Comprehending the internal structure of the Moon is crucial for uncovering its formation and evolution. The existence of the lunar core can be proved by several pieces of evidence, including electromagnetic sounding analyses, mass and moment of inertia analyses, and seismic analyses. However, the precise size and composition of the lunar core are still unknown. In this study, the induced magnetic field generated by the lunar metallic core is illustrated through a three-dimensional MHD simulation. Several cases have been discussed in which the lunar core are set with different electrical conductivities and thicknesses. Compared to the hybrid model, our MHD model can calculate more accurate results with a more refined grid. Our simulation can capture the variations of parameters (plasma densities, temperature, and flow speed) in original and final conditions, while the hybrid model cannot.

How to cite: Yi, S., Xu, X., Xie, L., Wang, X., Xu, Q., Zhou, Z., Man, H., Luo, L., He, P., and Yang, P.: Three-dimensional MHD simulation of lunar induced magnetic field generated by lunar metallic core, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4978, https://doi.org/10.5194/egusphere-egu24-4978, 2024.

We know from spacecraft measurements that the crust of the Moon is heterogeneously magnetized. With the exception of a few magnetic anomalies related to craters and swirls, the origin of most of the lunar magnetic anomalies is not understood. Here we evaluate the performance of an inversion methodology, initially conceived to infer the direction of the underlying magnetization from magnetic field measurements, commonly referred to as Parker's method, to elucidate the origin of the magnetic sources by constraining the location and geometry of the underlying magnetization. We assess the performance of the method by conducting a variety of tests, using synthetic magnetized bodies of different geometries. These have been chosen such that they mimic  the main geological structures potentially magnetized within the lunar crust. Our test results show that the Parker method successfully localizes and delineates the two-dimensional surface projection of subsurface three-dimensional magnetized bodies, when certain conditions are fulfilled. In particular, the magnetization should be close to unidirectional, and the magnetic field data should have a higher spatial resolution than the smallest dimension of the magnetized body as well as a high signal-to-noise ratio. As an additional evaluation test, we applied this inversion methodology to two lunar magnetic anomalies that are associated with visible geological features, the Mendel-Rydberg impact basin and the Reiner Gamma swirl. For Mendel-Rydberg,  our analysis shows that the strongest magnetic sources are located within the basin's inner ring in agreement with previous studies showing that during an impact, the crust inside the newly formed crater undergoes demagnetization and potentially remagnetization (if an ambient magnetic field is present). For Reiner Gamma, we found the strongest magnetic sources form a narrow dike-like body that emanates from the center of the Marius Hills volcanic complex. The reason that only one such dike emanating from Marius Hills is magnetized could be linked to an atypical iron-metal composition or to the lunar ambient magnetic field being only intermittently present. Future applications of this method can focus on constraining the origin of the many lunar magnetic anomalies that are not associated with visible geological features.

How to cite: Oliveira, J. S., Vervelidou, F., Wieczorek, M. A., and Diaz Michelena, M.: Constraints on the spatial distribution of lunar crustal magnetic sources from orbital magnetic field data, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-20166, https://doi.org/10.5194/egusphere-egu24-20166, 2024.

Lunar Vertex, selected as NASA’s first Payloads and Research Investigations on the Surface of the Moon (PRISM) delivery, will explore a portion of Reiner Gamma (7.585° N, 58.725° W) with instruments mounted on a lander and small rover. Reiner Gamma (RG) is home to a magnetic anomaly, a region of magnetized crustal rocks. The RG magnetic anomaly is co-located with the type example of a class of irregular high-reflectance markings known as lunar swirls. The Lunar Vertex payload was designed to address three science goals: (1) test hypotheses for the origin of the RG magnetic anomaly, (2) test hypotheses for the origin of the RG swirl, and (3) determine the structure of the RG mini-magnetosphere. The payload suite consists of three instruments on the lander, and two instruments on a small commercial rover.

The Lunar Vertex payload will be carried to the lunar surface on a commercial lander as part of NASA's Commercial Lunar Payload Services (CLPS) program. The lander and payload are designed for operation during one lunar daylight period (i.e., no night operations or survival). NASA selected Intuitive Machines as the CLPS provider for the Reiner Gamma delivery. At the time of this writing, the launch will be no earlier than June of 2024.

Lander Instruments: The three Lunar Vertex lander instruments were delivered to Intuitive Machines in June 2023. The Magnetic Anomaly Plasma Spectrometer (MAPS), built by the Southwest Research Institute, is capable of measuring the ion and electron velocity distribution over a 292.5° x 90° FOV from 8 eV/e to 17.5 keV/e. The Vector Magnetometer–Lander (VML) suite, built by APL, is comprised of a tetrahedral array of four commercial fluxgate magnetometers mounted on the bottom of a 0.5-meter mast, with a science-grade dual-ring core fluxgate magnetometer at the top of the mast. Together, MAPS and VML will characterize the magnetic field and surface plasma environment within RG. The Vertex Camera Array (VCA) suite, built by Redwire, is a set of three clusters of three RGB cameras. VCA images will be used to characterize the landing site geology and to understand the physical properties of the lunar regolith around the lander.

Rover and Rover Instruments: The rover vehicle is from vendor Lunar Outpost. The rover instruments were integrated with the vehicle at APL, and environmental testing was carried out on the integrated system. The Vector Magnetometer–Rover (VMR), built by APL, is also comprised of a tetrahedral array of commercial fluxgate sensors, mounted on a 0.2-meter mast. With VML, VMR will characterize local spatial structuring of the magnetic field at RG. The Rover Multispectral Microscope (RMM), mounted inside the rover body, is a close-up imager that can provide information on soil texture, as well as active LED illumination at a set of UV to NIR wavelengths chosen for their utility in determining the composition and maturity state of the regolith. The rover will be delivered to Intuitive Machines in early January 2024.

How to cite: Vines, S., Ho, G., and Blewett, D. and the The Lunar Vertex Science Team: The Lunar Vertex PRISM Payload: Ready for the Moon, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-21717, https://doi.org/10.5194/egusphere-egu24-21717, 2024.

Ground motion observations on planetary objects are a prerequisite for a detailed understanding of their interior structure and evolution. The imaging of the near surface structure - in particular on the Moon - has strong practical implications. First, the race is on to detect ice-bearing rocks near the surface from which water could be extracted and used as a resource for crewed missions. Second, due to the substantial bombardment of the lunar surface with meteorites and the lack of an atmosphere, observatories or habitats may have to be built underground. It has been proposed that cavities from ancient lava flows below the lunar surface could be used to place infrastructure. Current mission plans for geophysical exploration focus on static seismic sensors/arrays that would be restricted to the area they can explore.      
With the NEPOS project we want to go beyond these restrictions and develop concepts for mobile seismic arrays that work in an autonomous way using robotic technology. The scientific challenges include the understanding of wavefield effects of icy rocks and caves in a strongly scattering environment, the provision of optimal source-receiver configurations to detect them, as well as an integrated data-processing workflow from observation to subsurface image including the quantification of uncertainties.   
In order to solve these challenges, we first developed a Digital Twin for wave propagation in the strongly heterogeneous lunar crust to generate synthetic seismic data using the spectral element code SALVUS. We compared the synthetic seismograms to data from the Apollo 17 Lunar Seismic Profiling Experiment (LPSE) and find that their main characteristics coincide. We further generated synthetic seismograms for a variety of network configurations and subsurface heterogeneities, which will be used to test appropriate imaging methods for the lunar subsurface structure. Due to the presence of strongly scattering media ambient noise tomography seems to be a promising method, as was already shown in previous studies. We apply seismic interferometry to LPSE data, as well as to our synthetic seismograms, to reconstruct Green’s functions, which give us information on the subsurface properties.

How to cite: Keil, S., Igel, H., Bernauer, F., Shutin, D., Shin, B.-S., Nierula, K., Reiss, P., Sesko, R., and Lindner, F.: The NEPOS Project: Near-Surface Seismic Exploration of Planetary Bodies with Adaptive Networks, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-9849, https://doi.org/10.5194/egusphere-egu24-9849, 2024.

Seismic observation is a powerful tool to investigate the Earth’s geological activities and internal structure and has also been applied to the Moon and Mars [e.g., Latham et al., 1969; Banerdt et al., 2020]. For the Moon, a seismic network was constructed on the nearside during the Apollo missions, and nearly eight years of observation provided us with more than 13,000 seismic events [Nakamura et al., 1981]. These events have contributed to understanding the seismicity rate on the Moon and its internal structure [e.g., Garcia et al., 2019; Nunn et al., 2020], both of which are important to know the current geological activity level and trace back to the thermal evolution in the past.

In the Apollo lunar seismic observation, two types of seismometers were installed: Long-Period (LP) and Short-Period (SP) seismometers. While the LP sensor has sensitivity at 0.2 – 1.5 Hz, the SP is sensitive at 1 – 10 Hz [e.g., Nunn et al., 2020]. In previous studies, the LP data were mainly used. In fact, all the cataloged events were detected solely using the LP data [Nakamura et al., 1981]. On the other hand, because of numerous unnatural signals and/or spikey noises, the majority of SP data remained unanalyzed after the initial description of high-frequency quakes by Duennebier and Sutton (1974a, 1974b) [e.g., Frohlich and Nakamura, 2006; Knapmeyer-Endrun and Hammer, 2015]. This fact implies that there are potential seismic events only identifiable in the SP data, and the lunar seismicity might be underestimated.

Lately, Onodera (2023) denoised all the SP data and performed an automatic event detection. As a result, he discovered about 22,000 new seismic events, including thermally driven quakes (thermal moonquakes), impact-induced events, and tectonic-related quakes (shallow moonquakes). While the former two types are useful to understand the surface evolution or degradation processes, the latter type is closely related to the seismic activity level of the Moon. Here, I focus on shallow moonquakes. In the past, since only 28 shallow moonquakes were identified, it was difficult to give a detailed description of their source mechanism, regionality, and correlation with tidal force. In this study, using the newly discovered 46 shallow moonquakes, I’m trying to give new insights into this type of event.

In the presentation, I will describe the general characteristics of newly discovered shallow moonquakes (e.g., waveforms and spectral features) and summarize the estimated source parameters (such as energy release, seismic moment, and body wave magnitude).

References

• Banerdt et al. (2020), Nat. Geosci., 13(3), 183-189.
• Duennebier and Sutton (1974a), JGR, 79(29), 4365-4374.
• Duennebier and Sutton (1974b), JGR, 79(29), 4351-4363.
• Frohlich and Nakamura (2006), Icarus, 185(1), 21-28.
• Garcia et al. (2019), Space Sci. Rev., 215(8), 50.
• Knapmeyer-Endrun and Hammer (2015), JGR Planets, 120 (10), 1620-1645.
• Latham et al. (1969), Science, 165(3890), 241-250.
• Nakamura et al. (1981), UTIG Technical Report, No. 118.
• Nunn et al. (2020), Space Sci. Rev., 216(5), 89.
• Onodera (2023), ESSOAr, DOI: 22541/essoar.169841663.38914436/v1

How to cite: Onodera, K.: Newly Discovered Shallow Moonquakes: General Characteristics and Source Parameters, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-1694, https://doi.org/10.5194/egusphere-egu24-1694, 2024.

NASA selected a new in-situ seismic experiment, Farside Seismic Suite (FSS), onboard CP-12 lander with the landing site at the farside of the Moon in Schrödinger Basin. This future mission should provide us with the data to further constrain lunar interior and the Moon seismicity. Due to the single-station nature of the mission, localisation of the newly detected events will be challenging. Therefore, in this study we develop a pipeline for the deep moonquake (DMQ) source region localisation on the legacy of the data acquired during the Apollo missions. We are interested into DMQs since their source regions, called nests, on the near side have been identified, and since their occurrence patterns follow specific spatial and temporal patterns. Spatial patterns are related to tsp=ts-tp travel time measurement. We can show that based on tsp measurements we can form group of nests, called sets, that share similar travel times within error bars and therefore we cannot distinguish between nests that belong to the same set just using the travel time information. Temporal patterns are related to the fact that occurrence of DMQs is closely related to the monthly motion of the Moon around the Earth. Different nests correspond differently to three lunar months: synodic, draconic, anomalistic. By combining the spatial and temporal patterns we try to characterise different nests and exploit this information for their prediction. For this purpose we develop a machine learning model for nets classification. An input data into model we use orbital parameters related to the monthly motion of the Moon around Earth, which we relate to different nests. The ML model is learned to classify between nests that belong to the sam set. We report that models are achieving an accuracy over 70% when those are trained to classify =< 4 nests within the set, and better than 90% when only two DMQ nests are in the same set. This approach opens up a new way to DMQ location estimate, on the near and farside of the Moon, when captured by the future FSS single-station seismometers or other seismic stations on the Moon. 

How to cite: Majstorović, J., Lognonné, P., Kawamura, T., and Panning, M.: Relating deep moonquake source regions from Apollo missions with their temporal and spatial patterns using machine learning, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-8297, https://doi.org/10.5194/egusphere-egu24-8297, 2024.

We present LunarLeaper, a robotic explorer concept in response to the ESA 2023 Small Missions call. Pits, volcanic collapse features with near-vertical walls, have been identified across the lunar and Martian surface. These pits are high priority exploration destinations because some, referred to as skylights, might provide access to subsurface lava tube systems. Lava tubes are of particular interest for future human exploration as they offer protection from harmful radiation, micrometeorites and provide temperate and more stable thermal environments compared to the lunar surface. We propose to use a small legged robot (ETH SpaceHopper, <10 kg), to access and investigate the pit edge, using its ability to access complex and steep terrain more safely than a wheeled rover. LunarLeaper will land in Marius Hills within a few 100 m of the pit and traverse across the lateral extent of the hypothesized subsurface lava tube. On its traverse it will take measurements with a ground penetrating radar and a gravimeter, measurements that will allow us to survey the subsurface structure and detect and map lava tube geometry if present. The robot will approach the pit edges and acquire high resolution images of the pit walls containing uniquely exposed layers of the geophysically mapped lava flows and regolith layers. These images will allow not only scientific advances of lunar volcanism and regolith formation, but also enable assessment of the stability of the pit structure and its use as a possible lunar base. The mission is expected to last 1 lunar day. The robot could be delivered to the surface by a small lander, as they are currently developed and planned by various national and commercial agencies and hop off the landing platform without the need for a robotic arm. It is highly flexible in accommodation and can thus make full use of the new international lunar ecosystem.

How to cite: Mittelholz, A., Stähler, S. C., Kolvenbach, H., Bickel, V., Church, J., Hamran, S.-E., Karatekin, O., Ritter, B., Aaron, J., Anhorn, B., Coloma, S., de Palézieux dit Falconnet, L., Grott, M., Ogier, C., Robertsson, J., and Walas, K.: Lunarleaper – Unlocking a Subsurface World, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-21578, https://doi.org/10.5194/egusphere-egu24-21578, 2024.

The surfaces of planetary bodies reflect their evolution through primary surface shaping via their continuous evolvement over time. Surface formation and degradation processes need to be understood in detail to infer the timescales over which these processes operate.

Planetary surfaces which are heavily cratered offer the opportunity to investigate various aspects of the cratering processes which are initiated when an impactor strikes their surface and ejects rock fragments from the impact point upon the newly-formed crater cavity and its surroundings (e.g. Hörz, F. and Cintala, M., 1997). Among the ejecta material from the impact are boulders covering a wide range of sizes (e.g. Nagori,R. et al., 2024). Dependent on the planet’s environment and the size of the impact fragments, these boulders can form either secondary craters or simply become subject to the various environmental forces which ultimately add through different degradation processes to the formation of planetary regolith. To understand many of the aspects of the above processes, size distributions of both the impact-generated boulders and secondary craters need to be understood (e.g. Cadogan, P., 2024).

As many of the techniques to identify boulders and small craters on albedo images are using shadow-based identification methods one has to be aware that ambiguities can arise through complex topographies and overlapping surface features. These factors can modify the shape of the shadow and make the identification of its borders difficult, thereby preventing a precise determination of both it’s location and it’s radius.

To obtaining high-quality statistics for boulders and craters over large and varied planetary surfaces, machine learning and deep learning methods have been applied to automate the tedious human based detection work (e.g. DeLatte, D. et al, 2019). However, little attention has been paid to investigate the influence of the training sets on the success rates of these efforts (Mall, U. et al., 2023). We are investigating in this study the influence of crater training sets, originating from specifically chosen lunar areas on the resulting confusion matrices produced by specific convolution neural networks and compare these with the results found from traditional imaging methods.

Cadogan, P., (2024), Automated precision counting of small lunar craters - A broader view, Icarus, Volume 408, 2024,115796.

DeLatte, D.M., Crites, S.T., Guttenberg, N., Yairi, T. (2019), Automated crater detection algorithms from a machine learning perspective in the convolutional neural network era, Advances in Space Research, Volume 64, Issue 8, Pages 1615-1628.

Hörz, F. and Cintala, M. (1997), The Barringer Award Address Presented 1996 July 25, Berlin, Germany: Impact experiments related to the evolution of planetary regoliths. Meteoritics & Planetary Science, 32: 179-209. https://doi.org/10.1111/j.1945-5100.1997.tb01259.x.

Mall, U., Kloskowski, D., Laserstein, P., (2023), Artificial intelligence in remote sensing geomorphology—a critical study, Front. Astron. Space Sci., 30 November 2023, Sec. Planetary Science , Volume 10 – 2. https://doi.org/10.3389/fspas.2023.1176325.

Nagori,R., Dagar, A. K., Rajasekhar, R.P., (2024),  Age estimation and boulder population analysis of the West crater at Apollo 11 landing site using Orbiter High Resolution Camera on board Chandrayaan-2 mission, Planetary and Space Science, Volume 240, 2024, 105828.

How to cite: Mall, U., Surkov, Y., and Cadogan, P.: How do training sets influence crater and boulder detection in machine learning?, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-12084, https://doi.org/10.5194/egusphere-egu24-12084, 2024.

As an important physical property of the Moon, the lunar crustal density provides evidence for the early evolution process of the Moon, such as the asymmetry of its nearside and farside. The apparent density is the average value of the bulk density at a certain depth. The gravity inversion method is an effective tool of determining the apparent density distribution of the lunar crust. Benefiting from the lunar GRAIL mission's high-precision gravity field models, it is theoretically possible to establish a global high-resolution apparent density model through the gravity inversion. However, there are two major problems, namely, the accuracy and efficiency of the inversion. To solve these problems, different from the admittance methods, we develop a high-precision apparent density mapping method in the spherical coordinate. The improved 2D Gauss-Legende formula and adaptive subdivision algorithm are adopted to calculate the high-precision gravity anomalies of the Tesseroid cells. The parallel algorithm based on OpenMP is involved to improve the calculation efficiency of the global data. And the Cordell iterative algorithm is utilized to derive the apparent density model fitting the real gravity anomalies. The synthetic data tests verify the accuracy and efficiency of our method. Subsequently, we use LOLA topographic data to correct the gravity anomalies obtained from GRAIL and derive the global lunar Bouguer gravity anomalies. The lunar crust thickness model given by Wieczorek et al (2013) is chosen as the bottom interface of the density layer. As a result, we obtain a global high-resolution lunar crust apparent density model with a resolution of about 20 km by the presented mapping method. Our model shows that the apparent density of the lunar crust ranges from about 2200 - 2900 kg/m³ with a mean value of about 2600 kg/m³. The Procellarum KREEP Terrane (PKT) and the large impact basins present higher apparent density, while the Feldspathic Highlands Terrane (FHT) varies around the mean apparent density, and there is a significant variation within the South Pole-Aiken Basin Terrane (SPAT). Our apparent density distribution around the PKT and FHT is significantly relevant to the surface grain density model derived from the current FeO and TiO₂ abundance map. However, our apparent density distribution around the SPAT differs from the surface grain density, suggesting a more complex density structure in this region.

How to cite: Yang, J. and Guo, L.: The apparent density distribution of the lunar crust revealed by the spherical coordinate-based mapping method, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-3166, https://doi.org/10.5194/egusphere-egu24-3166, 2024.

How to cite: Nguyen, D. T., Jacquemoud, S., Lucas, A., Douté, S., Ferrari, C., Coustance, S., Marcq, S., and Meygret, A.: Unveiling the characteristics of the lunar surface by massive inversion of the Hapke model, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-17062, https://doi.org/10.5194/egusphere-egu24-17062, 2024.

Hyperspectral images, despite their rich spectral information, often suffer from low spatial resolution due to physical constraints in imaging sensors. However, when higher spatial resolution data of the same scene are available, we can perform data fusion to generate hyperspectral images with high spatial resolution. This fused data can be viewed as the output of a synthetic sensor that combines the high spatial and spectral resolution data acquired by different sensors. This fusion allows for new applications with increased accuracy, such as high-resolution mapping of minerals and surface materials. Imaging spectroscopy facilitates the identification and discrimination of materials and their constituents. Data fusion enhances both the spatial and spectral characteristics of the initial data. It is based on the synergistic exploitation of data from different sources, aiming to produce superior results. By integrating data from The Moon Mineralogy Mapper (M3) by NASA and the Imaging Infrared Spectrometer (IIRS) by ISRO, we can improve the spatial and spectral resolutions, enhance measurement accuracy, and reduce uncertainties. This will enable a more precise assessment of the mineral composition of the area of interest. The objective is to fuse high spatial resolution data, which has discontinuities in the spectral domain, with low spatial resolution data that has continuous spectra. The ultimate goal is to estimate an image with high spatial and spectral content, providing a more comprehensive and accurate understanding of the area of interest. We replaced the noisy bands in the M3 and IIRS data and used cubic convolution to resample the M3 bands to the IIRS band’s native spatial resolution. However, the M3 bandwidth is different from the IIRS bandwidths. Nevertheless, this gap-filling procedure will allow us to identify endmembers. As a followup study we are going to employ a spectral unmixing technique to obtain endmembers information and high-resolution abundance matrices from the initial images. Data fusion helps overcome the limitations of individual datasets, exploit the strengths of different sensors, and extract more valuable information.

How to cite: Ivanov, I. and Filchev, L.: Fusion of IIRS and M3 data for the purpouse of finer resolution mineral mapping, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-292, https://doi.org/10.5194/egusphere-egu24-292, 2024.

Sulfides are common minerals in lunar rocks and have great implications for lunar magma origin and subsequent evolution. Pentlandite as an important sulfide, usually coexisted with troilite, which could indicate the geological thermal history of lunar rocks. Previous researchers proposed three potential mechanisms to explain the origin of pentlandite in lunar soil: (i) the reaction between mobilized sulfur and metallic FeNi, ilmenite and an Fe-bearing silicate; (ii) it is formed by the reaction between migrating Ni and troilite; (iii) pentlandite may exsolve from the Ni-rich troilite during the cooling of rocks. Here, we used the scanning electron microscopy (SEM), X-Ray electron probe micro-analyzer (EPMA) and transmission electron microscopy (TEM) to decipher the formation mechanisms of pentlandite in Chang’e-5 (CE-5) lunar soils. Our results show that pentlandites occurred as lamella and veinlets in troilites from basalts and breccias, forming a troilite-pentlandite assemblage. Crystallographic data from TEM provide the first robust evidence that pentlandites from both basalts and breccias were exsolved from the host troilite during the magma cooling, rather than formed by the reaction between mobilized sulfur and metallic FeNi, or mobilized Ni with troilite. Furthermore, we found taenite was exsolved from pentlandite in lunar breccia, forming a troilite-pentlandite-taenite assemblage. Given exclusively exsolved taenite and higher Ni content in troilite in breccia than that in basalts, it suggests the origin of pentlandite in breccia may involve a geological process involving the addition of exotic meteorite materials. Finally, we established two atom shuffling models to describe the transformation mechanism from troilite to pentlandite, and pentlandite to taenite. This work provides new insights into the origin and geological evolution of lunar sulfides, and also provides new method for the study of mineral evolution in other extraterrestrial samples.

How to cite: Tang, X., Gu, L., Tian, H., Li, Q., and Li, J.: Origin of pentlandite in Chang’e-5 lunar soils revealed by transmission electron microscopy, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-14455, https://doi.org/10.5194/egusphere-egu24-14455, 2024.

The Andrade rheological law ε(t)=ε₀+βt^α has been introduced by Andrade in 1910 for the description of elongation in metal wires. Since then, this model has gained increasing popularity in geophysics and planetary sciences, being extremely effective in the description of numerous materials, including polycrystalline ices, amorphous solids and silicate rocks. Recently, many works in the field of planetology have adopted this model for the description of the response of solar system or extra-solar planets to tidal perturbations, especially for bodies whose properties are still poorly constrained. This is because the Andrade rheology can describe transient deformation using a low number of parameters, a highly valued characteristic for the study of planetary bodies for which few observational constraints are available, such as exoplanets. For the Moon, the Andrade rheology provides an accurate description of the viscoelastic tidal deformation, satisfying the observed frequency dependence of the quality factor.

While for uniform bodies described by a steady-state Maxwell rheology the analytical form of the time-dependent Love numbers (LNs) was established long ago, in the case of the transient Andrade model no closed-form solutions have been determined so far. This is mainly due to the fact that the planetary response is normally studied in the Fourier-transformed frequency domain or by numerical methods in the time domain. Closed-form expressions could be important since they have the potential of providing insight into the dependence of LNs upon the model parameters and the viscoelastic relaxation time-scales of the planet.

In this work, we focus on the Andrade rheological law in 1-D and we obtain a previously unknown explicit expression, in the time domain, for the relaxation modulus in terms of the Mittag-Leffler function E_α,β(z), a higher transcendental function that generalises the exponential function. Second, we consider the general response of a uniform, incompressible planetary model - the “Kelvin sphere” - studying the Laplace-transformed, the frequency domain and the time-domain LNs by analytical methods. By exploiting the results obtained in the 1-D case, we establish closed-form expressions of the time domain LNs and we discuss the frequency-domain response of the Kelvin sphere with Andrade rheology analytically.

Our findings exhibit a complex relation between the planet parameters and the resulting deformation. From the analysis of the frequency-dependent LNs we show that dissipation in Earth-like planets is strongly dependent upon the choice of the planet density, rigidity and viscosity, while the variation of the Andrade creep parameter α has an effect that is limited to short-period tidal forcing. Concurrently, the study of the time dependent LNs shows that α regulates the duration of the transient phase, while the remaining parameters set the value of elastic limit, and the rate at which  the fluid limit is reached. Finally, some examples concerning the tidal deformations of the Moon are presented to point out the relevance that the Andrade rheology assumes in this particular case.

How to cite: Consorzi, A., Melini, D., Gonzáles-Santander, J. L., and Spada, G.: Love numbers for an Andrade planet, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-8305, https://doi.org/10.5194/egusphere-egu24-8305, 2024.