest that pre-impact topography is a plausible cause of the differences in floor elevation within Al-Biruni. Other factors may also play a role in this process, affecting lava flow by altering the topography of the crater floor after the impact. Thus, regardless of whether the lava inside the crater is impact-generated or comes from outside the crater, altering topography at different stages of the cratering process is an essential factor in creating the sloped terrain on the crater floor.

1. Introduction

Impact craters are important geological landforms that record the surface evolution of the Moon [1]. Crater floors, especially in large and complex craters, show a dynamic landscape shaped by the impact process. Initially, intense compression at the impact site causes a rapid expansion of a temporary cavity as material is excavated, displaced, and sometimes melted. This material unloads the underlying crust, favoring magma ascent to the crater floor [2]. As the crater forms, displaced and melted material that remains accumulates on the floor, significantly shaping its final structure during the modification stage. Mare-filled craters and Floor-Fractured Craters (FFCs) [3,4] represent direct evidence of crater floor modification by magmatism. Concurrently, the formation of features like terraces, central peaks, peak rings, and multiple rings in complex craters adds additional complexity to the terrain. Thus, the topography of the lunar crater floor provides a window to decipher magmatism [5,6] and surface reshaping [7].

Differences in the surface elevation of the crater floor may be a common feature in many impact craters on the Moon [6,7,8,9,10]. Wall collapse, different subsidence due to melt cooling and impact dynamics are considered possible causes of floor elevation differences during the crater formation [7]. Wall collapse will elevate the floor by depositing an abundance of rock fragments onto the adjacent section [11]. The impact cratering process forms a dynamic mixture of melt and rock on the floor. As the melt column cools, it triggers subsidence of the crater floor [12], resulting in localized elevation variations. Impact dynamics, including the direction and angle of impact, impactor velocity, pre-impact target topography, and target material properties influence crater morphology and melt movement [13,14], resulting in variations in crater floor elevation. The variation in crater floor elevation and characteristics can reveal different stages or processes involved in crater formation. If there is a difference in elevation on the crater’s floor during the early stages of the crater formation, meaning that one part is lower than another, the molten material or lava flows would naturally flow towards the lower area [7]. If the floor elevation differences arise during the final modification stages, under these conditions, the impact melt deposit would have become sufficiently viscous, preventing it from draining from the higher elevation areas to the lower ones [8]. Thus, by analyzing these differences, researchers can gain insights into the complex processes that shape crater floors and improve their understanding of impact cratering events.

In this study, we focused on the Al-Biruni crater (92.62°E, 18.06°N), a mare-filled crater with significant floor elevation differences, located in the Mare Marginis. The volcanism in this region was influenced by pre-existing structures in the lunar crust created by large-scale impacts [15]. The Al-Biruni crater is an ideal area for studying the effects of pre-impact and impact processes on crater floor elevation differences. However, previous studies have mainly focused on differences in crater floor elevations, specifically in coherent floor sections covering impact melt deposits [7,8]. To our knowledge, information about elevation differences on the floors of mare-filled craters remains unknown. Do one or all of the aforementioned factors contribute to the elevation difference of the mare-filled crater floor? Magma can fill the crater either from the subsurface or from outside, resulting in the formation of a mare-filled crater. Are the processes involved in reshaping the surface of the crater floor the same? To address these questions, this study conducted a detailed topographical analysis to quantify how lava modified the crater’s morphological parameters. From these characteristics, we evaluated the impact of the crater modification stage on the elevation differences in the floor. Additionally, the accumulation of lava flow may be prone to topographic lows on the moon [16]. The study also investigated the emplacement conditions of magma resulting from impacts to understand how magma reshapes the crater floor. Furthermore, the general patterns of craters with significant elevation differences in various geological environments are elucidated.

2. Geologic Setting

Al-Biruni is an impact crater on the far side of the Moon (Figure 1), near the Mare Marginis region. The crater has a diameter of 81 km [17] and lies to the south of Joliot and northeast of the Goddard craters (Figure 2). Its floor is mostly flat with a few minor craters (Figure 3), the most notable being Al-Biruni C, which has a diameter of 9.5 km [12] and is located close to the northeastern wall. Basalt of the same age as that of Mare Marginis [13], has filled the Al-Biruni crater (Figure 2). Mare Marginis (13.3°N, 86.1°E) is a large mare situated at the eastern nearside–farside boundary [15]. The age of the basalt of Mare Marginis is late Imbrian, varying from 3.38 to 3.88 Ga [18]. Volcanism in the western Mare Margins may have lasted up to approximately 3.1 Ga [15]. Surface chemistry derived from Clementine data shows the basalt of Mare Marginis contains moderate iron (15–18 wt% FeO) and titanium (2.5–3.5 wt% TiO₂) [19]. After calibration of the Chang’e-5 samples, which provide valuable insights into young volcanic activity on the Moon and serve as an indispensable ground truth for accurately mapping Moon’s surface chemistry [20], the FeO and TiO₂ weight percent maps were updated using Kaguya data [21] (Figure 4 and Figure 5). The basalts of Mare Marginis were initially believed to be located within the Marginis Basin (20°N, 84°E), which had a diameter of approximately 580 km [22]. However, topographic and GRAIL data confirmed that the basalts of Mare Marginis are not emplaced within any impact basin [23,24]. Furthermore, pre-existing crustal structures generated by the Crisium and Smythii Basins play an important role in the volcanism of Mare Marginis [15].

3. Methods and Data

The compositional analysis of the basalt deposits in the Al-Biruni crater was conducted to understand the geological controls on basalt emplacement. The lunar surface abundances of FeO and TiO₂ used in this study are derived from reference [21]. These abundances are obtained from SELENE (KAGUYA) multiband imager (MI) data, which include data with rich spectral information and high spatial resolution. It features five UV-visible spectral bands at 415, 750, 900, 950, and 1001 nm, along with four near-infrared bands at 1000, 1050, 1250, and 1550 nm. The spatial resolution is 20 m for the visible bands and 62 m for the near-infrared bands, achieved at an orbital altitude of 100 km [25]. The MI data include 9 spectral bands, in UV–vis and NIR spectroscopy, with a spatial resolution of 59 m/pixel [26] after topography shadow correction. Eight wavebands, i.e., 415, 750, 900, 950, 1001, 1050, 1250, and 1550 nm, were employed to calculate the abundances of the FeO and TiO₂ by removing similar bands, i.e., 1000 nm and 1001 nm [21] (Yang et al., 2023). The MI mosaics cover a latitude range of +/−65 degrees. The spectral angle parameters such as θ_Ti and θ_Fe can effectively eliminate the influence of space weathering on the calculation of FeO and TiO₂ contents [27,28]. In the work of [21], θ_Ti and θ_Fe were calculated from MI data using the following algorithms.

θ_Ti = arctan{[(R415/R750) − 0.208]/(R750 − (−0.108))}

θ_Fe = arctan{[(R950/R750) − 1.250]/(R750 − 0.037)}

where R415, R750, and R950 represent the reflectance values at the wavelengths of 415 nm, 750 nm, and 950 nm, respectively, in the MI data. After correcting for space weathering effects, the spectral features of the MI and the corresponding lunar sample sites, including the Apollo data series, Luna data series, and Chang’E-5 data, are available. Then the relationships between oxide abundances and spectral albedo characteristics are established. Finally, a deep learning algorithm was designed to develop FeO and TiO₂ inversion models and acquire more accurate lunar surface chemical contents. The detailed inversion model, along with the evaluation and validation of the FeO and TiO₂ product, can be found in reference [21].

The SLDEM2015 data were used to quantify the morphology of the Al-Biruni crater. The SLDEM2015 dataset covers latitudes from 60°S to 60°N, offering a horizontal resolution of 512 pixels per degree (approximately 60 m at the equator), and it boasts a typical vertical accuracy of ~3–4 m [29]. Four elevation profiles across the Al-Biruni crater were generated to depict its morphological characteristics using SLDEM2015 (Figure 6a). The mare has flooded the crater floor of Al-Biruni. The depth of Al-Biruni C was measured to estimate the possible thickness of the lava covering the crater floor of Al-Biruni.

For the Moon, the transition from simple to complex impact craters generally occurs at a diameter of about 15–20 km [30]. The diameters of Al-Biruni and Al-Biruni C are 81 and 9.5 km, respectively [17]. In this study, Al-Biruni is assumed to have formed as a complex crater, whereas Al-Biruni C is considered a simple crater. The crater diameter (D) is a fundamental morphometric parameter used to estimate the original crater depth (d) [31,32]. A newly compiled global crater database provides improved values for lunar crater morphometric parameters based on high-resolution remote sensing images and altimetry data [33]. This database includes the power-law fits for various lunar morphometric parameters as a function of crater diameter. For Al-Biruni, we estimated the central peak height using empirical formulas.

Table 1. Simple power-law relations for Al-Biruni crater morphometric parameters. The diameter (D) represents the mean rim-to-rim diameter of the Al-Biruni crater, which measures 81 km. The empirical equation used is derived from reference [33].

Parameter	Empirical Equation	Results (km)
Central peak height Hpeak	0.005D1.297	1.5

presents equations from reference [33] for estimating the morphometric parameters of Al-Biruni.

The one-dimensional thermo-mechanical lava flow model PyFLOWGO [34] was applied to understand the basalt emplacement in Al-Biruni. PyFLOWGO is specifically designed for cooling-limited flows [34]. It tracks various parameters such as lava velocity, channel dimensions, temperature, and physical state (solid/liquid) until a stopping condition is met. The input data for PyFLOWGO include slope versus distance, lava rheological and thermal parameters, and initial eruption conditions. In this study, slope profiles across the Al-Biruni floor were extracted from SLDEM2015 [29] using the QuickMap tool (https://quickmap.lroc.asu.edu, accessed on 18 June 2024). Boundary conditions associated with the basalt scenario for Tycho were adopted from reference [28]. The rheological and thermal parameters can be found in Supplementary Table S1. We utilized PyFLOWGO to determine whether the lava flow was a cooling-limited flow or not. It should be noted that PyFLOWGO was used to model the impact melt flows for the basalt composition of Tycho [35]. However, some impact melt flows exhibit similar emplacement dynamics to lava flows [35]. Therefore, we have utilized the model results as an analogy to depict the potential emplacement of the lava flow in Al-Biruni.

4. Results

The floor of Al-Biruni exhibits high TiO₂ and FeO contents (Figure 5). Most areas of the crater floor have TiO₂ concentrations ranging from 2 to 5 wt% (Figure 5). The largest patches with elevated TiO₂ levels are located on the NE side of Al-Biruni. Generally, the variations in FeO content (wt%) on the crater floor are greater than those on the crater walls. The floor shows a high FeO content (wt%) (indicated by a red hue). The TiO₂ and FeO contents of the Al-Biruni floor are comparable to those of Mare Marginis (Figure 4). In contrast, Al-Biruni C, displays high TiO₂ and low FeO contents.

According to the empirical equation presented in Table 1, the expected central peak height (H_peak) is1.5 km. Four elevation profiles across Al-Biruni illustrate its morphological characteristics. Elevation profile B, extending from NE to SW and crossing Al-Biruni C, shows that the NE crater rim is approximately 100 m higher than the SW crater rim (Figure 6b). This profile also indicates an asymmetrical structure in Al-Biruni C, with a step-like wall terrace formed on the SW side. Elevation profile C, a vertical profile through Al-Biruni, shows nearly equal elevation on the N and S sides (Figure 6c). No wall terrace is present on either side, and the crater floor appears relatively flat.

Profile D, extending from the northwest (NW) to southeast (SE) side of the Al-Biruni (Figure 6d), reveals a wall terrace on the NW side of Al-Biruni. Similar to profile B, there is a noticeable elevation difference between the NW and SE sides. A prominent landform on the crater floor is a mare ridge. In elevation profile E, the western (W) and eastern (E) sides exhibit similar elevations, with a wall terrace and mare ridge observed on the E side wall and floor, respectively, of Al-Biruni (Figure 6e). In summary, the crater floor’s topography inclines towards the W or NW, showing a significant elevation difference. This topographic inclined direction is associated with the presence of mare ridge (Figure 7). One ridge is located on the west side of the crater floor, with a steeper forelimb compared to the backlimb (Figure 8a). Al-Biruni C has a diameter of 9.5 km, and the elevation profile was drawn across it (Figure 6a), showing a measured depth of 3.7 km (Figure 8b).

The slope profile shown in Figure 6a was used in the PyFLOWGO model. Over a distance of 25 km, this profile indicates an average slope of 2.5 degrees (Figure 8c). The model results demonstrate the core temperature of the lava flow decreases from 1128.85 °C to 1128.835 °C (Figure 9). The core temperature remains almost unchanged. A similar pattern is observed in the spatial variation in lava viscosity. The value of flow viscosity is nearly constant (Figure 9).

5. Discussion

5.1. Possible Factors Influencing Elevation Differences on Crater Floor

Unloading of the underlying lunar crust due to an impact crater can supply a driving force for magma stalling at depth [2]. As the magma intrudes and spreads laterally beneath the crater, it inflates, lifting and fracturing the overlying crater floor [36]. If the unloading associated with the impact crater is substantial and the crust is relatively thin, the ascending magma may break through the crust and erupt at the surface [37,38,39]. This can result in magma covering part or all of the crater floor. When the floor is partially covered, it can exhibit topographic and morphological diversity related to the cratering process [7,8]. Significant elevation differences are a common feature on lava-covered crater floors [7,8].

Four potential explanations for the elevation differences on the floor have been summarized [7,40]: differential subsidence due to melt cooling, wall collapse, impact conditions, and structural failure. Basin-scale topographic relief might result from thermal contraction, as observed in the Orientale basin [41], where impact melt material ponded and cooled in the inner ~320 km diameter depression basin, reaching a maximum depth of approximately 20–25 km [12]. It is possible that a large amount of impact melt material induces the topographic elevation differences due to rapid surface heat loss and relatively slower axisymmetric conduction to the sides and floor of the impact melt pond [35]. However, in the case of the complex craters such as Jackson (71 km) and Tycho (85 km) on the highlands, subsidence due to melt cooling seems an unlikely cause for the elevation differences, given the smaller size and lesser volume of impact melt compared to the Orientale basin [7]. Similarly, subsidence due to melt cooling is not considered a likely cause of the elevation differences on the floor of Al-Biruni, which is similar in diameter to Jackson and Tycho. Additionally, there are no fractures or cracks on the Al-Biruni floor resulting from melt or lava cooling. Instead, basaltic lava cooling and solidification lead to surface contraction, causing buckling and the formation of ridges (Figure 7). In other words, thermal contraction results in local-scale landforms and does not impact the entire floor.

If wall collapse was the primary cause of the observed elevation differences on the crater floor, it would have contributed abundant rock fragments to crater floor, which can increase the elevation of the floor [11]. However, no megaclasts are distributed across the floor in the Al-Biruni crater (see Figure 3). This absence could be explained by the possibility that the megaclasts are covered by lava flows. It is worth noting that even a central peak, which should be approximately 1.5 km tall according to Table 1, was buried by the lava flow. Regardless, wall collapse affects the lava flow path by altering the topography of the crater floor as part of the cratering process, particularly during the final modification stages [8].

The impact conditions include the impact direction and angle, impactor velocity, pre-impact target topography and target material properties. Given the available data, it is challenging to estimate all of these parameters accurately, especially impactor velocity and target material properties. If the rim of the impact crater is lowest in the direction of the incoming impactor, impact melt will spill out from the rim in that direction [5]. Around the crater, there is a patch of impact melt material to the NW of the impact crater (Figure 3b). If the ballistic ejecta originated from the transient cavity, we infer that the impact direction for Al-Biruni may have been from the NW. The topographic profile from NW to SE shows that the rim height to the NW is lower than that to the SE. However, this inferred impact direction does not align with the inclined trend of the crater floor in Al-Biruni. Therefore, the impact direction alone cannot explain the observed elevation differences on the crater floor. This discrepancy may be due to the influence of the pre-impact topography of the targeted region. Pre-impact topography is a potential factor controlling crater morphology [42], impact melt movement [5], and lateral variations in mare thickness [43]. Volcanism in Mare Marginis was also influenced by pre-existing crustal structures generated by large-scale impacts, such as those that created the Crisium and Smythii Basins [15]. The cases of Jackson [7] and other complex craters of Copernican age [8] support this possibility.

Structural failure along a major plane of weakness is the primary reason for tilting of the crater floor. For this to occur, several conditions must be met: the impact melt or lava flow needs to have sufficient viscosity [7]. Regardless of the stage in the cratering process when substantial structural damage causes topographical variations, if the viscosity of the impact melt or lava flow is low, the melt or lava may cover the lower elevation. Notably, there are no observed occurrences of melt or lava covering the crater floor. In the case of the Al-Biruni crater, the mare flood completely covers the crater floor. From the images and elevation profile (Figure 6), there is no indication of a central peak. According to the empirical formula, the expected height of central peak is around 1.5 km. Therefore, the mare flood covered the crater floor to a thickness of approximately 1.5 km in Al-Biruni. It should be pointed out that the lack of spatial distribution data on mare lava thickness on the floor of Al-Biruni means that relying solely on the presence or absence of a central peak is insufficient for drawing a solid conclusion about the thickness of the mare on the floor. Additionally, the degradation of the central peak introduces uncertainty regarding the thickness of the mare. Analysis of the FeO and TiO₂ abundance in Al-Biruni suggests that the basaltic lava on the crater floor had a lower viscosity, similar to the lunar mare basalt [39]. The model results show that the viscosity and core temperature of the lava flow remained nearly constant over a 25 km distance (Figure 9). This suggests that the lava flow on the crater floor may not be cooling-limited but rather volume-limited. A cooling-limited flow slows down due to cooling and increasing viscosity, causing it to spread laterally. This typically marks the end of the central channel, and the flow eventually stops once it has cooled enough to impede forward motion [34]. In contrast, a volume-limited flow does not exhibit the same increasing cooling rate and viscosity down the flow. The lava at the flow front remains relatively hot with lower viscosity, often resulting in a complex morphology due to breakouts from the stalled front [44]. We infer that the ridge on the floor, marked by a yellow dashed line in Figure 7, may have formed due to pressure from the lava flow, which can cause localized uplifts or deformation in the surrounding crust, potentially resulting in ridge-like structures. The simplest explanation for the modeled viscosity and core temperature is that a large amount of magma erupted rapidly from the deep mantle to the surface [39] at near-liquidus temperatures [45]. Therefore, the structural failure mechanism may not be suitable for explaining the elevation differences observed in the crater floor.

5.2. Paradigm of Elevation Difference on Crater Floor

In complex impact craters, significant elevation differences on the floor can occur, regardless of whether the floor is covered by impact melt or mare basaltic lava. These elevation variations are primarily caused by wall collapse during the crater formation process and the pre-impact topography that existed before the crater formed [7,8]. Wall collapse introduces clasts of varying sizes at different locations within the crater, which influences the flow and distribution of melt or lava, thereby affecting the floor’s relief. Essentially, the crater floor relief is affected in similar ways in both cases. The effect of wall collapse can prevail in the crater formation. During this process, the mixing of impact melt and rock can create elevation differences on a crater scale [7]. In craters where the lava originates from beneath the crater, it can lead to different elevation features compared to craters where lava breaches the crater rim from outside sources. In the latter case, the lava filling the crater can lead to distinct elevation changes on the floor. Post-impact topography may be the main cause for the elevation differences on a crater floor which is covered by lava flow from outside the crater. For example, in the Herodotus crater [10], the crater walls may have slumped or collapsed inward, altering the surface of the floor. Such changes in topography can confine and redirect flowing lava, affect its ability to spread, and modify its surface morphology. It is important to note that these changes must occur before the lava flow is emplaced. If the crater floor was originally sloped, this pre-existing topography could influence the current floor elevation. Therefore, regardless of whether lava is impact-generated or sourced from outside, pre-existing topography is crucial in shaping the sloped terrain of the crater floor. Other factors may also contribute to floor relief changes at various stages of cratering, affecting the lava flow or melt pathways and further increasing the elevation differences on the floor. To better understand these processes, future research should include statistical analysis of impact craters with sloped floors across the Moon. This approach will provide deeper insights into the cratering process and its effects on crater floor elevation.

6. Conclusions

In this study, we analyzed remote sensing images and topographic profiles of the Al-Biruni crater to determine that the elevation difference between its western and eastern floors is 248 m. The maximum depth of the lava flow infilling the crater may reach up to 3.7 km. We evaluated four potential scenarios to explain the variations in floor elevation within Al-Biruni: differential subsidence due to melt cooling, wall collapse, impact conditions, and structural failure. It is possible that the pre-impact topography contributed to these differences in floor elevation. Additionally, changes in topography during various stages of the cratering process or post-modification play a crucial role in shaping the sloped terrain observed on the crater floor.