Volcanic history in the Smythii basin based on SELENE radar observation

Elucidation of the subsurface structure in the Smythii basin on the moon is important for understanding lunar volcanic history. Two lava units (Units 1 and 2) cover this basin. The spatial subsurface structure below Unit 2 is unknown. We used SELENE/Lunar Radar Sounder data to identify four subsurface boundaries at 130, 190, 300, and 420 m depths. The radar is reflected at the paleo-regolith layer sandwiched among lava flows, which is supported by a simple radar reflection/transmission model. The spatial distribution of subsurface boundaries demonstrates the deposition of Unit 2 on the subsidence in Unit 1. A simple loading model explained the maximum depth of subsidence (~500 m) and indicated that lithospheric thickness in the Smythii basin was ~24 km at 3.95 Gya. The estimated growth rate of the lithosphere was ~60 km/Ga during 3.95 to 3.07 Gya. After the formation of the Smythii basin at ~4.11 Gya, Unit 1 and Unit 2 deposited with eruption rates of ~8.4 × 10−4 km3/yr by 3.95 Gya and ~7.5 × 10−6 km3/yr by 3.07 Gya respectively. The timing of decline in volcanic activity in the Smythii basin differs from that for the lunar nearside maria, indicating the diversity of volcanism in various lunar areas.

Lunar volcanic history is crucial for understanding lunar thermal evolution [1][2][3][4] . After the formation of the moon ~4.5 Gya (i.e. gigayears ago), melt in the lunar magma ocean remained in the lunar mantle and affected the duration of lunar volcanic activity according to the lunar thermal evolution model 5,6 . During the late heavy bombardment period (~4.0-3.8 Gya) 7,8 , many basins formed on the lunar surface, and magma continued to erupt over a long time on the near side (especially in the Procellarum KREEP Terrane area) rather than the far side 3 .
In this study, we focused on the Smythii basin (1°S, 87°E), located between the lunar near and far sides (Fig. 1a). This circular basin 9,10 formed during the Pre-Nectarian era (before 3.92 Gya) 3 and has five ring structures, which are ~130, 185, 270, 370, and 565 km in radius based on photogeologic mapping 11 . After basin formation, lava partially erupted and was deposited inside the basin, forming two mare units: Units 1 and 2 ( Fig. 1a) 12,13 . The geological map of Fig. 1a has previously been published in the United States Geological Survey [https://pubs. er.usgs.gov/publication/i948].
Based on Apollo 15/X-ray data, Unit 1 is composed of early volcanic material, which is relatively older than that of Unit 2 12 . Unit 2, the young mare unit of the Smythii basin 3 , is located in the northeast part of the basin (Fig. 1a) and is composed of lava of uniform mineral composition (comprising FeO and TiO 2 ) 14 . A ridge (hereafter "Ridge A") following an east-west direction was formed on Unit 2. In general, lunar ridges are formed by a thermal decrease in lunar radius 15 and by lava-flow loading 1,2 . Based on the crater chronology, the age of Unit 2 is 3.14 Ga (i.e. giga-annum or billion years) 3 , but the formation ages of Unit 1 and the Smythii basin have not yet been investigated clearly.
Based on the empirical relationship between the basin's diameter and depth, the depth of the mare's bottom (i.e. mare thickness) was estimated to be 1.28 km on average 16 . In addition, the ejecta composition of several craters on Unit 2 suggested that the mare thickness became shallower along the radial distance from the mare centre 17 .
Lunar subsurface structures have been investigated via seismic surveys and radar exploration 18,19 . The SELENE radar exploration detected one subsurface boundary at a depth of ~250 m in Unit 2 18 , and several subsurface boundaries below Unit 2 have also been reported 19 . However, the spatial distribution of these subsurface Results Fig. 2a,b show the radargram obtained by the LRS data. Other radargrams and these tracks are also shown in Figs S1-S3. We identified four subsurface boundaries in Unit 2, namely subsurface boundaries 1-4. Fig. 2c-h show the echo intensity as a function of depth (i.e. A-scope plot) at locations i-vi, indicated in Fig. 2b. We could not confirm the subsurface echo at locations i and vi (Fig. 2c,h) but identified the clear peaks of subsurface echo in locations ii-v ( Fig. 2d-g). Fig. 3a-d show the spatial distributions of the identified subsurface boundaries. The average depths of these subsurface boundaries are 130 ± 20, 190 ± 60, 300 ± 60, and 420 ± 50 m, respectively. Fig. 3e shows the range of the measured depth of each subsurface boundary. The deepest subsurface echo was ~500 m, located at 0.87°N, 87.41°E (i.e. within the narrowest circle in Fig. 3d). The shallow subsurface boundaries 1 and 2 are widely distributed in Unit 2 ( Fig. 3a,b). These subsurface areas have a wide diameter of ~195 km, surface area of ~3.0 × 10 4 km 2 , and centre at 1.60°N, 88.60°E (Table S1). The deep subsurface boundaries 3 and 4 are constrained within narrower areas inside the wide circles (Fig. 3c,d). The area of subsurface boundary 3 has an intermediate diameter of 90 km, surface area of 6.4 × 10 3 km 2 , and centre at 1.10°N, 88.00°E. The area   of subsurface boundary 4 has a narrow diameter of 45 km, surface area of 1.6 × 10 3 km 2 , and centre at 1.40°N, 87.70°E. In addition, most subsurface boundaries were identified on the southern side of Ridge A. The volume of lava below Unit 2 was at least (6.6 ± 2.7) × 10 3 km 3 , based on the simple multiplication of each layer's thickness and each subsurface circle area.  www.nature.com/scientificreports www.nature.com/scientificreports/

Discussion
We first discuss the depths of the subsurface boundaries and the cause of radar reflection. Ono et al. 18 found one subsurface boundary below Unit 2 (~1.0°N, ~87.4°E), which corresponds to the subsurface boundary 2 in this study. The subsurface boundaries detected in this study are a few hundred metres deep and shallower than the total lava thickness in the Smythii basin (1.28 km) 16 ; the LRS detected echoes not from the basin's bottom but from a boundary between the lava layers. In addition, the ejecta composition around the small craters on Unit 2 ( Fig. 5 and Table S2) shows an intermediate composition between Units 1 and 2, which indicates that Unit 2 deposited on Unit 1. Craters 4 and 5 locate around the centre of Unit 2, and these ejecta compositions are similar to the composition of Unit 2. This indicates that these craters do not excavate down to the depth of Unit 1; the boundary between Units 1 and 2 is deeper than ~420 m at the centre of Unit 2 according to the crater excavation depth (d exc = 0.1 × 0.84 × Diameter) 20 (Table S2), which is consistent with the depth of the deepest subsurface echo (~500 m).
Besides, we can expect that the boundary depth between Units 1 and 2 is relatively shallow on the north of Ridge A. For example, Craters 7 and 8 are located at the north of Ridge A, and the composition of Crater 7 is similar to that of Unit 1, while the composition of Crater 8 is similar to that of Unit 2. The excavation depths of these craters, namely ~210 m to ~320 m for Craters 7 and 8 (Table S2), can restrict the boundary depth between Units 1 and 2 around these craters. This is roughly consistent with the observation result that the shallow subsurface boundaries 1 and 2 slightly exist on the north of Ridge A but the deep subsurface boundaries 3 and 4 do not. We could not extensively determine the thickness of Unit 2 on the north of Ridge A. The reason for a small amount of shallow subsurface boundaries 1 and 2 on the north of Ridge A may be due to the non-uniform thickness of Unit 2 on the area. www.nature.com/scientificreports www.nature.com/scientificreports/ In general, the radar reflection is caused by the permittivity contrast, which is derived from the existence of the regolith layer or the mineral composition contrast (TiO 2 and FeO). In this study, we support the existence of the buried paleo-regolith layer under Unit 2 by using a simple radar reflection/transmission model (Method and Fig. S4). This model uses the following parameters: the contents of TiO 2 and FeO in Units 1 and 2, porosity of Units 1 and 2 (φ), and time delay (i.e. round-trip time) between the surface and subsurface echo (Δt). The surface mineral compositions are TiO 2 = 1.54 wt.% and FeO = 8.73 wt.% in Unit 1, and TiO 2 = 4.15 wt.% and FeO = 16.66 wt.% in Unit 2 as per the analysis of SELENE/Multiband Imager data 21,22 . Based on these compositions, the estimated bulk permittivity values of Units 1 and 2 are 6.61 and 7.73, respectively. Assuming that φ = 7% based on the Apollo sample 23 and Δt = 3.33 × 10 −6 s based on the depth of the deepest subsurface echo (~500 m), the estimated level of the deepest subsurface echo was about −35 dB with respect to the level of surface echo. As shown in Fig. 2, the LRS mainly detected the strong subsurface echoes of −20 dB or more; the mineral composition contrast between Units 1 and 2 cannot explain the observed radar reflection. If a regolith layer exists under Unit 2, the estimated level is about −17 dB, which is close to the level of the deepest subsurface echo (Fig. 2).
The existence of the buried paleo-regolith layer suggests that the lava of Unit 2 was discretely erupted and deposited. Since there are four subsurface boundaries under Unit 2, the lavas erupted at least five separate times. If the lunar lava deposited quickly, the average pause interval between lava eruptions for Unit 2 is ~0.18 Ga, which was simply calculated by dividing the formation period of Unit 2 (3.95 to 3.07 Ga) by 5. Thus, this pause interval can contribute to the development of the paleo-regolith layer. After the formation of the Smythii basin at ~4.11 Gya, the lava of Unit 1 finished depositing in a short time (by ~3.95 Gya); this rapid deposition may explain why the LRS cannot identify the subsurface echoes under Unit 1.
Next, we focused on the spatial distribution of the subsurface boundaries in Unit 2 (Fig. 3). Mare Smythii has semi-major and -minor axes (~420 and ~330 km, respectively), and a surface area of 1.1 × 10 5 km 2 (Table S1). The shallow boundaries 1 and 2 lie within the wide circle. The spatial distribution of subsurface boundary 1 is relatively narrower than that of subsurface boundary 2, which indicates that Unit 2 is composed of at least two different subunits. The subsurface boundaries 3 and 4 narrowly distribute within the wide circle. The deepest location of the subsurface boundary was 0.87°N, 87.41°E (i.e. within the smallest circle), which differs from the geological centre of Mare Smythii (1.00°S, 87.00°E) (see the star in Fig. 3). The spatial structure based on the subsurface circles in Fig. 3 suggests that Unit 2 deposited on a ground subsidence on Unit 1, because the all-subsurface layers are deposited in parallel and the edges of the strata fade with depth, giving the appearance of bowls. We inferred that this subsidence was produced by the loading deflection of Unit 1.
Using a simple loading model 1 (see Method), for example, suppose that Unit 1, with a radius of ~100 km (i.e. load), deposited on the lithosphere of thickness (T litho = ~24 km) when Unit 1 formed (~3.95 Gya). Then, we can explain the observed subsidence depth (~500 m). This lithospheric thickness is consistent with the result of Solomon and Head 2 ; the lithospheric thickness grows with time. The growth rate of the lithosphere in the Smythii basin is higher than ~60 km/Ga during 3.95 to 3.0 Gya, based on the results of this study (T litho = 24 km at 3.95 Gya) and those of Solomon and Head 2 (T litho ≥ 75 km at ~3.0 Gya). On the other hand, lunar thermal evolution model showed that the growth rate was ~75 km/Ga during 3.95 to 3.0 Gya based on the result of Spohn et al. 5 (e.g., the curve showing 1073 K in their Fig. 2b), which is consistent with the result for the Smythii basin. www.nature.com/scientificreports www.nature.com/scientificreports/ Finally, we discuss the volume and eruption rate of lava in the Smythii basin. The total thickness of the lava in the Smythii basin was 1.28 km 16 and the surface area of Mare Smythii was 1.1 × 10 5 km 2 . Thus, the total volume of lava in Mare Smythii was ~1.4 × 10 5 km 3 , which is much higher than the volume of Unit 2 (6.6 × 10 3 km 3 ) (Table S2); the Smythii basin is almost covered by the lava of Unit 1 (~1.3 × 10 5 km 3 ). The estimated eruption rate of the lava in Unit 1 was ~8.4 × 10 −4 km 3 /yr during 4.11 to 3.95 Gya, which is close to the average rate corresponding to the lunar near side maria (~10 −3 to ~10 −5 km 3 /yr) 24 . This indicates that the volcanic activity in the Smythii basin was extremely intensive before 3.95 Gya. Thereafter, at least 6.6 × 10 3 km 3 of lava erupted in Unit 2 by 3.07 Gya, the eruption rate being ~7.5 × 10 −6 km 3 /yr during 3.95 to 3.07 Gya, which is lower than the average rate for the lunar near side maria.
The eruption rate rapidly decreased after ~3.4 Gya in the lunar nearside maria 24 , but after 3.95 Gya in the Smythii basin; the timing of decline in volcanic activity differs between the lunar nearside maria and the Smythii basin. The low eruption rate was caused by the increase in lithospheric thickness owing to lunar thermal cooling 2 or by the depletion of the lava source in the lunar mantle 5 . Therefore, the state of lunar thermal evolution probably differs among the lunar nearside, farside, and boundary between the two hemispheres (such as the location of the Smythii basin). If lunar thermal cooling was dominant, the growth of the lithosphere after 3.95 Gya (>~60 km/ Ga) may have prevented the eruption of lava. A comprehensive understanding of volcanic history in various areas would shed light on the complexities of lunar thermal evolution.

Methods
Average depths of subsurface boundaries 1 to 4. We used the LRS data to investigate the subsurface structures in the Smythii basin. The LRS is an observation instrument that performs global subsurface radar sounding 25 and transmits electromagnetic waves of 4-6 MHz at an interval of 75 m along the SELENE orbital track from an altitude of ~100 km from the lunar surface. It measures the time delay difference between the surface and subsurface echoes (Δt) 25 . The LRS data cover the area spanning 8°S-5°N to 81°E-92°E (Fig. 1b), which includes 90 tracks. To eliminate clutter noise caused by lunar surface topography, we used synthetic aperture radar (SAR)-processed LRS data 26 [http://darts.isas.jaxa.jp/planet/pdap/selene/index.html.en]. The elimination capability of noise was shown by Kobayashi et al. 26 (e.g., see their Figs 8 and 9). The synthetic aperture is 5 km, and the spatial resolution is ~0.8 km along the orbital track direction and ~4 km along the longitude direction. Based on the analysis of Ono et al. 18 , we identified four subsurface boundaries from the continuity of the subsurface echo along the latitude, and confirmed the existence of subsurface echoes between adjacent orbits. The depth of the subsurface boundary at a local location ( ε d bulk ) is given by bulk radar bulk bulk where c is the speed of electromagnetic wave in a vacuum (3 × 10 8 m/s), ε bulk is the bulk permittivity of the subsurface layer, and d radar is the apparent radar depth, which is calculated by assuming that ε bulk is the same as that in a vacuum (ε = 1 bulk ). The bulk permittivity of lunar basalt is 4-11 based on the Apollo basalt samples 27 , mode value of which is 6 to 7 in permittivity histogram. In this study, we supposed that ε = 6 bulk , so the depth at local location (d 6 ) is given as If the standard deviation of permittivity is ±5, the subsurface boundary depth has the standard deviation of ~17% with reference to d radar .
We measured the depths (d 6 ) of both ends of the continuous subsurface boundary along the latitude on the radargram. For example, the measured locations are shown on the surface echo (see the 10 white points on the surface echo shown in Fig. 2b). Subsequently, we estimated the average depth for each subsurface boundary (d ave ) as where N is the total number of measured locations for a subsurface boundary, and ∑ d 6 is the summation of all average subsurface boundary depths. However, there are caveats in the calculation of Eq. 4. For example, we identified the outcrop of the subsurface boundary, edge depth of which is 0 m. We excluded the zero depth when using Eq. 3. The error of subsurface boundary depth was simply obtained from the standard deviation of the data set used in Eq. 3.
crater chronology. To determine the surface ages of the Smythii basin, Unit 1, and Unit 2 based on the crater chronology, we first measured the crater size-frequency distribution (CSFD) for Unit 1. The CSFD was obtained using the SELENE/TC Ortho map data 28 (Fig. 4) [http://darts.isas.jaxa.jp/planet/pdap/selene/index. html.en]. These data were resampled to the spatial resolution of ~74 m/pixel. Subsequently, we fitted the measured CSFD to the crater production function (Eq. 4) 4 : www.nature.com/scientificreports www.nature.com/scientificreports/ where D is the crater diameter [km], N(D) is the cumulative number of craters per km 2 larger than D, and a 0 and a n are the coefficients based on the study by Neukum 29 . Thus,N(1), that is, the cumulative number of craters on the grey curve of 10 0 km diameter (e.g. Fig. 4e), is obtained. Finally, we estimated the surface age of Unit 1 (t [Ga]) by substituting N(1) in the crater chronology function (Eq. 5) 4 : where A, B, and C are the coefficients based on the study by Neukum 29 . To make these calculations smooth, we used Craterstats 2.0 software 30 . The error of surface age was based on the definition of previous study 3 .
Radar reflection/transmission model. We analytically calculated the echo intensity using a simple radar reflection/transmission model 25 . For example, we considered three layers (i.e., vacuum, Unit 1, and Unit 2) (Fig. S4). The intensity ratio of the surface and subsurface echoes is given as where R 0,2 , R 2,1 , and tan δ are as follows: R 0,2 and R 2,1 are reflection coefficients on the boundaries between the vacuum and Unit 2 and between Unit 2 and Unit 1 respectively, Δt is the time delay between the surface and subsurface echoes, f is frequency (5 MHz), tan δ is the loss tangent of Unit 2, and C is the mineral composition (TiO 2 + FeO [wt.%]). ε _ bulk 0 is the permittivity of vacuum (ε _ bulk 0 = 1). ε _ bulk 1 and ε _ bulk 2 are the bulk permittivities of Units 1 and 2, which are approximated on the basis of the effective medium theory 31 : grain grain φ is the porosity of the subsurface layer, and ε grain is pore-free permittivity (i.e. grain permittivity) of the subsurface layer 32,33 .  (Fig. 5) and φ = 7% based on the Apollo sample 23 , ε bulk_1 is 6.27 and ε bulk_2 is 7.27. If Δt = 3.33 × 10 −6 s based on the depth of the deepest subsurface echo (~500 m), the level of the subsurface echo is about −35 dB with respect to level of the surface echo as per Eq. 6. Considering that the permittivity of Unit 1 is equal to that of the regolith (ε = _ 2 bulk 1 ), we can estimate that the echo level is about −17 dB using Eq. 6.
Loading model. We analytically calculated the subsidence of Unit 1 based on a simple loading model 1 . For example, we supposed a lava load (i.e. Unit 1) on the lithosphere (Fig. S5). In this study, the load has a radius r of 97.5 km with reference to the radius of Unit 2, a thickness h of 1.28 km, and bulk density ρ unit1 , and the lithosphere has a thickness T litho of 24 km. The subsidence (w) is given by the basic partial differential equation 34 .
= .  a r (21) When x is 0, the maximum depth of subsidence is given by Eq. 19: