Constraining Europa's ice shell thickness with fundamental mode surface wave dispersion

Strike‐slip faults on Europa may slide back and forth in response to diurnal tidal stresses, which could generate significant frictional heating near the surface. Previous shear heating models assumed fault sliding rates a priori, without showing how the sliding rate is connected to the resolved stresses acting on the fault. Here, I calculate the cyclic displacement along tidally driven faults. I use a Mohr‐Coulomb failure criterion to determine the frictional failure depth, which varies throughout the tidal cycle. The displacement on the fault is calculated assuming an elastic broken plate model. The magnitude of cyclic displacements along a fault depends upon the coefficient of friction and the shear modulus of the ice shell. If Europa's ice shell is weak, diurnal tidal stress can cause faults on Europa to slide back and forth by ~0.1 to 2 m each cycle. Such large amounts of cyclic slip may be enough to frictionally heat the ice and potentially produce near‐surface melting. If Europa's ice shell has the strength of intact ice, faults become less responsive to cyclic tidal stresses and would only slide 0.01 to 0.2 m per cycle.

During recent decades, data from space missions have provided strong evidence of deep liquid oceans underneath a thin outer icy crust on several moons of Jupiter, particularly Europa. But these observations have also raised many unanswered questions regarding the oceanic motions generated under the ice, or the mechanisms leading to the geological features observed on Europa. By means of direct numerical simulations of Europa's interior, we show here that Jupiter's magnetic field generates a retrograde oceanic jet at the equator, which may influence the global dynamics of Europa's ocean and contribute to the formation of some of its surface features by applying a unidirectional torque on Europa's ice shell.

Fracture penetration in planetary ice shells

IntroductionEnceladus exhibits several remarkable characteristics, including a unique cryovolcanic activity [1] accompanied by anomalous heat flux [2], large ice shell thickness variations [e.g., 3], and a complex geological history recorded on the surface [4]. These features result from a complex interplay of internal and external forces operating over various temporal scales. Here, our main objective is to provide a comprehensive synthesis of various processes affecting the stress state of the ice shell from tidal to geological time scales. We study the individual contributions and assess their relative importance. We focus on the eccentricity-driven diurnal stresses enhanced by frictional faults [5-6]  and the effect of viscoelasticity. On longer time scales, we assess the impact of non-synchronous rotation [7]. We also investigate the possible role of the long-term viscous flow [3] driven by gravitational instabilities due to the variable ice shell thickness.Model set-upTo achieve the objectives, we model the elastic or viscoelastic response of the ice shell with variable ice shell thickness with frictional faults to eccentricity tides and non-synchronous rotation. On long-time scales, we investigate the viscous flow resulting from the ice shell thickness variations [3]. In all cases, we employ FE method [8] in order to include the 3D character of the ice shell thickness variations and the presence of faults.Eccentricity tidesTo assess the stress associated with eccentricity tides, we account for variations in ice shell thickness and the presence of frictional faults. Considering the short time scale of 1.37 days and assuming a conductive temperature profile, we model the ice shell's rheology as elastic. The mechanical properties of the fault zone are approximated using a Mohr-Coulomb-type yield criterion [5]. During one orbital period, stress reaches up to 100 kPa in the vicinity of faults and for a low friction coefficient (Fig. 1). The stress regime changes from compressional to extensional and vice versa with depth mainly in the direction parallel to the faults due to the bending stresses. Due to nonlinear friction law, the response is coupled over various periods, effectively contributing to stresses on other time scales. In particular, the friction leads to the emergence of a background static stress in the model. The amplitude of the background stress increases with the friction coefficient and can become comparable to the diurnal component for high friction coefficients.Non-synchronous rotationThe stress associated with possible non-synchronous rotation (NSR) of Enceladus is examined, taking into account variations in the ice shell thickness. This analysis considers a time scale ranging from 0.01 to 1 million years (Myr) for the period of NSR, as indicated by Patthoff et al. [7]. In our study, we adopt a viscoelastic (Maxwell) rheology, where the viscosity follows an Arrhenius dependence on temperature. A conductive temperature profile is assumed to characterize the thermal dependence of the ice rheology. Our simulations predict that the stress induced by NSR can reach approximately 4 MPa, dominating in stress magnitude among the investigated mechanisms. Furthermore, due to viscoelastic relaxation on NSR periods, a low-stress layer develops near the bottom boundary in the region of decreased viscosity (Fig. 2). However, this layer's impact on surface stress is found to be limited across all studied cases (bottom viscosity ≥1014 Pas). These findings highlight the importance of considering non-synchronous rotation, if present, and its associated viscoelastic effects when evaluating stress dynamics in Enceladus' icy shell.Viscous flowWe quantify the flow and stress triggered by gravitational instabilities arising from uneven ice shell thickness [3]. On a geological time scale, we model the ice shell as a viscous fluid using the Boussinesq approximation while also incorporating the gravitational signal from the boundaries. We observe significant changes in the flow characteristics, transitioning from radial high-velocity flow (low viscosity contrast) to low-velocity tangential flow concentrated within a thin layer of low viscosity (high viscosity contrast). The maximum surface stress associated with the viscous flow is approximately 0.5 MPa (Fig. 3). Our results also emphasize the dependence of surface stress on the local ice shell thickness, with compressive stress associated with locally thin ice shells.SummaryOur findings suggest that non-synchronous rotation induces the most significant stress, up to approximately 4 MPa, while surface stress from viscous flow reaches around 0.5 MPa, with compressive regimes in areas of the thinnest ice shell. Eccentricity tides induce comparatively lower stress, peaking at around 100 kPa in the South Polar Terrain. Frictional faults contribute to background stress, influenced by rheological properties, with viscoelastic effects proving negligible. This comprehensive assessment sheds light on the complex dynamics shaping Enceladus' icy surface.AcknowledgementsThis study received funding from the Czech Science Foundation under project number 22-20388S. The computations were conducted at the IT4Innovations National Supercomputing Center (e-INFRA CZ, ID:90254).

Pits, domes, and small chaos on Europa's surface are quasi‐circular features a few to a few tens of kilometers in diameter. We examine if injection of water sills into Europa's ice shell and their subsequent evolution can induce successive surface deformations similar to the morphologies of these features. We study the dynamics of water spreading within the elastic part of the ice shell and show that the mechanical properties of ice exert a strong control on the lateral extent of the sill. At shallow depths, water makes room for itself by lifting the overlying ice layer and water weight promotes lateral spreading of the sill. In contrast, a deep sill bends the underlying elastic layer and its weight does not affect its spreading. In that case, the sill lateral extent is limited by the fracture toughness of ice and the sill can thicken substantially. After emplacement, cooling of the sill warms the surrounding ice and thins the overlying elastic ice layer. As a result, preexisting stresses in the elastic part of the ice shell increase locally to the point that they may disrupt the ice above the sill (small chaos). Disruption of the surface also allows for partial isostatic compensation of water weight, leading to a topographic depression at the surface (pit), of the order of ~102 m. Complete water solidification finally causes expansion of the initial sill volume and results in an uplifted topography (dome) of ~102m.

Heat flow, lenticulae spacing, and possibility of convection in the ice shell of europa

Ground-based spectroscopy of Jupiter's moon Europa, combined with gravity data, suggests that the satellite has an icy crust roughly 150 km thick and a rocky interior. In addition, images obtained by the Voyager spacecraft revealed that Europa's surface is crossed by numerous intersecting ridges and dark bands (called lineae) and is sparsely cratered, indicating that the terrain is probably significantly younger than that of Ganymede and Callisto. It has been suggested that Europa's thin outer ice shell might be separated from the moon's silicate interior by a liquid water layer, delayed or prevented from freezing by tidal heating; in this model, the lineae could be explained by repetitive tidal deformation of the outer ice shell. However, observational confirmation of a subsurface ocean was largely frustrated by the low resolution (>2 km per pixel) of the Voyager images. Here we present high-resolution (54 m per pixel) Galileo spacecraft images of Europa, in which we find evidence for mobile 'icebergs'. The detailed morphology of the terrain strongly supports the presence of liquid water at shallow depths below the surface, either today or at some time in the past. Moreover, lower-resolution observations of much larger regions suggest that the phenomena reported here are widespread.

Large-scale dynamics and the fate of salts in Europa's icy shell

The icy satellites of the giant planets Jupiter and Saturn are among the most interesting celestial bodies in our Solar System. The interpretation of various remote sensing observations performed by the Voyager, Galileo and Cassini-Huygens missions strongly suggests that many icy satellites harbor a subsurface water ocean underneath the ice shell covering the satellites. Since the availability of liquid water is one of the prerequisites for the origin and evolution of life as we know it, the characterization of the physical properties of the putative subsurface oceans (and the overlying ice shells) has become a key research topic in planetary sciences. Due to the unavailability of direct means to explore these internal oceans, the relevant physical properties of the interior need to be derived from the combined interpretation of remote sensing measurements of observables such as the strength of the induced magnetic field, the amplitude of tidal deformations, the strength of gravity perturbations due to tides and the amplitude of forced longitudinal librations. This dissertation concentrates on the development of a unified and self-consistent physical model to determine the tidal and rotational response of a viscoelastic icy satellite with an internal water ocean. The developed tidal-rotational model is then applied to analyze the relation between the aforementioned observables (with the exception of the induced magnetic field) and the physical properties that characterize the internal structure of an icy satellite. The results in this thesis strongly suggest that the measurement of the libration amplitude of Europa’s shell with an accuracy of a few meters has the potential to provide a reasonable constraint on the rigidity of the ice-I shell in combination with measurements of the tidal response (Love numbers) at the surface. However, the modelling presented here is not extensive enough to support a strong conclusion regarding whether the ice shell thickness could be inferred from combined measurements of the libration amplitude and tidal Love numbers at the surface of Europa.

Europa, the most visibly active icy moon of Jupiter, is a prime target for the search for life in the outer solar system. Two spacecraft missions, Europa Clipper from the National Aeronautics and Space Administration (NASA) and the Jupiter Icy Moon Explorer (JUICE) from the European Space Agency (ESA), will observe its surface, probe its interior structure, and characterize the space environment starting in 2030. Occasional eruptions of water sourced from Europa’s interior may provide a window on the interior conditions and habitability of the moon. Here, we investigate the storage and evolution of briny water in Europa’s ice shell and propose a framework to interpret spectral, thermal, radar and gravity data collected by future missions. We show that it is possible to discriminate between water erupting from the deep ocean or from shallow liquid reservoirs using combined measurements of the material’s salinity, surface temperature and ice shell thickness.

The ice shell on Enceladus, an icy moon of Saturn, exhibits strong asymmetry between the northern and southern hemispheres, with all known geysers concentrated over the south pole, even though the expected pattern of tidal forced deformation should be symmetric between the north and south poles. Using an idealized ice-evolution model, we demonstrate that this asymmetry may form spontaneously, without any noticeable a priori asymmetry (such as a giant impact or a monopole structure of geological activity), in contrast to previous studies. Infinitesimal asymmetry in the ice shell thickness due to random perturbations are found to be able to grow indefinitely, ending up significantly thinning the ice shell at one of the poles, thereby allowing fracture formation there. Necessary conditions to trigger this hemispheric symmetry-breaking mechanism are found analytically. A rule of thumb we find is that, for Galilean and Saturnian icy moons, the ice shell can undergo hemispheric symmetry breaking only if the mean shell thickness is around 10 to 30 km.

Craters are probes of planetary surface and interior properties. Here we measure depths, widths, and spacing of circumferential ring‐graben surrounding the two largest multiring impact structures on Europa, Tyre and Callanish. We estimate formation conditions including the ice shell structure. The radial extension necessary to form these graben is thought to be caused by asthenospheric drag of warmer, more ductile ice and/or water flowing toward the excavated center of the crater, under a brittle‐elastic lithospheric lid. Measurements of graben depths from stereo‐photoclinometric digital elevation models result in estimates of displacement, strain, and stress experienced by the ice shell. Graben widths are used to estimate the intersection depth of the bounding normal faults, a quantity related to the brittle‐ductile transition depth that approximates elastic shell thickness during crater collapse. Heat flows at the time of crater formation as well as ice lithosphere and total shell thickness are thus also constrained. Average widths and depths tend to decrease with increasing distance from the structure center, while inter‐graben spacing generally increases. Varied assumptions yield plausible total conductive ice shell thickness estimates between 4–8 and 2.5–5 km for Tyre and Callanish, respectively, and heat flows of ∼70–115 (±30) mW m−2 for realistic thermal conductivities, consistent with other geophysical estimates for Europa. Higher heat flows are consistent with thin (≲10 km), conductive ice shells and impact breaching, or penetration of the stagnant lid for a convecting ice shell. Callanish, geologically younger, formed in a time or region of greater heat flow than Tyre.

Messungen der Planetengezeiten erlauben es, wichtige Rückschlüsse auf die innere Struktur und damit die Entstehung und thermale Entwicklung von Planeten und Monden zu ziehen. Die Gezeiten-Lovezahl h2 beschreibt die radiale Oberflächenverformung durch Gezeiten. Auf dem Planeten Merkur würde eine erfolgreiche Messung von h2 die Existenz eines möglichen festen inneren Kerns beweisen und dabei helfen, seine Größe zu bestimmen. Auf Jupiters Mond Ganymed erlaubt h2 es, Rückschlüsse auf die Dicke der äußeren Eisschale zu ziehen, falls ein unterirdischer Ozean existiert. In dieser Dissertation wird eine Methode zur Bestimmung von h2 aus globalen Laseraltimetrie-Datensätzen vorgestellt. Anders als frühere Arbeiten, die die radiale zeitliche Verformung an Kreuzungspunkten bestimmten, wendet diese Methode einen globalen Ansatz an, in dem gleichzeitig für die Verformung und die globale zeitunabhängige Topografie, die mithilfe von zweidimensionalen kubischen B-Splines auf einem Plattkartengitter dargestellt wird, gelöst wird. Der erste Schritt ist eine Validierung der Methode durch eine Anwendung auf den Mond. Auf dem Mond verursachen Gezeitenkräfte eine radiale Verformung mit einem maximalen Spitze-Tal-Wert von ungefähr 25 cm, womit ihre Detektion eine große Herausforderung darstellt. Das Lunar Orbiter Laser Altimeter auf der Raumsonde Lunar Reconnaissance Orbiter hat über 7 Milliarden Entfernungsmessungen aufgenommen. Das erhaltene Ergebnis für h2 stimmt gut mit dem einer früheren Arbeit überein, wodurch die Methode validiert wird. Der zweite Schritt ist die Berechnung der erwarteten Genauigkeit der Bestimmung des h2-Werts vom Merkur durch die BepiColombo-Mission. Die Analyse unabhängiger synthetischer Datensätze des BepiColombo Laser Altimeters führt zu einer Kenngröße für die Genauigkeit von h2. Das Experiment berücksichtigt Fehler, die durch die unbekannten Eigenschaften der Merkurtopografie, die Leistung und Fehlausrichtung des Instruments, die Orbitbestimmung und Ungenauigkeiten in Merkurs Rotationsmodell verursacht werden. Die Detektion eines festen inneren Kerns ist unter allen Fehlerszenarien möglich. Im Falle optimistischer Fehlerszenarien ist es außerdem möglich, seine Größe mit einer Genauigkeit von ungefähr 150 km zu bestimmen, wenn der Kern größer als 800 km ist. Die Hauptfehlerquellen sind die kleinskalige Merkurtopografie und die Fehlausrichtung des Instruments. Eine weitere Anwendung der Methode ist die Bestimmung von Größen, die die planetare Rotation und Librationen beschreiben. Im Falle von Ganymed wird eine gemeinsame Bestimmung von h2 und den Amplituden ausgewählter Librationen unter Verwendung von Daten, die vom Ganymede Laser Altimeter auf der Raumsonde Jupiter Icy Moons Explorer aufgenommen werden, es erlauben, hinreichend starke Rückschlüsse auf diese Parameter zu ziehen, um die Existenz eines unterirdischen Ozeans zu beweisen, und wertvolle Einblicke in die Eigenschaften der äußeren Eisschale liefern. Eine zukünftige Anwendung der in dieser Dissertation vorgestellten Methode auf Daten, die die Raumfahrtmissionen BepiColombo und Jupiter Icy Moons Explorer aufnehmen werden, wird signifikant zu unserem geophysikalischen Verständnis von Merkur und Ganymed beitragen.

Enceladus's ice shell structure as a window on internal heat production

We investigate the effects of methane clathrates on Titan’s thermal and seismic structure. The Dragonfly mission is planned to arrive at Titan in 2033 with a payload that includes a seismic package. The seismic instruments are tasked with recording seismic events and recovering the internal structure. Here, we explore whether differences in thermal and seismic profiles between a pure water ice shell and an ice shell with a clathrate lid could be detectable with seismic instrumentation. Due to their lower thermal conductivity, clathrates reduce the conductive lid thickness thus altering the thermal profile. The differences between seismic velocities of clathrates and pure water ice, coupled with changes in the thermal profile, indicate the clathrate lid will create lower seismic velocities, particularly for the upper 10 km of the surface ice shell. The differences in P and S velocity at the surface are 2.9% and 4.5%, respectively, and reach up to 8.4% (for both P and S) at a depth of 9.6 km. Due to changes in thermal profile, the seismic attenuation of the ice shell will change such that clathrates will suppress surface wave amplitudes relative to the pure water ice model. The clathrate lid will further create minor changes (≤2.0%) in the surface wave dispersion curves. Dragonfly, or other future seismic investigations, could provide evidence for or against the presence of a clathrate lid by constraining the thermal and seismic profile of Titan’s ice shell, by measuring the relative amplitudes of the surface to body waves, or by constraining the surface wave dispersion with high accuracy and precision.