Isamu Matsuyama

Mars undergoes seasonal tidal forcing as a result of its eccentric orbit and the tilt of its rotation axis relative to the Sun ¹ . Response to this forcing produces temporal variations in the Martian gravity field and is sensitive to the internal structure of the planet ^2–4 . Using tracking data from the Mars Global Surveyor (MGS), Mars Odyssey (ODY) and Mars Reconnaissance Orbiter (MRO) spacecraft ^5–7 , we demonstrate that degree-3 components of the time-variable gravity field of Mars differ by up to 300% from predictions for a spherically symmetric planet ^8–10 . These deviations can be explained if the effective shear modulus of the mantle varies by >20% over a roughly north–south pattern that closely aligns with the surface expression of the Martian crustal dichotomy ¹¹ . On the basis of this correlation, we infer preservation of a 200–400 °C thermal anomaly in the present-day mantle below the southern highlands of Mars. This temperature variation could reflect regional mantle convection ^12,13 or insulation by the thick southern highlands crust of Mars that has persisted over several billion years ^14,15 .

The lunar nearside and farside exhibit striking geological and geophysical differences. Although a variety of mechanisms, including asymmetric crystallization, tidal heating, mantle overturn, and moonlet accretion, have been proposed to explain this dichotomy, its origin remains a fundamental and open question. The extent to which these asymmetries penetrate into the lunar interior likewise remains unresolved. Here we jointly invert the latest static and time-variable (tidal) gravity measurements to construct a three-dimensional tomographic model of the lunar mantle. We find that the nearside mantle is up to 1.5% denser and 4% less rigid than the farside, defining a hemispheric-scale interior compositional asymmetry that extends throughout the mantle rather than being confined to the crust and shallow interior as previously assumed. The inferred density and rigidity contrasts are most consistent with a nearside mantle that is comparatively iron-rich, warmer, and wetter than the farside, in agreement with geochemical constraints from the Chang'e-5 and Chang'e-6 sample return missions and surface heatflow measurements from Apollo 15 and 17 and Blue Ghost Mission 1. The thermochemical anomaly is strongest in the upper mantle and provides geophysical evidence that the Moon’s primordial differentiation generated a long-lived hemispheric mantle dichotomy through asymmetric magma-ocean crystallization and nearside sequestration of KREEP-rich cumulates through some degree of lunar magma ocean overturn. These results imply that relics of early lunar differentiation remain preserved throughout the present-day mantle and may also explain the Moon’s long-wavelength degree-2 gravity structure without requiring a fossil rotational–tidal bulge.

Introduction Tidal observations have provided crucial insight into the interior of various Solar System bodies; including Mercury (1), Venus (2), the Moon (3, 4), Mars (5, 6), Jupiter (7), Io (8) and Titan (9, 10). Previous efforts to characterize planetary interior structures using tides have focused on inferring one-dimensional (i.e., radial) structure. However, lateral variations in properties can induce patterns of tidal deformation that are distinct from those produced by radial structure, thus allowing for a 3D characterization of the interior through future detailed observations of time-varying gravity or shape.In a spherically symmetric body, the tidal response mirrors the wavelength of the tidal forcing. However, lateral heterogeneities cause mode coupling (i.e., interaction between forcing and response at mutually distinct harmonics). This wavelength-dependent variation in tidal deformation forms the basis of tidal tomography — a technique that seeks to constrain internal 3D structure by measuring the body's tidal response across different wavelengths (11–14).Here, we present the first application of tidal tomography beyond Earth, explore its potential use in ongoing missions, and advocate for its broader consideration in future planetary exploration efforts.First Uses of Tidal Tomography Beyond Earth Due to the high precision required to detect signals associated with 3D structure, tidal tomography had been applied only to the Earth (15). But, recently, a reanalysis of GRAIL Lunar gravity data has revealed a nearside/farside dichotomy in the Moon’s mantle from its unexpectedly large-amplitude degree three response, suggesting a ~100K thermal anomaly (16). While this constitutes the first application of this technique to an extraterrestrial body, more examples might soon follow. Juice’s 3GM instrument will be precise enough to unveil variations of Ganymede’s outer ice shell of a few percent its mean shell thickness (17). The effects of 3D tides might also be recorded on the surface of planetary bodies. The distribution of Io’s volcanoes might be indicative of tidal dissipation in a body with an asthenosphere with a laterally varying melt distribution (18). Future Applications of Tidal Tomography The first use of tidal tomography beyond Earth demonstrates the potential to map the three-dimensional interior structure of planetary bodies remotely. We argue that future missions should consider using tidal tomography to characterize 3D structures in planetary interiors. Enceladus is perhaps the clearest example. Static gravity and shape data hints at thickness variations in Enceladus’ crust (19, 20), which are expected to drive an exceptionally large-amplitude mode coupled tidal response for the body (12, 21, 22). Lateral variations in interior properties are the fingerprint of processes relevant to habitability (e.g., ocean circulation, the distribution of tidal heating). With the tiny Saturnian moon being one of the top priority planetary science targets for both ESA and NASA, tidal tomography should be considered in future Enceladan missions.Figure 1: Schematic representation of the tidal response of the Moon to various tidal components for a 1D and a 3D MoonReferences1. S. Padovan, J. L. Margot, S. A. Hauck, W. B. Moore, S. C. Solomon, J Geophys Res Planets. 119, 850–866 (2014).2. A. S. Konopliv, C. F. Yoder, Geophys Res Lett. 23, 1857–1860 (1996).3. I. Matsuyama et al., Geophys Res Lett. 43, 8365–8375 (2016).4. J. G. Williams et al., J Geophys Res Planets. 119, 1546–1578 (2014).5. C. F. Yoder, A. S. Konopliv, D. N. Yuan, E. M. Standish, W. M. Folkner, Science (1979). 300, 299–303 (2003).6. L. Pou et al., J Geophys Res Planets, in press, doi:https://doi.org/10.1029/2022JE007291.7. D. 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Vesta, the only differentiated rocky protoplanet explored by a spacecraft, offers insight into early planetary formation. The Divalia Fossae, surface troughs comparable in size to the Grand Canyon, encircle two-thirds of the equator. Two giant impacts reshaped the southern hemisphere, where an older basin is partially superposed by the younger Rheasilvia basin. The origin of the Divalia Fossae is widely accepted as directly linked to the Rheasilvia impact, either by tectonics caused immediately by the impact, up-spinning, or secondary cratering. We present several geologic constraints that support a tectonic origin of the troughs due to the adjustment of Vesta’s spin axis to a geoid changed by both large impacts. The best fit to Vesta’s gravitational field corresponds to a spin axis reorientation of 3° that, when coupled with despinning, induces a stress state that predicts Divalia Fossae’s established location, fracture type, and orientation. These insights underline the importance of tectonic processes in the early evolution of protoplanets.

Jupiter’s moon Io is a highly compelling target for future exploration that offers critical insight into tidal dissipation processes and the geology of high heat flux worlds, including primitive planetary bodies, such as the early Earth, that are shaped by enhanced rates of volcanism. Io is important for understanding the development of volcanogenic atmospheres and mass exchange within the Jupiter system. However, fundamental questions remain about the state of Io’s interior, surface, and atmosphere, as well as its role in the evolution of the Galilean satellites. The Io Volcano Observer (IVO) would advance answers to these questions by addressing three key goals: (A) determine how and where tidal heat is generated inside Io, (B) understand how tidal heat is transported to the surface of Io, and (C) understand how Io is evolving. IVO was selected for Phase A study through the NASA Discovery program in 2020, and, in anticipation of the next New Frontiers (NF) opportunity, an enhanced IVO-NF mission concept would increase the Baseline mission from 10 flybys to 20, with an improved radiation design; employ a Ka-band communication system to double IVO’s total data downlink; add a wide-angle camera for color and stereo mapping; add a dust mass spectrometer; and lower the altitude of later flybys to enable new science. This study compares the architecture, instrument suite, and science objectives for Discovery (IVO) and NF (IVO-NF) missions to Io. IVO can achieve outstanding science results at the Discovery level, but we advocate for continued prioritization of Io for NF.

The Moon undergoes periodic tidal forcing due to its eccentric and oblique orbit around the Earth¹. The response to this tidal interaction drives temporal changes in the lunar gravity field and is sensitive to the satellite’s internal structure^2–4. We use data from the NASA GRAIL spacecraft^5–9 to recover the time-varying lunar gravity field, including a degree-3 gravitational tidal Love number, k ₃. Here, we report our estimated value of k ₃ = 0.0163 ± 0.0007, which is about 72% higher than that expected for a spherically symmetric moon¹⁰. Such a large k ₃ can be explained if the elastic shear modulus of the mantle varies by about 2–3% between the nearside and farside⁴, providing an observational demonstration of lateral heterogeneities in the deep lunar interior. This asymmetric structure suggests preservation of a predominantly thermal anomaly of roughly 100–200 K in the nearside mantle that formed surface mare regions 3–4 billion years ago¹¹ and could influence the spatial distribution of deep moonquakes¹².

The Moon's frequency‐dependent tidal response, expressed as temporal variations in its gravity field through the Love number and as dissipation through the quality factor , provides information about its interior structure. Lunar laser ranging has provided measurements for , but so far no frequency‐dependent values for have been determined. We provide the first spacecraft measurements of and at two frequencies, monthly and yearly, from an analysis of Gravity Recovery and Interior Laboratory and Lunar Reconnaissance Orbiter radio tracking data. Interior modeling indicates that these values can be matched only with a low‐viscosity zone at the base of the lunar mantle, even when using complex rheological laws to model the mantle's response. The existence of this zone has profound implications for the Moon's thermal state and evolution.

Body tides reveal information about planetary interiors and affect their evolution. Most models to compute body tides rely on the assumption of a spherically symmetric interior. However, several processes can lead to lateral variations of interior properties. We present a new spectral method to compute the tidal response of laterally heterogeneous bodies. Compared to previous spectral methods, our approach is not limited to small-amplitude lateral variations; compared to finite element codes, this approach is more computationally efficient. While the tidal response of a spherically symmetric body has the same wavelength as the tidal force; lateral heterogeneities produce an additional tidal response with a spectra that depends on the spatial pattern of such variations. For Mercury, the Moon, and Io, the amplitude of this signal is as high as 1%–10% of the main tidal response for long-wavelength shear modulus variations higher than ∼10% of the mean shear modulus. For Europa, Ganymede, and Enceladus, shell-thickness variations of 50% of the mean shell thickness can cause an additional signal of ∼1% and ∼10% for the Jovian moons and Encelaudus, respectively. Future missions, such as BepiColombo and JUICE, might measure these signals. Lateral variations of viscosity affect the distribution of tidal heating. This can drive the thermal evolution of tidally active bodies and affect the distribution of active regions.

Several solar system moons harbor subsurface water oceans; extreme internal heating or solar irradiation can form magma oceans in terrestrial bodies. Tidal forces drive ocean currents, producing tidal heating that affects the thermal−orbital evolution of these worlds. If the outermost layers (ocean and overlying shell) are thin, tidal dynamics can be described using thin-shell theory. Previous work assumed that the ocean and shell's thickness and density are uniform. We present a formulation of thin-shell dynamics that relaxes these assumptions and apply it to several cases of interest. The tidal response of unstratified oceans of constant thickness is given by surface gravity and Rossby waves, which can resonate with the tidal force. The oceans of the outer solar system are too thick for gravity wave resonances, but high-amplitude Rossby waves can be excited in moons with high orbital obliquity. We find that meridional ocean thickness variations hinder the excitation of Rossby waves, decreasing tidal dissipation and increasing the inclination damping timescale, which allows us to reconcile the present inclination of the Moon with the existence of a past long-lived magma ocean and to explain the inclination of Titan and Callisto without invoking a recent excitation. Stratified oceans can support internal gravity waves. We show that dissipation due to internal waves can exceed that resulting from surface gravity waves. For Enceladus, it can be close to the moon’s thermal output, even if the ocean is weakly stratified. Shear due to internal waves can result in Kelvin–Helmholtz instabilities and induce ocean mixing.