Numerical modelling of the artificial impacts on the Moon
Authors: Rajšić Andrea , Miljković Katarina , Wojcicka Natalia , Onodera Keisuke , Collins Gareth , Kawamura Taichi , Lognonne Philipe , Wieczorek Mark , Daubar Ingrid 
Published: July 2021

Introduction: A possible source of seismic activity on Mars is meteoroid impacts [5]. Nevertheless, in the first Martian year of the the NASA InSight Mission [2] no signal has been unambiguously associated with an impact event [4]. This calls for further investigation of meteorite strikes and the relationship between impact conditions and the seismic signals they generate. One of the ways to understand the seismic signature of meteoroid impacts is to analyze already existing data from other planetary bodies.
During the Apollo era, over one thousand seismic signals were recorded on the Moon [e.g. 12]. Part of the Apollo seismic experiments were artificial impacts of Lunar modules (LM) and Saturn booster drops (S-IVB). Artificial impacts are considered large scale controlled experiments, because the exact position of the crater and the impactor parameters that made it are known. In this work, we model S-IVB artificial impacts on the Moon, using the iSALE-2D shock physics hydrocode [e.g., 1, 3, 21]. We simulated both the crater formation and the pressure wave propagation and attenuation. We examined size of the crater, cratering efficiency, impact momentum transferred to the target and two seismic parameters: seismic efficiency and seismic moment, and compared these measurements to the existing data [e.g., 10, 8, 7].
One challenge with modelling the S-IVB artificial impacts is the realistic presentation of the projectile. The Apollo S-IVB boosters were hollow aluminum cylinders, with a very low bulk density of 23 gcm&#8722;3 and mass of 14 t. The booster was 17.8 m long and 6.6 m in radius. The impact speed at the ground level was 2.54-2.66 kms&#8722;1. The drop angle was reported to be between 13.2&#9702; and 35&#9702; from vertical. [e.g., 14, 19]. There were five such impacts, and they all impacted into mare basalts and made elliptical craters (long and short axis in between 29.71 m and 38.7 m) with a central mound (crater depth was roughly estimated to 2-3 m) [e.g., 14].
Numerical modelling: All simulations in this work used the iSALE-2D shock physics hydrocode [e.g., 1, 3, 21]. To exclude any influence of target properties, all simulations used the same uniform target model of a 44% porous basaltic regolith [20, 15]. The mass and impact velocity of the projectile in our simulations were the same in all simulations and consistent with the experi- ments. Given the axial symmetry of the mesh geometry employed, we investi- gated five simplified representations of the irregularly shaped projectile. Three cases had a geometry of right-cylinder, with 90% porosity and different dimen- sions: 1. 11.7 m radius and height 0.5 m; 2. 5.8 m radius and 2 m height; 3. 0.992 m radius and 16.7 m height. The last two cases were spheroids: one was non-porous aluminum sphere with 1.06 m radius and the other one was 90% porous and had a radius of 2.3 m [13,21]. To calculate momentum transfer, the vertical component of the seismic moment and seismic efficiency we use approaches described extensively in previous studies [9, 7, 20, 15].
Here, we focus only on the vertical component of the seismic moment Mz [11, 7, 20]. To calculate seismic efficiency we used the same approach described in numerous previous work [e.g., 9, 20, 15].Results: The shape of the projectile has a substantial effect on crater for- mation but little effect on the seismic signature of the impact. The largest crater was formed in Case 3, while the best agreement with observed crater properties was provided by Case 1 (for depth) and Case 5 (diameter). The porosity of the projectile affected the size of the mound at the bottom of the crater, which supports the idea that the observed central mounds at the bottom of the ob- served craters are projectile remenants [14]. The seismic efficiency k 10&#8722;6 and seismic moment Mz4 1010 Nm were of the same order of magnitude for all cases. This seismic efficiency is in agreement with lower estimates of [10], and the seismic moment is consistent with the scaling proposed in [17, 16, 20, 6].Conclusion: We have successfully replicated the S-IVB artificial impacts on the moon with iSALE2D, producing craters that are consistent with obser- vations in their approximate dimensions and morphology. The simulations also constrain the seismic efficiency and seismic moment of the artificial impacts, which are relatively insensitive to the density and shape of the impactor. The low seismic efficiency determined here for artificial impacts on the Moon may help explain the non-detection of impacts by InSight in the first Martian year of operating. Moreover, the insensitivity of seismic moment to impactor density and shape suggests that results from the Apollo seismic experiment of these artificial impacts are useful analogs for small impacts on Mars that can be used to better inform their detectability by InSight [17, 16, 20, 6].
[1]&#160;&#160; Amsden A.A. et al. 1980. Technical report.
[2] Banerdt B.W. et al. 2020. Nature Geoscience, pages 1&#8211;7.[3] Collins G.S. et a. 2004. Meteoritics &amp; Planetary Science, 39(2):217&#8211;[4] Daubar I.J. et al. 2020. Journal of Geophysical Research: Planets 125(8).[5] Daubar I.J. et al. 2018. Space Science Reviews, 214(8):1&#8211;68.[6] Fernando B. et al. 2020 Journal of Geophysical Research: Planets.[7] Gudkova T. et al. 2015. Earth and Planetary Science Letters, 427:57&#8211;65.[8] Gudkova TV et al. 2011. Icarus, 211(2):1049&#8211;1065.[9] Guldemeister &amp; Wunnemann K.2017. Icarus, 296:15&#8211;27.[10] Latham G. et al. 1970. Science, 170(3958):620&#8211;626.[11] Lognonne P. et al. 2009. Journal of Geophysical Research: Planets, 114(E12).[12] Lognonne &amp; &#160;Mosser B.1993. &#160;Surveys in Geophysics, 14(3):239&#8211;302.[13] Lundborg N. 1968. International Journal of Rock Mechanics and Mining Sciences &amp; Geomechanics Abstracts, volume 5, pages 427&#8211;454.[14] Plescia J.B. et al. 2016. Planetary and Space Science, 124:15&#8211;35.[15] Rajsic A., et al. 2021. Journal of Geophysical Research: Planets.[16] Teanby N.A. 2015. Icarus, 256:49&#8211;62.[17] Teanby N.A. &amp; Wookey J. 2011. Physics of the Earth and Planetary Interiors, 186(1-2):70&#8211;80.[18] Tillotson J.H. Technical report.[19] Wagner RV., et al. 2017. Icarus, 283:92&#8211;103,[20] Wojcicka N. et al. 2020. Journal of Geophysical Research: Planets. 125(10)[21] Wunnemann K., et al. 2006. Icarus 180(2).