Cenozoic India-Asia collision driven by mantle dragging the cratonic root

The driving force behind the Cenozoic India-Asia collision remains elusive. Using global-scale geodynamic modeling, we find that the continuous motion of the Indian plate is driven by a prominent upper-mantle flow pushing the thick Indian lithospheric root, originated from the northward rollover of the detached Neo-Tethyan slab and sinking slabs below East Asia. The maximum mantle drag occurs within the strong Indian lithosphere and is comparable in magnitude to that of slab pull (1013 N m-1). The thick cratonic root enhances both lithosphere-asthenosphere coupling and upper-plate compressional stress, thereby sustaining the topography of Tibetan Plateau. We show that the calculated resistant force from the India-Asia plate boundary is also close to that due to the gravitational potential energy of Tibetan Plateau. Here, we demonstrate that this mantle flow is key for the formation of the Tibetan Plateau and represents part of a hemispheric convergent flow pattern centered on central Asia.

The role of plume-lithosphere interaction in Hawaii-Emperor chain formation

Paleolatitudes of volcanic rocks reveal that prominent changes in volcanic trend of the Hawaii-Emperor hotspot chain represent meridional migration of the magma source. However, models assuming latitudinal plume migration fail to explain the observed age distribution, rock composition, and erratic paleolatitude changes of the oldest Emperor seamounts. Here we use data-assimilation models to better reproduce the Hawaii-Emperor hotspot track by systematically considering plate reconstruction, plume-lithosphere interaction, and simplified melt generation and migration. Our results show that plate drag and plume-ridge interaction are both important in explaining the observed seamount ages. These shallow dynamic processes could account for 50% of the observed paleolatitude's secular reduction and erratic variations over time, where the necessary southward migration of the Hawaiian plume root is significantly less than previously thought. We conclude that plume-lithosphere interaction represents a common mechanism in affecting hotspot track, and has important implications in understanding mantle dynamics and plate reference frames.

Western US intraplate deformation controlled by the complex lithospheric structure

The western United States is one of Earth's most tectonically active regions, characterized by extensive crustal deformation through intraplate earthquakes and geodetic motion. Such intracontinental deformation is usually ascribed to plate boundary forces, lithospheric body forces, and/or viscous drag from mantle flow. However, their relative importance in driving crustal deformation remains controversial due to inconsistent assumptions on crustal and mantle structures in prior estimations. Here, we utilize a fully dynamic three-dimensional modeling framework with data assimilation to simultaneously compute lithospheric and convective mantle dynamics within the western United States. This approach allows for quantitative estimations of crustal deformation while accounting for the realistic three-dimensional lithospheric structure. Our results show the critical role of the complex lithospheric structure in governing intraplate deformation. Particularly, the interaction between the asthenospheric flow and lithospheric thickness step along the eastern boundary of the Basin and Range represents a key driving mechanism for localized crustal deformation and seismicity.

Paleogene India-Eurasia collision constrained by observed plate rotation

The Cenozoic India-Eurasia collision has had profound impacts on shaping the Tibetan plateau, but its early history remains controversial due to uneven availability of constraints. Recent plate reconstructions reveal two prominent counterclockwise rotation (azimuthal change) rate peaks of the Indian plate at 52-44 and 33-20 Ma, respectively, which could bear key information about this collision history. Using fully dynamic three-dimensional numerical modeling, we show that the first rotation rate peak reflected the initial diachronous collision from the western-central to eastern Indian front, and the second peak reflected the full collision leading to strong coupling between India and Eurasia. Further comparison with observation suggests that the initial and complete India-Eurasia collision likely occurred at 55 ± 5 and 40 ± 5 Ma, respectively, an inference consistent with key geological observations. We suggest that this collision history is instructive for studying the tectonic history of the Tibetan plateau and its surrounding areas.

Influence of the asthenosphere on earth dynamics and evolution

The existence of a thin, weak asthenospheric layer beneath Earth's lithospheric plates is consistent with existing geological and geophysical constraints, including Pleistocene glacio-isostatic adjustment, modeling of gravity anomalies, studies of seismic anisotropy, and post-seismic rebound. Mantle convection models suggest that a pronounced weak zone beneath the upper thermal boundary layer (lithosphere) may be essential to the plate tectonic style of convection found on Earth. The asthenosphere is likely related to partial melting and the presence of water in the sub-lithospheric mantle, further implying that the long-term evolution of the Earth may be controlled by thermal regulation and volatile recycling that maintain a geotherm that approaches the wet mantle solidus at asthenospheric depths.

A South Pole-Aitken impact origin of the lunar compositional asymmetry

The formation of the largest and most ancient lunar impact basin, South Pole-Aitken (SPA), was a defining event in the Moon's evolution. Using numerical simulations, we show that widespread mantle heating from the SPA impact can catalyze the formation of the long-lived nearside-farside lunar asymmetry in incompatible elements and surface volcanic deposits, which has remained unexplained since its discovery in the Apollo era. The impact-induced heat drives hemisphere-scale mantle convection, which would sequester Th- and Ti-rich lunar magma ocean cumulates in the nearside hemisphere within a few hundred million years if they remain immediately beneath the lunar crust at the time of the SPA impact. A warm initial upper mantle facilitates generation of a pronounced compositional asymmetry consistent with the observed lunar asymmetry.

High 3He/4He in central Panama reveals a distal connection to the Galápagos plume

We report the discovery of anomalously high ³He/⁴He in “cold” geothermal fluids of central Panama, far from any active volcanoes. Combined with independent constraints from lava geochemistry, mantle source geochemical anomalies in Central America require a Galápagos plume contribution that is not derived from hotspot track recycling. Instead, these signals likely originate from large-scale transport of Galápagos plume material at sublithospheric depths. Mantle flow modeling and geophysical observations further indicate these geochemical anomalies could result from a Galápagos plume-influenced asthenospheric “mantle wind” that is actively “blowing” through a slab window beneath central Panama. The lateral transport of plume material represents a potentially widespread yet underappreciated mechanism that scatters enriched geochemical signatures in mantle domains far from plumes.

It is well established that mantle plumes are the main conduits for upwelling geochemically enriched material from Earth's deep interior. The fashion and extent to which lateral flow processes at shallow depths may disperse enriched mantle material far (>1,000 km) from vertical plume conduits, however, remain poorly constrained. Here, we report He and C isotope data from 65 hydrothermal fluids from the southern Central America Margin (CAM) which reveal strikingly high ³He/⁴He (up to 8.9R_A) in low-temperature (≤50 °C) geothermal springs of central Panama that are not associated with active volcanism. Following radiogenic correction, these data imply a mantle source ³He/⁴He >10.3R_A (and potentially up to 26R_A, similar to Galápagos hotspot lavas) markedly greater than the upper mantle range (8 ± 1R_A). Lava geochemistry (Pb isotopes, Nb/U, and Ce/Pb) and geophysical constraints show that high ³He/⁴He values in central Panama are likely derived from the infiltration of a Galápagos plume–like mantle through a slab window that opened ∼8 Mya. Two potential transport mechanisms can explain the connection between the Galápagos plume and the slab window: 1) sublithospheric transport of Galápagos plume material channeled by lithosphere thinning along the Panama Fracture Zone or 2) active upwelling of Galápagos plume material blown by a “mantle wind” toward the CAM. We present a model of global mantle flow that supports the second mechanism, whereby most of the eastward transport of Galápagos plume material occurs in the shallow asthenosphere. These findings underscore the potential for lateral mantle flow to transport mantle geochemical heterogeneities thousands of kilometers away from plume conduits.

Deep continental roots and cratons

The formation and preservation of cratons-the oldest parts of the continents, comprising over 60 per cent of the continental landmass-remains an enduring problem. Key to craton development is how and when the thick strong mantle roots that underlie these regions formed and evolved. Peridotite melting residues forming cratonic lithospheric roots mostly originated via relatively low-pressure melting and were subsequently transported to greater depth by thickening produced by lateral accretion and compression. The longest-lived cratons were assembled during Mesoarchean and Palaeoproterozoic times, creating the stable mantle roots 150 to 250 kilometres thick that are critical to preserving Earth's early continents and central to defining the cratons, although we extend the definition of cratons to include extensive regions of long-stable Mesoproterozoic crust also underpinned by thick lithospheric roots. The production of widespread thick and strong lithosphere via the process of orogenic thickening, possibly in several cycles, was fundamental to the eventual emergence of extensive continental landmasses-the cratons.

Plume-driven recratonization of deep continental lithospheric mantle

Cratons are Earth's ancient continental land masses that remain stable for billions of years. The mantle roots of cratons are renowned as being long-lived, stable features of Earth's continents, but there is also evidence of their disruption in the recent^1-6 and more distant^7-9 past. Despite periods of lithospheric thinning during the Proterozoic and Phanerozoic eons, the lithosphere beneath many cratons seems to always 'heal', returning to a thickness of 150 to 200 kilometres^10-12; similar lithospheric thicknesses are thought to have existed since Archaean times^3,13-15. Although numerous studies have focused on the mechanism for lithospheric destruction^2,5,13,16-19, the mechanisms that recratonize the lithosphere beneath cratons and thus sustain them are not well understood. Here we study kimberlite-borne mantle xenoliths and seismology across a transect of the cratonic lithosphere of Arctic Canada, which includes a region affected by the Mackenzie plume event 1.27 billion years ago²⁰. We demonstrate the important role of plume upwelling in the destruction and recratonization of roughly 200-kilometre-thick cratonic lithospheric mantle in the northern portion of the Slave craton. Using numerical modelling, we show how new, buoyant melt residues produced by the Mackenzie plume event are captured in a region of thinned lithosphere between two thick cratonic blocks. Our results identify a process by which cratons heal and return to their original lithospheric thickness after substantial disruption of their roots. This process may be widespread in the history of cratons and may contribute to how cratonic mantle becomes a patchwork of mantle peridotites of different age and origin.

Deep slab seismicity limited by rate of deformation in the transition zone

Deep earthquakes within subducting tectonic plates (slabs) are enigmatic because they appear similar to shallow earthquakes but must occur by a different mechanism. Previous attempts to explain the depth distribution of deep earthquakes in terms of the temperature at which possible triggering mechanisms are viable, fail to explain the spatial variability in seismicity. In addition to thermal constraints, proposed failure mechanisms for deep earthquakes all require that sufficient strain accumulates in the slab at a relatively high stress. Here, I show that simulations of subduction with nonlinear rheology and compositionally dependent phase transitions exhibit strongly variable strain rates in space and time, which is similar to observed seismicity. Therefore, in addition to temperature, variations in strain rate may explain why there are large gaps in deep seismicity (low strain rate), and variable peaks in seismicity (bending regions), and, possibly, why there is an abrupt cessation of seismicity below 660 km.

Influence of the Thickness of the Overriding Plate on Convergence Zone Dynamics

The important role played by the upper plate in convergence zones dynamics has long been underestimated but is now more and more emphasized. However, the influence of its thickness and/or strength on orogenic systems evolution remains largely unknown. Here we present results from 3D thermo-mechanical numerical simulations of convergence zones (including oceanic subduction followed by continental subduction/collision), in which we vary the rheological profile of the overriding plate (OP). For this, we systematically modify the crustal thickness of the overriding lithosphere and the temperature at the Moho to obtain a thermal thickness of the overriding lithosphere ranging from 80 to 180 km. While all models share a common global evolution (i.e., slab sinking, interaction between slab and the 660 km discontinuity, continental subduction/collision, and slab breakoff), they also highlight first-order differences arising from the variations in the OP strength (thermal thickness). With a thin/weak OP, slab rollback is favored, the slab dip is low, the mantle flow above the slab is vigorous, and the trench migrates at a high rate compared to a thick/strong OP. In addition, slab breakoff and back-arc basin formation events occur significantly earlier than in models involving a thick OP. Our models therefore highlight the major role played by the thickness/strength of the OP on convergence zone dynamics and illustrate its influence in a quantitative way.

The Role of Crustal Buoyancy in the Generation and Emplacement of Magmatism During Continental Collision

During continental collision, considerable amounts of buoyant continental crust subduct to depth and subsequently exhume. Whether various exhumation paths contribute to contrasting styles of magmatism across modern collision zones is unclear. Here we present 2D thermomechanical models of continental collision combined with petrological databases to investigate the effect of the main contrasting buoyancy forces, in the form of continental crustal buoyancy versus oceanic slab age (i.e., its thickness). We specifically focus on the consequences for crustal exhumation mechanisms and magmatism. Results indicate that it is mainly crustal density that determines the degree of steepening of the subducting continent and separates the models' parameter space into two regimes. In the first regime, high buoyancy values (∆ρ > 500 kg/m3) steepen the slab most rapidly (to 45-58°), leading to opening of a gap in the subduction channel through which the subducted crust exhumes ("subduction channel crustal exhumation"). A shift to a second regime ("underplating") occurs when the density contrast is reduced by 50 kg/m3. In this scenario, the slab steepens less (to 37-50°), forcing subducted crust to be placed below the overriding plate. Importantly, the magmatism changes in the two cases: Crustal exhumation through the subduction channel is mainly accompanied by a narrow band of mantle melts, while underplating leads to widespread melting of mixed sources. Finally, we suggest that the amount (or density) of subducted continental crust, and the resulting buoyancy forces, could contribute to contrasting collision styles and magmatism in the Alps and Himalayas/Tibet.

Strong plates enhance mantle mixing in early Earth

In the present-day Earth, some subducting plates (slabs) are flattening above the upper–lower mantle boundary at ~670 km depth, whereas others go through, indicating a mode between layered and whole-mantle convection. Previous models predicted that in a few hundred degree hotter early Earth, convection was likely more layered due to dominant slab stagnation. In self-consistent numerical models where slabs have a plate-like rheology, strong slabs and mobile plate boundaries favour stagnation for old and penetration for young slabs, as observed today. Here we show that such models predict slabs would have penetrated into the lower mantle more easily in a hotter Earth, when a weaker asthenosphere and decreased plate density and strength resulted in subduction almost without trench retreat. Thus, heat and material transport in the Earth’s mantle was more (rather than less) efficient in the past, which better matches the thermal evolution of the Earth.

The subducting plates can either penetrate straight into the lower mantle or flatten in the mantle transition zone, yet slab dynamics in the past remains unclear. Here, using subduction models, the authors predict that a hotter early Earth was probably more favourable to lower mantle slab penetration.

Western US intermountain seismicity caused by changes in upper mantle flow

Understanding the causes of intraplate earthquakes is challenging, as it requires extending plate tectonic theory to the dynamics of continental deformation. Seismicity in the western United States away from the plate boundary is clustered along a meandering, north-south trending 'intermountain' belt. This zone coincides with a transition from thin, actively deforming to thicker, less tectonically active crust and lithosphere. Although such structural gradients have been invoked to explain seismicity localization, the underlying cause of seismicity remains unclear. Here we show results from improved mantle flow models that reveal a relationship between seismicity and the rate change of 'dynamic topography' (that is, vertical normal stress from mantle flow). The associated predictive skill is greater than that of any of the other forcings we examined. We suggest that active mantle flow is a major contributor to seismogenic intraplate deformation, while gravitational potential energy variations have a minor role. Seismicity localization should occur where convective changes in vertical normal stress are modulated by lithospheric strength heterogeneities. Our results on deformation processes appear consistent with findings from other mobile belts, and imply that mantle flow plays a significant and quantifiable part in shaping topography, tectonics, and seismic hazard within intraplate settings.

Advantages of a conservative velocity interpolation (CVI) scheme for particle-in-cell methods with application in geodynamic modeling

The particle-in-cell method is generally considered a flexible and robust method to model the geodynamic problems with chemical heterogeneity. However, velocity interpolation from grid points to particle locations is often performed without considering the divergence of the velocity field, which can lead to significant particle dispersion or clustering if those particles move through regions of strong velocity gradients. This may ultimately result in cells void of particles, which, if left untreated, may, in turn, lead to numerical inaccuracies. Here we apply a two-dimensional conservative velocity interpolation (CVI) scheme to steady state and time-dependent flow fields with strong velocity gradients (e.g., due to large local viscosity variation) and derive and apply the three-dimensional equivalent. We show that the introduction of CVI significantly reduces the dispersion and clustering of particles in both steady state and time-dependent flow problems and maintains a locally steady number of particles, without the need for ad hoc remedies such as very high initial particle densities or reseeding during the calculation. We illustrate that this method provides a significant improvement to particle distributions in common geodynamic modeling problems such as subduction zones or lithosphere-asthenosphere boundary dynamics.

Could giant basin-forming impacts have killed Martian dynamo?

The observed strong remanent crustal magnetization at the surface of Mars suggests an active dynamo in the past and ceased to exist around early to middle Noachian era, estimated by examining remagnetization strengths in extant and buried impact basins. We investigate whether the Martian dynamo could have been killed by these large basin-forming impacts, via numerical simulation of subcritical dynamos with impact-induced thermal heterogeneity across the core-mantle boundary. We find that subcritical dynamos are prone to the impacts centered on locations within 30° of the equator but can easily survive those at higher latitudes. Our results further suggest that magnetic timing places a strong constraint on postimpact polar reorientation, e.g., a minimum 16° polar reorientation is needed if Utopia is the dynamo killer.

Deep water recycling through time

We investigate the dehydration processes in subduction zones and their implications for the water cycle throughout Earth's history. We use a numerical tool that combines thermo-mechanical models with a thermodynamic database to examine slab dehydration for present-day and early Earth settings and its consequences for the deep water recycling. We investigate the reactions responsible for releasing water from the crust and the hydrated lithospheric mantle and how they change with subduction velocity (v_s ), slab age (a) and mantle temperature (T_m). Our results show that faster slabs dehydrate over a wide area: they start dehydrating shallower and they carry water deeper into the mantle. We parameterize the amount of water that can be carried deep into the mantle, W (×10⁵ kg/m²), as a function of v_s (cm/yr), a (Myrs), and T_m (°C):[Formula: see text]. We generally observe that a 1) 100°C increase in the mantle temperature, or 2) ∼15 Myr decrease of plate age, or 3) decrease in subduction velocity of ∼2 cm/yr all have the same effect on the amount of water retained in the slab at depth, corresponding to a decrease of ∼2.2×10⁵ kg/m² of H₂O. We estimate that for present-day conditions ∼26% of the global influx water, or 7×10⁸ Tg/Myr of H₂O, is recycled into the mantle. Using a realistic distribution of subduction parameters, we illustrate that deep water recycling might still be possible in early Earth conditions, although its efficiency would generally decrease. Indeed, 0.5-3.7 × 10⁸ Tg/Myr of H₂O could still be recycled in the mantle at 2.8 Ga.

KEY POINTS

Deep water recycling might be possible even in early Earth conditions We provide a scaling law to estimate the amount of H₂O flux deep into the mantle Subduction velocity has a a major control on the crustal dehydration pattern.

Visualization of Flow Behavior in Earth Mantle Convection

A fundamental characteristic of fluid flow is that it causes mixing: introduce a dye into a flow, and it will disperse. Mixing can be used as a method to visualize and characterize flow. Because mixing is a process that occurs over time, it is a 4D problem that presents a challenge for computation, visualization, and analysis. Motivated by a mixing problem in geophysics, we introduce a combination of methods to analyze, transform, and finally visualize mixing in simulations of convection in a self-gravitating 3D spherical shell representing convection in the Earth's mantle. Geophysicists use tools such as the finite element model CitcomS to simulate convection, and introduce massless, passive tracers to model mixing. The output of geophysical flow simulation is hard to analyze for domain experts because of overall data size and complexity. In addition, information overload and occlusion are problems when visualizing a whole-earth model. To address the large size of the data, we rearrange the simulation data using intelligent indexing for fast file access and efficient caching. To address information overload and interpret mixing, we compute tracer concentration statistics, which are used to characterize mixing in mantle convection models. Our visualization uses a specially tailored version of Direct Volume Rendering. The most important adjustment is the use of constant opacity. Because of this special area of application, i. e. the rendering of a spherical shell, many computations for volume rendering can be optimized. These optimizations are essential to a smooth animation of the time-dependent simulation data. Our results show how our system can be used to quickly assess the simulation output and test hypotheses regarding Earth's mantle convection. The integrated processing pipeline helps geoscientists to focus on their main task of analyzing mantle homogenization.

Origin of Columbia River flood basalt controlled by propagating rupture of the Farallon slab

The origin of the Steens-Columbia River (SCR) flood basalts, which is presumed to be the onset of Yellowstone volcanism, has remained controversial, with the proposed conceptual models involving either a mantle plume or back-arc processes. Recent tomographic inversions based on the USArray data reveal unprecedented detail of upper-mantle structures of the western USA and tightly constrain geodynamic models simulating Farallon subduction, which has been proposed to influence the Yellowstone volcanism. Here we show that the best-fitting geodynamic model depicts an episode of slab tearing about 17 million years ago under eastern Oregon, where an associated sub-slab asthenospheric upwelling thermally erodes the Farallon slab, leading to formation of a slab gap at shallow depth. Driven by a gradient of dynamic pressure, the tear ruptured quickly north and south and within about two million years covering a distance of around 900 kilometres along all of eastern Oregon and northern Nevada. This tear would be consistent with the occurrence of major volcanic dikes during the SCR-Northern Nevada Rift flood basalt event both in space and time. The model predicts a petrogenetic sequence for the flood basalt with sources of melt starting from the base of the slab, at first remelting oceanic lithosphere and then evolving upwards, ending with remelting of oceanic crust. Such a progression helps to reconcile the existing controversies on the interpretation of SCR geochemistry and the involvement of the putative Yellowstone plume. Our study suggests a new mechanism for the formation of large igneous provinces.

Thermochemical structures beneath Africa and the Pacific Ocean

Large low-velocity seismic anomalies have been detected in the Earth's lower mantle beneath Africa and the Pacific Ocean that are not easily explained by temperature variations alone. The African anomaly has been interpreted to be a northwest-southeast-trending structure with a sharp-edged linear, ridge-like morphology. The Pacific anomaly, on the other hand, appears to be more rounded in shape. Mantle models with heterogeneous composition have related these structures to dense thermochemical piles or superplumes. It has not been shown, however, that such models can lead to thermochemical structures that satisfy the geometrical constraints, as inferred from seismological observations. Here we present numerical models of thermochemical convection in a three-dimensional spherical geometry using plate velocities inferred for the past 119 million years. We show that Earth's subduction history can lead to thermochemical structures similar in shape to the observed large, lower-mantle velocity anomalies. We find that subduction history tends to focus dense material into a ridge-like pile beneath Africa and a relatively more-rounded pile under the Pacific Ocean, consistent with seismic observations.

Finite-frequency tomography reveals a variety of plumes in the mantle

We present tomographic evidence for the existence of deep-mantle thermal convection plumes. P-wave velocity images show at least six well-resolved plumes that extend into the lowermost mantle: Ascension, Azores, Canary, Easter, Samoa, and Tahiti. Other less well-resolved plumes, including Hawaii, may also reach the lowermost mantle. We also see several plumes that are mostly confined to the upper mantle, suggesting that convection may be partially separated into two depth regimes. All of the observed plumes have diameters of several hundred kilometers, indicating that plumes convey a substantial fraction of the internal heat escaping from Earth.

Mantle-circulation models with sequential data assimilation: inferring present-day mantle structure from plate-motion histories

Data assimilation is an approach to studying geodynamic models consistent simultaneously with observables and the governing equations of mantle flow. Such an approach is essential in mantle circulation models, where we seek to constrain an unknown initial condition some time in the past, and thus cannot hope to use first-principles convection calculations to infer the flow history of the mantle. One of the most important observables for mantle-flow history comes from models of Mesozoic and Cenozoic plate motion that provide constraints not only on the surface velocity of the mantle but also on the evolution of internal mantle-buoyancy forces due to subducted oceanic slabs. Here we present five mantle circulation models with an assimilated plate-motion history spanning the past 120 Myr, a time period for which reliable plate-motion reconstructions are available. All models agree well with upper- and mid-mantle heterogeneity imaged by seismic tomography. A simple standard model of whole-mantle convection, including a factor 40 viscosity increase from the upper to the lower mantle and predominantly internal heat generation, reveals downwellings related to Farallon and Tethys subduction. Adding 35% bottom heating from the core has the predictable effect of producing prominent high-temperature anomalies and a strong thermal boundary layer at the base of the mantle. Significantly delaying mantle flow through the transition zone either by modelling the dynamic effects of an endothermic phase reaction or by including a steep, factor 100, viscosity rise from the upper to the lower mantle results in substantial transition-zone heterogeneity, enhanced by the effects of trench migration implicit in the assimilated plate-motion history. An expected result is the failure to account for heterogeneity structure in the deepest mantle below 1500 km, which is influenced by Jurassic plate motions and thus cannot be modelled from sequential assimilation of plate motion histories limited in age to the Cretaceous. This result implies that sequential assimilation of past plate-motion models is ineffective in studying the temporal evolution of core-mantle-boundary heterogeneity, and that a method for extrapolating present-day information backwards in time is required. For short time periods (of the order of perhaps a few tens of Myr) such a method exists in the form of crude 'backward' convection calculations. For longer time periods (of the order of a mantle overturn), a rigorous approach to extrapolating information back in time exists in the form of iterative nonlinear optimization methods that carry assimilated information into the past through the use of an adjoint mantle convection model.