Geoid Anomalies Research Articles

Crustal and tectonic structure of Northern Mozambique inferred by 2D gravity modeling

The northern region of Mozambique has a complex geological history, with an evolution that spans from the Precambrian Era to the Phanerozoic Era. In this work, we have integrated gravity and geothermal data to delineate the geotectonic evolution of the region, by estimating the thickness of the crust and the lithosphere through which was essential to generate a representative crustal model. It was necessary to complement the knowledge of structural geometry and tectonic evolution of the region. The data used in this study are the Bouguer and geoid anomalies, topography data, and radiogenic heat. These data were pre-processed, topography and geoid anomaly data were filtered by low-pass filter in the frequency and harmonic domains to remove undesirable effects associated with the sources. The data were used to estimate the thickness of the crust and lithosphere, as well as to determine the mean density distribution within the mantle. This was achieved by using a one-dimensional approach, considering the principle of local isostatic compensation, associated with equations governing the distribution of temperature in the crust. The Bouguer anomaly was used to generate a representative crustal 2D model of this region. The results showed that the crust is thinner in Nampula and Cabo Delgado provinces, with thickness ranging from 27 to 31 km, whereas in Niassa varies between 33 and 39 km. The analysis of lithospheric thickness indicates that the provinces of Nampula and Cabo Delgado present a thinning of the lithosphere, with values ranging from 150 to 165 km. Rather than Niassa province which exhibits a thicker lithosphere, ranging from 165 to 195 km. The obtained results underwent a comparative analysis with prior investigations, unveiling a noteworthy concurrence among these findings.

Lithospheric Structure and Extensional Style of the Red Sea Rift Segments

Abstract The Red Sea provides an opportunity to study the processes during the transition from continental rifting to early-stage seafloor spreading during ocean initiation. We delineate variations of lithospheric architecture and the nature of extension along the Red Sea region through joint interpretation of gravity and geoid anomalies and gravity-topography transfer functions. We use lithospheric-scale models to compare stretching factors with upper mantle gravity anomaly, residual mantle Bouguer anomaly, and effective elastic thickness. Based on our observations, the Red Sea is divided into four segments; each having distinct lithospheric characteristics and stretching styles. These are: (i) southernmost Red Sea and Danakil having regionally weak and stretched lithosphere, (ii) southern Red Sea with fully developed seafloor spreading and asymmetric lithospheric architecture, (iii) central Red Sea having discontinuous magma accretion with newly formed seafloor spreading, and (iv) northern Red sea with a stronger lithosphere and limited stretching revealing a stage of continental rifting. In these segments, lithospheric stretching correlates with regions of weak lithosphere, including a regime of sublithospheric plume channel beneath the southern Red Sea. The Zabargad fracture zone between the central and northern segments is revealed as a major lithosphere-scale boundary that may act as a barrier to the propagation of seafloor spreading into the northern Red Sea. The weak and highly stretched lithosphere in this region may indicate the onset of a new spreading cell. Our results conclude that the evolution of the Red Sea is more complex than the previously suggested kinematic models of simple “unzipping” and illustrate that several extensional styles can exist within different segments during the initial stages of ocean formation.

Deep genesis of the high heat flow anomaly in the Okinawa Trough

The Okinawa Trough (OT) is characterized by high heat flow anomalies up to 10,000 mW/m2 (especially in the middle area), which is rarely seen in heat flow research all over the world. The genesis of the high heat flow anomaly is probably related to mantle upwelling. However, the deep genesis is yet to be studied. We used heat flow values collected from the Global Heat Flow Database to calibrate the locations of high heat flow anomalies. Gravity data were used to calculate the residual geoid and interlayer geoid anomalies, which can help in characterizing the morphology of mantle upwelling beneath the OT. Earthquake hypocenter distribution maps were presented to show the position of the Philippine Sea Plate beneath the OT. According to P-wave tomography profile and previous research, we discussed the deep genesis of the high heat flow anomaly and proposed a preliminary model to explain the process. We suggest that the deep mantle upwelling, probably from a depth of −1200 km, enters the upper mantle through the front of the subducted Pacific plate. The deep mantle upwelling converges with the molten mantle flow caused by the fluid from the dehydration of the Pacific Plate and the Philippine Sea Plate. Two mantle upwelling branches were revealed to feed the southern OT (SOT) and Changbai Volcano, and the mantle upwelling under the middle OT (MOT) was the second branch from the mantle upwelling branch under the SOT. The MOT should be more influenced by mantle upwelling from deep sources with extremely high temperatures.

How the Indian Ocean Geoid Low Was Formed

AbstractThe origin of the Earth's lowest geoid, the Indian Ocean geoid low (IOGL) has been controversial. The geoid predicted from present‐day tomography models has shown that mid to upper mantle hot anomalies are integral in generating the IOGL. Here we assimilate plate reconstruction in global mantle convection models starting from 140 Ma and show that sinking Tethyan slabs perturbed the African Large Low Shear Velocity province and generated plumes beneath the Indian Ocean, which led to the formation of this negative geoid anomaly. We also show that this low can be reproduced by surrounding mantle density anomalies, without having them present directly beneath the geoid low. We tune the density and viscosity of thermochemical piles at core‐mantle boundary, Clapeyron slope and density jump at 660 km discontinuity, and the strength of slabs, to control the rise of plumes, which in turn determine the shape and amplitude of the geoid low.

Mantle compositional structure and dynamics of the Arabia-Eurasia collision zone: Insights from integrated thermochemical modelling

The tectonic evolution of the Arabia-Eurasia collision zone is enigmatic due to our poor knowledge of the compositional structure of the Zagros keel and the sub-lithospheric mantle beneath the Iranian plateau. Here, we present a thermochemical model for the upper mantle, starting from the Arabian plate toward the Zagros keel (in SW Iran) and the Iranian plateau to the Kopet Dagh Mountains in NE Iran. The crustal and (sub) lithospheric mantle structure is constrained using receiver functions and high-resolution seismic tomography. The crustal density is obtained by converting local Vp velocity profiles to density. The presumed mantle composition/density of different tectonic units has been inferred from the composition of mantle-derived xenoliths in Pleistocene alkaline basalts of NE Iran, mantle xenoliths from Eastern Arabia, and integrated geophysical-petrological modeling of seismic tomography as well as Bouguer and geoid anomalies. Our results indicate that the lower part of the lithosphere in the Arabian plate is ∼ +25 kg/m3 denser than the sub-lithospheric mantle, which allows underthrusting of the Arabian lithosphere beneath the Iranian plateau. The Zagros core–an ultra-positive seismic velocity anomaly in the tomographic models– is modeled assuming a refractory “craton-like” composition, leading to a ∼-60 kg/m3 density contrast with its underlying fertile lithospheric mantle. We hypothesize that at least the upper ∼100 km of the hydrous Arabian lithosphere was compositionally cratonic before the collision-related shortening processes. In contrast, the anhydrous Iranian lithosphere has been refertilized during asthenosphere upwelling and mantle flows. The Iranian plateau is underlain by a cold sub-lithospheric body characterized by ∼ +25 kg/m3 density contrast with respect to the ambient asthenosphere.

Geodynamic, geodetic, and seismic constraints favour deflated and dense-cored LLVPs

Two continent-sized features in the deep mantle, the large low-velocity provinces (LLVPs), influence Earth's supercontinent cycles, mantle plume generation, and geochemical budget. Seismological advances have steadily improved LLVP imaging, but several fundamental questions remain unanswered, including: What is the true vertical extent of the buoyancy anomalies within these regions? And, are they purely thermal features, or are they also compositionally distinct? Here, we address these questions using a comprehensive range of geophysical observations. The relationship between measured geoid anomalies and long-wavelength dynamic surface topography places an important upper limit on the vertical extent of large-scale, LLVP-related density anomalies at ∼900 km above the core-mantle boundary (CMB). Instantaneous mantle flow modelling suggests that anomalously dense material must exist at their base to simultaneously reproduce geoid, dynamic topography, and CMB ellipticity observations. We demonstrate that models incorporating this dense basal layer are consistent with independent measurements of semi-diurnal Earth tides and Stoneley mode splitting functions. Our thermodynamic calculations indicate that the presence of early-formed, chondrite-enriched basalt in the deepest 100–200 km of the LLVPs is most compatible with these geodynamic, geodetic, and seismological constraints. By reconciling these disparate datasets for the first time, our results demonstrate that, although LLVPs are dominantly thermal structures, their basal sections likely represent a primitive chemical reservoir that is periodically tapped by upwelling mantle plumes.

Surface wave phase velocity variations underneath the Indian Ocean geoid low

The Indian plate has undergone a long tectonic journey since its separation from the Gondwanaland. Its protracted rift-drift motion has rendered several enigmatic features in the Indian Ocean. One such feature is the large geoid deficit (−106 m), observed in the south of Sri Lanka that is known as the Indian Ocean geoid low (IOGL). A broad consensus about plausible explanations behind the IOGL anomaly still remains elusive. For the first time, 17 Ocean Bottom Seismometers (OBSs) were deployed in the IOGL region to characterize the subsurface structural variations. Here, we examine the inter-station Rayleigh wave phase velocity variations within the period range of 15–197 s. We construct 1-D velocity-depth sections down to c.a.380 km or less along with N-S and E-W profiles, using ≥5.2 magnitudes (Mw) earthquake data that occurred at a depth ≤ 100 km at regional/teleseismic distances. Our result demarcates the regional Moho depths varying from c.a.11.6 ± 0.8 km to c.a.19.8 ± 1.2 km along the OBS array from south to north respectively. A thickened oceanic crust (c.a.9–10 km) is attributed to magmatic underplating in the lower crust near the aseismic Comorin ridge. The lithospheric thickness ranges between c.a.47.6 ± 2.9 km and c.a. 75.1 ± 3.6 km along a south-north profile. We observe a c.a. 20–23 km thick lithosphere-asthenosphere boundary (LAB). The depth interval between c.a.87 km and c.a. 280 km is characterized by a distinct low-velocity zone (LVZ). A thick LVZ appears to be associated with a thin lithosphere, which implies a hot thermal regime in the upper mantle. We envisage a possible connection of this hot thermal regime with the African LLSVP (large low shear velocity province) and/or a vertically deep mantle upwelling directly beneath the IOGL region. Our findings have significant implications for deciphering the possible causes behind the source of mantle upwelling, the large geoid anomaly and extensive lithospheric deformation across this region.

Correction: Effect of Mantle Viscosity Structures on Simulations of Geoid Anomalies in the Ross Sea Area

Correction: Effect of Mantle Viscosity Structures on Simulations of Geoid Anomalies in the Ross Sea Area

Effect of Mantle Viscosity Structures on Simulations of Geoid Anomalies in the Ross Sea Area

Effect of Mantle Viscosity Structures on Simulations of Geoid Anomalies in the Ross Sea Area

Strong influence of tomographic models on geoid prediction: Case studies from Indian Ocean and Ross Sea geoids

The geoid over the north Indian Ocean has a significantly large negative amplitude, even if the excess flattening of the Earth beyond its equilibrium shape is considered. The various mechanisms proposed for this geoid anomaly vary and acceptable geoid predictions are obtained for specific tomographic models only. In this study, we identified model-independent features in the mantle beneath the Indian Ocean and Ross Sea region by analyzing eight recent global tomographic models. We standardized each of the models and applied cluster analysis to regionalize geophysically significant features in various depth ranges. These regionalizations are compared grid-by-grid to construct vote-maps. They highlight the anomalous features consistent across models and their approximate dimensions. Low velocity anomalies of dVS ∼-1.1% in the ∼400–680 km depth range are consistent in almost all the models beneath the Indian Ocean and Ross Sea. High velocity anomalies of dVS≥1% at depths below 1600 km, incoherent in dimension and orientation, are also observed. High velocity anomalies are most likely subducted slabs while low velocity anomalies could be partial melts generated by hydration of mantle. Additionally, a consistent low velocity structure is seen throughout the mantle beneath the southwestern Indian Ocean and east Africa. It is mostly likely a plume rising from the African LLSVP. It connects to the probable partial melts beneath the Indian Ocean via a remnant trail. Forward modelling of the geoid using vote-maps reveals that the E-W extent of the Indian Ocean Geoid Low is precisely reproduced by the consistent low velocity anomalies in the upper mantle. However, the N-S extent, most likely dependent on lower mantle anomalies, is not expressed since the dimension, orientation and dVS characteristics of high velocity structures are inconsistent in different models. The inter-model agreement is insufficient to identify structure(s) seen across models that can explain the geoid low over the Ross Sea.

Уточнение глобальной модели геоида по данным GPS и нивелирования для территории Ферганской долины

The Republic of Uzbekistan currently uses the Baltic normal system of heights associated with the quasi-geoid surface. The introduction of innovative technologies of global navigation satellite systems (GNSS) made it possible to determine with high accuracy the geometric heights related to the Earth model — an ellipsoid. For a complex representation of spatial data and analysis of information about the territory, natural resources, man-made objects, their dynamics in the National Geographic Information System (NGIS), first of all, it is necessary to solve the problem of refining the reference vertical coordinate system and ensuring its connection with the global ones, namely, to ensure adjustment of these two height systems. The task is complicated by the fact that for the territory of the country there is no information about the quasi-geoid determined by modern methods, which are necessary for the transition from geometric ellipsoidal heights obtained using GPS measurements to normal heights which are used for solving a wide range of practical problems in various fields of environmental sciences. In recent years, global geopotential models of the Earth (GGM) calculated using various satellite missions has become an alternative solution to the problem. The study considers two high order GGMs (EGM2008 and GECO) to create a system of normal heights for the territory of the Fergana Valley. The height anomaly values for them reach the maximum for the region — about −49 m. The method of constructing parametric models (or corrective surfaces) using leveling and GPS measurements at “common points” was used to refine them. The range of corrections made was from −0.28 m to 0.29 m. Moreover, the GECO model was significantly improved compared to EGM2008 in the flatland part of the study area, which has large geoid anomalies. The Krasovsky ellipsoid and the corresponding Baltic height system were chosen as a reference surface to create in the future a grid for converting heights between local and geocentric coordinate systems. The results of a comprehensive statistical analysis made it possible to reveal that GECO gives a more accurate representation of the region’s relief and is recommended for solving practical problems in the Fergana Valley.

Do lower mantle slabs contribute in generating the Indian Ocean geoid low?

The Indian Ocean geoid low (IOGL) is one of the lowest geoid anomalies on Earth. Several theories have been proposed to explain this geoid low, including past subduction (Nerlich et al., 2016; Rao and Kumar, 2014), subduction coupled with low velocity anomalies in the upper mantle (Spasojevic et al., 2010) and hot, low density anomaly in the upper to mid mantle depths (Reiss et al., 2017; Ghosh et al., 2017). It was also argued by Ghosh et al. (2017) that subducted slabs in the lower mantle have minimal role to play in contributing to this geoid signal. We further investigate that claim here by looking at the geoid contributed from various processes (density vs dynamic topography) as well as by inspecting the contribution from different spherical harmonic degrees. Our current findings substantiate the earlier claim that lower mantle slabs indeed play a minimal role in creating this anomalous geoid low.

Crustal and upper mantle density structure below the Indian Ocean Geoid Low based on 3-D constrained potential field modelling: Inferences on causative sources

The Indian Ocean Geoid Low (IOGL) in the Central Indian Ocean is the largest geoid depression on the globe. Spectral decomposition of geoid anomalies reveals that a significant fraction (up to ~90%) of the IOGL is due to mass anomalies lying within the lower mantle (~ > 700 km). The crustal density structure and Moho depth variations obtained from 3-D gravity inversion along with the upper mantle density structure derived from SL2013sv tomographic model are used to compute the total geoid anomaly up to 700 km depth and compare it with degree-10 residual geoid anomaly map. Comparison of these two maps necessitated the presence of relatively shallow low- density sources within the upper mantle that were not resolved in the 3-D modelling. The presence of two anomalous sources: i) low S-wave velocities at the base of the LAB (4.4 km/s) and ii) an anomalous source of Vs = −1.0% at a depth of 320–400 km within the sub-lithospheric mantle observed in the tomographic model accounted for this difference. We model the geometry of these low-density anomalous bodies using 2-D joint gravity-geoid modelling, which reveals the total contribution of density structure up to the upper mantle depths (700 km) accounts for only 10% of the IOGL whereas the remaining part is primarily caused by mass anomalies in the lower mantle probably related to high-density subducted slabs or plume sources at the core-mantle boundary as proposed by earlier studies.

Comparison of along-track resolution of SARAL/AltiKa and ENVISAT-RA2 satellite altimeters over continental margins

ABSTRACT The objective of the present study is to systematically quantify the along-track resolution of Satellite for Argos and AltiKa (SARAL)/AltiKa and Environmental Satellite (ENVISAT)-RA2 altimeters over continental margins. Spectral coherence and power spectral density estimated from pairs of stacked (averaged) sea surface height (SSH) profiles from repeat tracks as a function of wave number are used to estimate along-track resolution and noise characteristics, respectively. The analyses were carried out along 96 SARAL/AltiKa and ENIVISAT-RA2 tracks covering continental margins of India, Gulf of Mexico, and South America. Our study clearly suggests that for all three sites the short-wavelength resolution of SARAL/AltiKa (15–18 km) is ~27–33% better than ENVISAT-RA2 (22–25 km) data. Variations in sediment thickness along the continental margins have significant influence in the along-track resolution of both altimeters. Strong geoid signals owing to thin sediments (0.1–0.3 km thick) along the South American margin provided higher resolution for both SARAL/AltiKa (15 km) and ENVISAT-RA2 (22 km) altimeters. Conversely, over the continental margins of India and Gulf of Mexico with huge sediment thickness (1–20 km), the resolution of SARAL/AltiKa and ENVISAT-RA2 drops to 18 and 25 km, respectively. We also observe that resolution of both altimeters is higher by 1–2 km for continental margins with narrow shelf. The present study has implications in the generation of high-resolution marine geoid and gravity anomalies using SARAL/AltiKa along with other altimeters.

Asthenospheric rheology beneath mainland China inferred from mantle flow simulation and shear-wave splitting measurements

Mantle rheology is an essential property to understand the dynamics and evolution of the Earth. Estimates of mantle viscosity date from Haskell's canonical estimate of 1021 Pa s. For the asthenosphere, as a mechanically weak layer beneath the lithosphere, estimates have varied over a large viscosity range from 4 × 1017 to 1 × 1022 Pa s. In this paper, we use global and regional tomography-based geodynamic models with lateral viscosity variations in both the lithosphere and the mantle to predict the asthenospheric flow field, then use D-Rex to calculate transverse isotropy axis which is taken as the proxy of the fast polarization direction of shear-wave splitting, and finally determine the asthensopheric viscosity beneath Mainland China under the constraints of seismic anisotropy examined by a shear-wave splitting technique. Our inference, 1.27–5.58 × 1020 Pa s, lies in the range of previous estimates, and is comparable to most global estimates inferred from global convection-related observables, glacial isostatic adjustment data, global long wavelength geoid anomalies or their combination, but slightly larger than asthenospheric viscosity in Africa (3.5 × 1019 Pa s) and global estimates (3–10 × 1019 Pa s) inferred from the shear-wave splitting measurements. These findings show asthenospheric viscosity inferred from shear-wave splitting data has a small spatial change (< one order of magnitude).

Gravity field of Sarmatia according to satellite data (model EIGEN-6S2) and its interpretation

The paper presents a brief overview of satellite observations of the CHAMP, GRACE and GOCE missions to study the Earth’s global gravity field, and the used mathematical apparatus in the form of an expansion of the geopotential in spherical harmonics. The application of satellite data in various fields of Earth Sciences is considered. As a basic global model of the Earth’s gravity field based on satellite data we used the EIGEN-6S2 model [Rudenko et al, 2014] that combines satellite mission data GRACE and GOCE, and also uses satellite data of LAGEOUS laser ranging. On its basis, the gravity field of Sarmatia was analyzed using the Free Air anomalies, Bouguer anomalies, the second radial derivative of the geopotential and the geoid heights. The geological units of Sarmatia and its surroundings are most clearly manifested in the Free Air anomalies and in the distribution of the second derivative of the geopotential, showing differences in the gravity field pattern of the Ukrainian Shield, the Voronezh Massif, and the Pripyat-Dnieper-Donets basin (PDDB) with characteristic anomalies of the general northwest strike. The continuation of the PDDB in a southeastern direction through the Karpinsky Swell to the northern part of the Caspian Sea confirms the existence of an extended ancient tectonic zone of the Sarmato-Turanian lineament. The geoid within Sarmatia shows in general a regional west-east gradient change from +40 m in the west to -10 m in the east. Such large-scale geoid changes are determined by the Sarmatia position between two global geoid anomalies — the maximum of the North Atlantic and the minimum of the Indian Ocean.

Constraints on Mantle Viscosity From Intermediate‐Wavelength Geoid Anomalies in Mantle Convection Models With Plate Motion History

AbstractThe Earth's long‐ and intermediate‐wavelength geoid anomalies are surface expressions of mantle convection and are sensitive to mantle viscosity. While previous studies of the geoid provide important constraints on the mantle radial viscosity variations, the mantle buoyancy in these studies, as derived from either seismic tomography or slab density models, may suffer significant uncertainties. In this study, we formulate 3‐D spherical mantle convection models with plate motion history since the Cretaceous that generate dynamically self‐consistent mantle thermal and buoyancy structures, and for the first time, use the dynamically generated slab structures and the observed geoid to place important constraints on the mantle viscosity. We found that non‐uniform weak plate margins and strong plate interiors are critical in reproducing the observed geoid and surface plate motion, especially the net lithosphere rotation (i.e., degree‐1 toroidal plate motion). In the best‐fit model, which leads to correlation of 0.61 between the modeled and observed geoid at degrees 4–12, the lower mantle viscosity is ∼1.3–2.5 × 1022 Pa⋅s and is ∼30 and ∼600–1,000 times higher than that in the transition zone and asthenosphere, respectively. Slab structures and the geoid are also strongly affected by slab strength, and the observations prefer moderately strong slabs that are ∼10–100 times stronger than the ambient mantle. Finally, a thin weak layer below the 670‐km phase change on a regional scale only in subduction zones produces stagnant slabs in the mantle transition zone as effectively as a weak layer on a global scale.

The topography of the Iberian Peninsula from integrated geophysical-petrological multi-data inversion

The topography of the Iberian Peninsula is characterized by the presence of Variscan and Alpine orogenic belts and foreland basins, but what sets it apart from the rest of Western Europe are the large elevated flat surfaces (700 m above sea-level on average) in its central parts. The origin and support of such high average topography, whether isostatic or dynamic in nature, is a matter of intense debate. To understand Iberian topography, it is key to have a reliable image of the present-day lithospheric thermochemical structure. So far, this structure remains poorly constrained, particularly at mantle level. The goal of this paper is to derive robust estimates of the thermal, compositional and density structure of the lithosphere beneath the Iberian Peninsula from an integrated geophysical-petrological probabilistic inversion of surface wave, elevation, geoid anomaly and heat flow data. Our inversion reveals an average lithospheric thickness of 80–100 km in the Iberian Peninsula with only moderate lateral variations. The most prominent lithospheric thickness change is a steep decrease from the central to the easternmost Pyrenees. The thinnest lithosphere in our models is found below the south-eastern Mediterranean margin (<80 km), overlapping with the Neogene Tallante-Cabo de Gata volcanic fields. The present-day thermochemical structure reveals a clear imprint of the geodynamic evolution of Iberia. Lithospheric thickness and, therefore, lithospheric geotherms are to a large extent related to Alpine Cenozoic compression and extension. The western Pyrenees and Iberian chains seem to have been affected by Mesozoic rifting processes that imprinted a fertile signature into the originally more refractory Variscan Iberian lithosphere. In the Betic domain to the south, the lithospheric thermochemical structure is likely conditioned by the ongoing Alboran subduction. Except for the Mediterranean margin, where we find evidence for moderate negative dynamic topography, most of the surface elevation in Iberia can be explained by lateral density contrasts associated with variations in crustal and lithospheric thickness and lithology.

Lithosphere Destabilization and Small‐Scale Convection Constrained From Geophysical Data and Analogical Models

AbstractThe destabilization of oceanic lithosphere by small scale convection at its base is important for providing a holistic picture of mantle/lithosphere coupling. We use three highly resolved tomography models to characterize the base of the oceanic lithosphere in the Pacific Ocean. Regions associated with abnormally thick lithosphere are associated with seafloor older than 100 Ma and are elongated parallel to the direction of present‐day Pacific plate motion. They are correlated with bathymetric lows and negative geoid anomalies (for l = 10–39 and l = 14–39), which can be accounted for by dynamic topography. They do not correlate with volcanic features. We interpret these regions of thickened lithosphere as evidence for sites of lithospheric instabilities where denser lithosphere detaches and sinks into the underlying mantle. To understand the phenomena at the origin of these lithospheric “drips,” we performed laboratory experiments. Fluids with different properties are heated from one side to generate a large‐scale convection and cooled from the top. This configuration results in the generation of small‐scale convection at the base of the upper cold thermal boundary layer. The experimental results show the existence of two possible structures: instabilities organized into longitudinal rolls, aligned in the direction of the large‐scale motion and 3D, time‐dependent cold plumes that drip from the base of the lithosphere and are sheared away by the large‐scale flow. The 3D plume morphology is similar to what we observe in tomography models. This provides insights into the phenomenology at the origin of the lithospheric drips observed in the geophysical data.

Isostasy with Love – I: elastic equilibrium

SUMMARY Isostasy explains why observed gravity anomalies are generally much weaker than what is expected from topography alone, and why planetary crusts can support high topography without breaking up. On Earth, it is used to subtract from gravity anomalies the contribution of nearly compensated surface topography. On icy moons and dwarf planets, it constrains the compensation depth which is identified with the thickness of the rigid layer above a soft layer or a global subsurface ocean. Classical isostasy, however, is not self-consistent, neglects internal stresses and geoid contributions to topographical support, and yields ambiguous predictions of geoid anomalies. Isostasy should instead be defined either by minimizing deviatoric elastic stresses within the silicate crust or icy shell, or by studying the dynamic response of the body in the long-time limit. In this paper, I implement the first option by formulating Airy isostatic equilibrium as the linear response of an elastic shell to a combination of surface and internal loads. Isostatic ratios are defined in terms of deviatoric Love numbers which quantify deviations with respect to a fluid state. The Love number approach separates the physics of isostasy from the technicalities of elastic-gravitational spherical deformations, and provides flexibility in the choice of the interior structure. Since elastic isostasy is invariant under a global rescaling of the shell shear modulus, it can be defined in the fluid shell limit, which is simpler and reveals the deep connection with the asymptotic state of dynamic isostasy. If the shell is homogeneous, minimum stress isostasy is dual to a variant of elastic isostasy called zero deflection isostasy, which is less physical but simpler to compute. Each isostatic model is combined with general boundary conditions applied at the surface and bottom of the shell, resulting in one-parameter isostatic families. At long wavelength, the thin shell limit is a good approximation, in which case the influence of boundary conditions disappears as all isostatic families members yield the same isostatic ratios. At short wavelength, topography is supported by shallow stresses so that Airy isostasy becomes similar to either pure top loading or pure bottom loading. The isostatic ratios of incompressible bodies with three homogeneous layers are given in analytical form in the text and in complementary software.