SUMMARY Mantle viscosity remains one of the largest outstanding uncertainties in global geodynamics. Time-dependent mantle circulation models that assimilate tectonic histories (MCMs) provide a way to test viscosity by assessing their present-day predictions against observations. This approach allows for the influence of viscosity on mantle density structure to be accounted for, which is not possible using instantaneous modelling approaches. Here we present the first systematic test of lower mantle viscosity against dynamic topography, the geoid, and seismic heterogeneity using high-resolution MCMs. Model density structure depends strongly on the assumed viscosity profile, which in turn controls the fit to seismic heterogeneity. The fit to dynamic topography and the geoid is further influenced by the instantaneous transmission of stresses to the surface. These two effects can either reinforce or counteract each other at different depths, which must be considered when attempting to match dynamic topography and geoid amplitudes. MCMs typically overestimate dynamic topography amplitudes. We find that it is possible to reduce these amplitudes by lowering viscosity in the upper lower mantle ($\approx$660–2000 km), though this comes at the expense of a reduced fit to the geoid and/or seismic heterogeneity. Our preferred viscosity profile provides an excellent fit to observed geoid amplitudes and the seismic heterogeneity of S40RTS. We also tested an alternate tectonic reconstruction with tomography-based refinements around the Pacific which improved the correlation with the observed geoid by $\approx$20 per cent. Our results show that MCMs can now reach a level of resolution and realism sufficient for comparison to multiple independent data sets, opening the door to systematic assessment of uncertain parameters which govern convection in the mantle.

Fluid dynamics simulations are a powerful tool for understanding processes in the Earth's deep interior. Mantle circulation models (MCMs), for example, provide important insight into the present-day structure of the mantle and its thermodynamic state when coupled with mineralogical models, which is essential information for other fields in the geosciences. The evolution of the heat flux through the core-mantle boundary, for instance, is a prerequisite for geodynamo simulations that aim to model the reversal frequency pattern of the Earth's magnetic field on geologic time scales. However, geodynamical modelling requires extensive knowledge of deep Earth properties and plate motions over time. Uncertainties in these model inputs propagate into the MCMs, which subsequently have to be evaluated with independent data, such as the seismological or geological record. Although state-of-the-art MCMs typically explain statistical properties of seismological data, they do not consistently reproduce the location of features in the mantle. In this contribution, we explore the effect of varying the absolute position of mantle structure on seismic data by applying first-order modifications to an initial MCM. Normal mode data are particularly well suited for assessing the resulting changes in the location of mantle structure, as they capture its long-wavelength component throughout the entire mantle. In addition, the global sensitivity of normal modes reduces the drawbacks of uneven data coverage. Specifically, we use two different seismic forward modelling approaches, an iterative direct solution method for computing full-coupling spectra and a splitting function calculation that is based on the self-coupling approximation. Our goal is to quantify the effects of a limited number of large-magnitude earthquakes, the adequacy of the self-coupling approximation, and the resolvability of relevant model differences through a comprehensive data analysis. Our synthetic forward modelling framework is moreover well suited for testing the depth sensitivity associated with specific frequency intervals in the spectrum that generally is inferred from seismic 1-D profiles within the splitting function approximation.

Mantle convection is driven by buoyancy forces in Earth’s interior. The resulting radial stresses generate vertical deflections of the surface, leaving traces in the geological record. Utilizing new data assimilation techniques, geodynamic inverse models of mantle flow can provide theoretical estimates of these surface processes, which can be tested against geological observations. These inverse models are emerging as powerful tools, providing the potential for tighter constraints on the relevant physical parameters governing mantle flow.The geodynamic inversions mentioned above require an estimate of the present-day thermal state of the mantle, which can be derived from seismic observations. Using thermodynamically self-consistent models of mantle mineralogy, it is possible to convert the seismic structure imaged by global tomographic models to temperature. However, both seismic and mineralogical models are significantly affected by inherent limitations and different sources of uncertainty. In addition, owing to the complexity of the mineralogical models, the relation between temperature and seismic velocities is highly non-linear and not strictly bijective: In the presence of phase transitions, different temperatures can result in the same seismic velocity, making the conversion from seismic heterogeneity to thermal structure non-unique.We investigate the theoretical ability to estimate the present-day thermal state of the mantle based on tomographic models in the case of isochemical convection. The temperature distribution from a 3-D mantle circulation model with earth-like convective vigour serves as the “true” temperature field. Using a closed-loop experiment, we aim to recover this initial model after: 1) mineralogical mapping from the “true” temperatures to seismic velocities, 2) application of a tomographic filter to mimic the effect of limited tomographic resolution, and 3) mapping of the “imaged” seismic velocities back to temperatures. We test and quantify the interplay of smoothed seismic structure due to tomographic filtering with different approximations for the conversion from seismic to thermal structure. Additionally, owing to imperfect knowledge of the parameters governing mineral anelasticity, we test the effects of changes to the anelastic correction applied in the mineralogical mapping. The observed mismatch between the recovered and initial temperature field is dominated by the effect of tomographic filtering, with a depth-dependent average error of up to 200 K. Additionally, we observe systematic large errors in the vicinity of phase transitions. Our results highlight that, given the current limitations of tomographic models and the incomplete knowledge of mantle mineralogy, magnitudes and spatial scales of a temperature field obtained from global seismic models will deviate significantly from the true state, even under the assumption of purely thermally driven mantle flow. Strategies to estimate the present-day thermodynamic state of the mantle must be carefully selected to minimize additional uncertainties.

One major objective in geodynamics is to create models of mantle flow that provide quantitative information to other Earth science disciplines. In this respect, geologically informed fluid dynamics simulations, such as mantle circulation models (MCMs) are a key component. In addition, thermodynamic models of mantle mineralogy are essential in that they can provide detailed information on material behaviour, such as density, thermal expansivity, elastic parameters and specific heat capacity, as a function of pressure and temperature for the geodynamic simulations. They are also required in the assessment of the MCMs to link temperatures to seismic velocities and density. This way, a number of secondary predictions, such as seismic, geodetic and geologic data, can be computed, which enables the validation of our models and the testing of geodynamic hypotheses by comparison to observations.Here, we focus specifically on the dynamic effects and seismic imprint of the mantle transition zone (TZ). The complex set of phase transformations, together with an increase in viscosity, in this depth range is expected to influence vertical mass flow between upper and lower mantle. Still, neither the associated dynamic effects nor the seismic structure of the TZ have conclusively been constrained to date. Using our highly scalable new mantle convection software TerraNeo, based on the matrix-free finite-element framework HyTeG, we present a suite of MCMs with different formulations of compressibility. Classically, compressibility is included in the mantle convection simulations in form of the truncated anelastic liquid approximation (TALA), and the effects of phase transformations are either neglected or incorporated in parametrized form at constant depth. A physically more complete treatment of compressibility has recently been introduced in the form of the ‘Projected Density Approximation’ (PDA; Gassmöller et al., 2020). The PDA is based on tabulated material properties from the thermodynamic mineralogical models, thus allowing us to self-consistently capture non-linear buoyancy effects specifically due to phase transitions in the simulation. Comparing MCMs using TALA and PDA, we will highlight effects of mineral phase transitions on the evolution of mantle flow over time, the resulting present-day temperature field, as well as its seismic signature.

Recent advances in computational capabilities make it possible to compute global geodynamic earth models at near earthlike convective vigor. This paves the way to systematically obtain a range of synthetic data from such models in an approach that is known as closed loop experiments. Here we present results from closed loop experiments in geodynamic earth models targeted at three classes of data that are sensitive to the mantle convection process, namely seismic data, global stress patterns as reflected by the world stress map, and continent scale stratigraphy processed for the distribution of conformable and unconformable successions in recently developed so called hiatus maps. Our results reveal effects from spatially variable data collection and quality (as expected), mantle flow geometries (less expected) and (still poorly known) histories of paleo mantle flow. We conclude that the derivation of process based synthetic data from geodynamic earth models provides crucial information for data interpretion, that closed loop experiments area powerful tool to link geodynamic earth models to data, and that closed loop experiments could be helpful to guide future data collection efforts.

Many geophysical studies require knowledge on the present-day temperature distribution in Earth's mantle. One example is geodynamic inverse models, which utilize data assimilation techniques to reconstruct mantle flow back in time. The thermal state of the mantle can be estimated from seismic velocity perturbations imaged by tomography with the help of thermodynamic models of mantle mineralogy. Unique interpretations of the tomographically imaged seismic heterogeneity can either be obtained by incorporating additional data sets or requires assumptions on the chemical composition of the mantle. However, even in the case of (assumed) known chemical composition, both the seismic and the mineralogical information are significantly affected by inherent limitations and different sources of uncertainty.Here, we investigate the theoretical ability to estimate the thermal state of the mantle from tomographic models in a synthetic closed-loop experiment. The 'true' temperature distribution of the mantle is taken from a 3-D mantle circulation model with Earth-like convective vigour. We aim to recover this reference model after: (1) mineralogical mapping from the 'true' temperatures to seismic velocities, (2) application of a tomographic filter to mimic the effect of limited seismic resolution, and (3) mapping of the 'imaged' seismic velocities back to temperatures. We test and quantify the interplay of tomographically damped and blurred seismic heterogeneity in combination with different approximations for the mineralogical 'inverse' conversion from seismic velocities to temperature. Owing to imperfect knowledge of the parameters governing mineral anelasticity, we additionally investigate the effects of over- or underestimating the corresponding correction to the underlying mineralogical model. Our results highlight that, given the current limitations of seismic tomography and the incomplete knowledge of mantle mineralogy, magnitudes and spatial scales of a temperature field obtained from global seismic models deviate significantly from the true state, even in the idealized case of known bulk chemical composition. The average deviations from the reference model are on the order of 50-100 K in the upper mantle and depending on the resolving capabilities of the respective tomography-can increase with depth throughout the lower mantle to values of up to 200 K close to the core-mantle boundary. Furthermore, large systematic errors exist in the vicinity of phase transitions due to the associated mineralogical complexities. When used to constrain buoyancy forces in time-dependent geodynamic simulations, errors in the temperature field might grow nonlinearly due to the chaotic nature of mantle flow. This could be particularly problematic in combination with advanced implementations of compressibility, in which densities are extracted from thermodynamic mineralogical models with temperature-dependent phase assemblages. Erroneous temperatures in this case might activate 'wrong' phase transitions and potentially flip the sign of the associated Clapeyron slopes, thereby considerably altering the model evolution. Additional testing is required to evaluate the behaviour of different compressibility formulations in geodynamic inverse problems. Overall, the strategy to estimate the present-day thermodynamic state of the mantle must be selected carefully to minimize the influence of the collective set of uncertainties.

Mantle slabs imaged by seismic tomography provide complementary subsurface information that could improve global plate reconstructions because they are indications of ancient tectonic plates. Linking mantle slabs to the surface plates requires approaches that follow geodynamic principles in a highly vigorous mantle. Here, we propose a new workflow that couples a slab unfolding approach and a mantle circulation model (MCM) through which tomotectonic reconstructions can be performed, evaluated and improved in a closed-loop experiment. We publish the most recent version of our unfolded-slab constrained, geodynamically self-consistent plate reconstruction, Tomopac2, in which comprehensive intra-oceanic subductions within the Pacific-Panthalassa realms are implemented. These intra-oceanic subductions are crucial for understanding the evolution of the mantle and surface tectonics in the central Pacific, western North America and East Asia since the Mesozoic. Our model also incorporates subduction along western South America. Our closed-loop experiment allows us to reinterpret published tomotectonic reconstructions based on the vertical sinking slabs hypothesis. We conclude that highly vigorous mantle flow that allows lateral slab transport up to 4000 km and non-constant sinking rates that deviate by up to 10 mm yr − 1 locally within an approximately 1000 km area must be accounted for in tomotectonic reconstructions.

Reconstructions of past mantle flow provide a powerful framework to sharpen our understanding of the dynamics and structure of the deep Earth. As a data-driven approach to geodynamic modelling, these reconstructions explicitly require an estimate of the present-day thermal state of the mantle, which can be derived from seismic tomography and an interpretation of observed mantle heterogeneity with mineral physics. Nonetheless, various uncertainties complicate the direct use of tomographic images. Critical issues are the spatially heterogeneous imaging quality, and the lack of definite metrics for seismic resolution and a practical quantification of model uncertainty. In many regions the patterns, but especially the amplitudes of velocity variations, are thus insufficiently constrained, making global tomography prone to drawing a dynamically inconsistent picture of the mantle’s buoyancy field. For geodynamic inferences, it is therefore vital to establish to what degree these current limitations affect our capacity to accurately reconstruct the mantle’s evolution back in time, and, where necessary, what strategies can be advised to address their impact.We introduce a tomographic-geodynamic framework designed to tackle this issue with the aid of closed-loop experiments. Based on a reference mantle circulation model (MCM), we set up a complete, synthetic tomographic experiment with the following key components: 1) S-wave finite-frequency traveltime residuals are obtained from seismograms predicted for the MCM, recorded at ~10,000 real station locations. Therefore, we use the global wave propagation code SPECFEM3D_GLOBE to simulate in total 3,800 teleseismic earthquakes accurate down to a shortest period of ~10s. 2) We sample the complete dataset on the basis of ray turning point locations to obtain an optimal and balanced illumination of the entire mantle. 3) We perform tomographic inversions with the SOLA method and paraxial finite-frequency kernels. The explicit computation of the inverse and the corresponding resolving kernels in SOLA allow us to create tomographically filtered representations of the `true` MCM heterogeneity. Furthermore, it gives us the possibility to analyze them together with associated local resolution and uncertainty estimates. The resulting synthetic tomographic images are generally able to reproduce the patterns of major anomalies from the MCM. Yet, the amplitudes and exact shapes remain difficult to recover, even in the case of optimized data coverage and tuning of inversion parameters towards highly localized and narrow resolving kernels. This work serves as the basis for subsequent testing of the tomographic input within adjoint mantle flow reconstructions to complete the closed-loop setup.

Interpretations of seismic tomography and applications of the resulting tomographic images, e.g. for estimating present-day mantle temperatures, require information on their resolution and uncertainty. Assessing these model properties is often difficult due to the large size of tomographic systems on global scales. In consequence, there have been only few attempts to consistently analyse the spatially variable quality of tomographic images of deep mantle structure. For linear problems, both resolution and uncertainty can be quantified with the tools provided by classic Backus–Gilbert (B–G) inversion. In this theory, averaging kernels define the local resolving power at each model parameter, while uncertainties represent the propagation of data errors into the model values. By using a more efficient variant of B–G inversion, the method of 'Subtractive Optimally Localized Averages' (SOLA), global tomography can be performed with complete information for model appraisal.Based on the SOLA framework, we present a concept for the assessment of the 3-D resolution information contained in a global set of averaging kernels. It is based on the rigorous estimation of resolution lengths from a 3-D Gaussian parametrization of the averaging kernels, together with a test for the robustness of this approximation. This is a necessary step because a perfectly bell-shaped or delta-like behaviour of resolution can not always be guaranteed in global tomography due to the inhomogeneous data coverage. Therefore, we also develop a classification scheme, which enables a basic identification of those averaging kernels that are too complex to be sufficiently described by the chosen definition of resolution length. We note that this approach is more generally applicable, i.e. it can be used with any explicitly available set of averaging kernels or point-spread functions, but also with alternative parametrizations.In the context of the SOLA method, our resolution analysis can be further used to locally calibrate the inversion parameters. This involves on the one hand the specification of a target (resolution) kernel. On the other hand, a trade-off parameter needs to be selected that regulates the fit of the averaging to the target kernel, and the conversely affected propagation of data errors.To this end, we apply our concept for robust resolution estimation to different sets of averaging kernels from SOLA inversions with varying parameter combinations. Most notably, we systematically increase the spatial extent of the target kernels (taken as 3-D Gaussian functions here as well). The final maps of global (and classified) resolution and uncertainty can be viewed together for a complete picture of the model quality. They reveal where, and for which target size and amount of error propagation, resolution lengths are meaningful and model values can be interpreted appropriately.

<p>For a thorough understanding of the impact of mantle convection on vertical motions of the lithosphere, computational modeling plays a crucial role. Mantle circulation can be modeled by solving the equations of motion of a fluid using Earth-like input parameters assimilating plate motions at the surface in discrete steps through time. Thus, a realistic Earth model relies on the robustness of the inserted information. However, apart from the general difficulty of inferring deep Earth’s properties, also the plate tectonic model introduces uncertainty. Especially the linking of relative plate motions to absolute position relies on controversial assumptions such as fixity of structures in the mantle (e.g., plumes or Large-Low-Shear-Velocity Provinces) or the association between subducted plates at depth and high velocity regions in tomographic images. The latter specifically are restricted by non-uniqueness and the need to regularize the inversions, distorting structures and damping heterogeneity amplitudes.</p> <p>In order to infer secondary results from an MCM, it is thus important to validate the model against independent observations. Here, we employ Earth’s free oscillations that feature global sensitivity to 3-D structure for model assessment, complementing our earlier work using seismic body wave data. To this end, the temperature field of a published MCM is converted to seismic velocity with the help of a thermodynamic model of mantle mineralogy. An effective forward approach for the computation of normal mode data from synthetic Earth models is the calculation of splitting functions, describing the distortion of characteristic frequency peaks in the spectrum induced by even degree structural heterogeneity. A general problem is that the sensitivity of normal modes with depth often shows oscillatory behaviour preventing a straight forward relation of frequency shifts to structure in a certain depth range. This can be mitigated by combining kernels of several modes via a Backus-Gilbert approach to obtain focused sensitivity in pre-specified depth ranges of the mantle. For testing the significance of relevant model differences in splitting function data, geometrical alterations mimicking changes in the absolute reference frame and viscosity were applied to a pre-computed MCM. Current results indeed indicate that normal mode data are sensitive to such model changes within their respective uncertainty ranges.</p>

SUMMARY The ability to construct time-trajectories of mantle flow is crucial to move from studies of instantaneous to time-dependent earth models and to exploit geological constraints for mantle convection modelling. However mantle convection is chaotic and subject to the butterfly effect: the trajectories of two identical mantle convection models initialized with slightly different temperature fields diverge exponentially in time until they become uncorrelated. Because one may use seismic inferences about the mantle state as a starting or terminal condition to project mantle flow forward or backward in time, and because the seismic inference is invariably subject to uncertainties, this seemingly would rule out any construction of robust mantle flow trajectories. Here we build upon earlier work which showed that assimilation of the horizontal component of the surface velocity field from a known reference model allows one to overcome the butterfly effect and to construct robust mantle flow trajectories, regardless of the choice of the initial state perturbation. To this end, we use high resolution 3-D spherical mantle convection models in four end-member configurations: an isoviscous purely internally heated model, an isoviscous purely bottom heated model, a model with a radial increase in viscosity along with pure internal heating as well as a model that combines the effects of radial viscosity increase, internal and bottom heating. In order to capture the impact of seismic filtering, we perturb the initial temperature fields of these end-member models through either radial or horizontal smoothing of the temperature field or the application of the tomographic filter of seismic model S20RTS. We assess the quality of the constructed model trajectories via a number of statistical measures as well as comparisons of their dynamic topography histories. The latter is an essential step since mantle flow cannot be directly observed but has to be inferred via its surface manifestations. Importantly, linking mantle flow to surface observations yields patterns representable on a latitude–longitude grid similar to meteorological observables such as precipitation. This invites the application of meteorological quality metrics, such as the power ratio and Taylor diagram, to assess the quality of mantle flow trajectories. We introduce these metrics for the first time in the context of mantle convection and demonstrate their viability based on the compact manner in which they summarize model performance.

The mantle transition zone (TZ) is expected to influence convective flow, but neither its structural characteristics nor dynamic effects have been conclusively constrained. Lateral temperature variations modulate the topography of associated seismic discontinuities at approximately 410 and 660 km depth (‘410’ and ‘660’). These discontinuities are related to mineral phase transitions and thus also sensitive to composition. Consequently, discontinuity topography can potentially provide insight on temperature and even phase composition at depth. It has been recognized that, in addition to phase transitions in olivine polymorphs, the transition of garnet to lower mantle minerals may impact particularly the ‘660’ at higher temperatures. However, the volume of material affected by this garnet transition and its dynamic implications have not yet been quantified. We address this question by predicting synthetic seismic structure and discontinuity topography of the TZ based on the temperature field of a 3-D mantle circulation model (MCM) for a range of relevant bulk compositions and associated mineralogy models. The models differ in complexity in terms of the number of incorporated oxide-components and include pyrolite, depleted mantle and mechanical mixing (MM) models. We thus create a suite of relevant hypothetical realizations of TZ seismic structure and major discontinuities. Our theoretical approach allows us to systematically investigate the effects of varying mineralogy, in combination with a dynamically constrained temperature field, on TZ structure. We explicitly relate major phase transitions as given by the mineralogical tables to specific topographic features of the ‘410’ and ‘660’ and quantify the relative impact of the different phases. Analyzing a number of statistical measures for our synthetic discontinuity topographies provides theoretical predictions on possible distribution and magnitude of real-world depth variations. Our study thus provides a framework for dynamically informed interpretations of seismically derived TZ structure in terms of mantle temperature and composition. It moreover gives insights on the potential dynamic behavior of the TZ by constraining the importance of garnet in our theoretical models. We find that garnet only occurs in regions with excess temperatures above 150 - 300 K, depending on phase composition. This leads to ~ 3 % garnet at the ‘660’ in a pyrolite mantle and ~ 1 % in MM. Absolute base temperatures could however be higher (or lower) than predicted by the MCM’s geotherm. For different plausible background temperature fields the garnet proportion at the ‘660’ could vary between ~ 1 and 39 % in pyrolite, while remaining largely unaffected in MM. Since not all warmer than average but only the hottest mantle regions see the garnet transition, dynamic effects of the ‘660’ might be even more complex than previously assumed.

<p>Mantle convection is primarily driven by gravitational forces acting on thermally buoyant structures in Earth's interior. The associated vertical stresses generate phases of uplift and subsidence of the surface, leaving observable traces in the geologic record. Utilizing new data assimilation techniques, geodynamic inverse models of mantle flow can provide theoretical estimates of these surface processes, which can be tested against geologic observations. These so-called mantle flow retrodictions are emerging as powerful tools that have the potential to allow for tighter constraints on the inherent physical parameters.</p> <p>To contain meaningful information, the inverse models require an estimate of the present-day buoyancy distribution within the mantle, which can be derived from seismic observations. By using thermodynamically self-consistent models of mantle mineralogy, it is possible to convert the seismic structure of global tomographic models to temperature. However, both seismic and mineralogical models are significantly affected by different sources of uncertainty and often require subjective modelling choices, which can lead to different estimated properties. In addition, due to the complexity of the mineralogical models, the relation between temperature and seismic velocities is highly nonlinear and not strictly bijective: In the presence of phase transitions, different temperatures can result in the same seismic velocity, further complicating the conversion between the two parameters.</p> <p> </p> <p>Using a synthetic closed-loop experiment, we investigate the theoretical ability to estimate the present-day thermal state of Earth's mantle based on tomographic models. The temperature distribution from a 3-D mantle circulation model with earth-like convective vigour serves as a representation of the "true" temperature field, which we aim to recover after a set of processing steps. These steps include the “forward and inverse” mineralogical mapping between temperatures and seismic velocities, using a thermodynamic model for pyrolite composition, as well as applying a tomographic filter to mimic the limited resolution and uneven data coverage of the underlying tomographic model. Owing to imperfect knowledge of the parameters governing mineral anelasticity, we test the effects of changes to the anelastic correction applied in forward and inverse mineralogical mapping. The mismatch between the recovered and the initial temperature field carries a strong imprint of the tomographic filter. Additionally, we observe systematic errors in the recovered temperature field in the vicinity of phase transitions. Our results highlight that, given the current limits of tomographic models and the incomplete knowledge of mantle mineralogy, amplitudes and spatial scales of a temperature field obtained through global seismic models will deviate significantly from the true state. Strategies to recover the present-day buoyancy field must be carefully selected in order to minimize additional uncertainties.</p>

Linking geodynamic models to observations from seismology is essential for improving our understanding of the present-day thermodynamic state of the mantle. From the geodynamic perspective, 3D mantle circulation models (MCMs) yield physically relevant predictions of the global distribution of buoyancy forces, while complementing information is available from seismic data and tomography that can reveal the location and morphology of mantle heterogeneity. Investigating this powerful interplay in a fully synthetic framework has great potential. It allows us to make robust interpretations of mantle structure provided that quantitatively meaningful comparisons can be made. This especially relates to the magnitudes of heterogeneity that can not be effectively constrained by the individual modelling approaches.Following this general concept, there are two possible links: 1) synthetic seismic data can be predicted from the MCM and statistically be compared against observed data. 2) the MCM gets modified by a tomographic operator (informing us about spatially variable seismic resolution and, if applicable, model uncertainty), and subsequently this filtered version gets compared against the corresponding tomographic image from real observations.Here, we discuss these two strategies together based on observed data for S-wave cross-correlation traveltime residuals that have been applied to global seismic tomography. Taking the same set of source-receiver configurations, synthetic traveltime predictions are computed in a state-of-the-art MCM using ray theory (RT), paraxial finite-frequency kernels (FFK), as well as cross-correlation measurements on synthetic seismograms (SPECFEM). The latter requires computationally demanding 3D-wavefield simulations using SPECFEM3D_GLOBE for an earthquake catalog comprising over 4,200 teleseismic events.These data sets can be used for tomographic filtering by application of the generalized inverse operator of the actual tomographic model. Filtered MCMs derived from the differently predicted data sets appear largely similar on a global scale with regards to the shape and amplitudes of imaged mantle heterogeneity. This is observed despite the lack of more accurate wave physics in RT or FFK and possible measurement errors for the SPECFEM data that, although being computed in a synthetic case, can not be completely ruled out. Stronger differences between filtered models appear in regions of higher image resolution where model uncertainty by propagated data errors can play a more prominent role.We discuss the impact of the different filtering strategies by comparing filtered models to the original MCM and synthetic traveltime residuals to the underlying real observations. The results strongly highlight the need for incorporating both resolution and model uncertainty in combined tomographic-geodynamic studies.

Geodynamic inverse models that aim at retrodicting past mantle evolution require accurate estimates of its thermodynamic present-day state. Tomographic models are in principle well suited to provide this information. However, a fundamental problem that impacts the quality of the retrodiction arises from their inherently limited resolving power and the fact that the magnitudes of seismic heterogeneity are difficult to constrain owing to the necessity to regularize the inversions (e.g. by norm damping). To get a better understanding of the magnitudes of heterogeneity in the mantle, one option is to predict seismic velocity variations from the temperature field of forward mantle circulation models (MCMs) in combination with thermodynamic models of mantle mineralogy. Temperature is not a free parameter in these models, but rather constrained by the underlying conservation equations and relevant input parameters. If the geodynamic models are run at earth-like Rayleigh number, temperature variations are expected to feature realistic magnitudes, which, together with the mineralogical mapping, should lead to realistic magnitudes of seismic heterogeneity. This has been investigated in previous studies by computing secondary predictions for the MCMs, such as seismic body wave traveltimes and geoid undulations. A complicating factor, however, is the trade-off between thermal and compositional variations that both may affect the seismic velocities. A further complexity arises from the fact that the elastic velocities of the mineralogical model need to be corrected for the effects of anelasticity, the parameters of which are poorly known. Thus, a range of seismic velocity values may still be possible for a given temperature. Here, we explore the possibility to use Earth's normal mode spectrum to narrow the range of plausible magnitudes of seismic heterogeneity in the mantle. To this end, we compute free-oscillation spectra with full coupling of modes below 3.5 mHz in our geodynamic models. In our analysis, we consider different measures to investigate whether the normal mode data may provide complementary information to earlier assessments of MCMs based on body waves. In addition to the direct misfit between spectra of real and synthetic data, the variance of a large number of stacked multiplets can be used to constrain the even degree covariance of lateral heterogeneity under certain assumptions. Using different realizations of seismic MCM structure that differ in terms of the anelastic temperature to velocity mapping, we will analyse the potential of normal mode data to put tighter constraints on the magnitudes of heterogeneity.

The post-perovskite (pPv) phase is often invoked as an explanation for seismic observations of discontinuities, anisotropy and anti-correlation between velocities in the lower mantle. Accurate interpretations of these features in terms of pPv are important, as the phase transition provides a much-needed temperature probe in the lowermost mantle. Robust observations of this phase transition have the potential to constrain the temperature of and heat flow across the core-mantle boundary and thus provide estimates of the heat budget and thermal evolution of the Earth. Traditionally, the presence of post-perovskite (pPv) has been inferred from observations of seismic discontinuities in the lowermost mantle. However, these only give a very patchy image of lateral variations in the presence of pPv due to the heterogeneous coverage of seismic data. In addition, interpretations are complicated by the fact that the properties and stability field of pPv remain uncertain from a mineral physics point of view. Here, we describe different proxies for the presence of post-perovskite, proposed based on global seismic tomography. To investigate their accuracy, we utilize synthetic tomography models derived from geodynamic modelling in combination with mineral physics and we compare the predicted presence to the true occurrence of pPv in the model. By using both high-resolution geodynamic models as well as filtered models that have been corrected for the limited resolution of seismic tomography, we can investigate whether a proxy works in theory (on the high-resolution versions) and also in practice (on the filtered models). We will discuss how we may be able to constrain the stability field of pPv based on comparisons with published tomographic models and make recommendations as to what has to improve in seismic tomography to make different proxies work.

Tomographic-geodynamic model comparisons are a key component in studies of the present-day thermodynamic state of the mantle. A fundamental prerequisite for quantitatively meaningful comparisons is “tomographic filtering” of the geodynamic model. This means that geodynamically predicted mantle structures have to be modified to account for the spatially variable resolving power of tomographic images, i.e. to mimic the effects of uneven data coverage and regularization. Different approaches for tomographic filtering are available, but it is so far unclear which one will be the method of choice in the context of computationally demanding retrodictions of past mantle flow. Here, we investigate the impact of the possible filtering approaches in a fully synthetic framework. For the first time in a mantle circulation model (MCM), we simulate 3D-wavefields and seismograms for an entire tomographic earthquake catalogue with over 4,200 events using SPECFEM3D_GLOBE. We use both classic filtering with the resolution operator R, as well as the recently introduced “generalized inverse projection” (GIP; Freissler et al. 2020) to generate tomographically filtered versions of the MCM. In the GIP method, the generalized inverse operator of a given tomographic image is applied to synthetic seismic data predicted from the geodynamic model, as well as to potential data errors, to obtain the filtered MCM plus the propagated error. Important to note, the same generalized inverse operator is applied to an observed data set to build the tomographic model. A physically accurate prediction of synthetic data, here realized with the seismograms from numerical wave propagation, thus enables GIP filtering to consistently reproduce the tomographic imaging process. This is an important methodological advantage over classic filtering with R, where an unphysically reparametrized version of the MCM is filtered directly in model space and seismic data errors can not be considered. In our study, GIP-filtered models are computed with cross-correlation S-wave traveltime residuals from the synthetic seismograms, as well as with banana-doughnut kernel and ray-theoretical traveltime predictions. The differently filtered models are compared against each other using statistical measures. By taking the GIP-filtered model that is based on the 3D-wavefield simulations as a reference, we can quantify the impact of reparametrization in classic filtering versus the lack of exact wave physics when using less accurate methods for traveltime predictions in the GIP filtering. Additionally, all filtered models can be compared to the underlying original structure of the MCM. Detailed knowledge of tomographic filtering effects with different strategies is required prior to efforts on the associated uncertainty quantification in data-driven geodynamic retrodictions of mantle evolution.

One major challenge in studies on mantle convection is to provide a physically consistent link between underlying geophysical hypotheses and predicted surface observables. Here, we first review recent developments targeted toward linking hypothetical temperature fields to seismic recordings in a quantitative way. By combining mantle circulation models with mineralogical thermodynamics and global 3-D seismic wavefield simulations, synthetic traveltime residuals can be computed that correctly capture the various nonlinearities in the relation to the underlying temperatures. We then highlight the importance of taking uncertainties in the input parameters into account when comparing to real data. Specifically, we investigate the effects of the poorly constrained parameters related to mineral anelasticity on the temperature-velocity conversion and the predicted traveltime residuals. The anelastic correction increases the temperature sensitivity of seismic velocities, particularly at high temperatures. Assuming maximum values plausible for the frequency dependence of attenuation and the activation enthalpy of the dissipative process, the temperature derivative of shear-wave velocity increases by more than 100% at the top, and up to 70% at the bottom of the lower mantle in regions of elevated temperatures. The standard deviation of the seismic traveltime residuals, however, is larger only by about 30% compared to the anharmonic case in consequence of the multiple nonlinearity of the physical situation at hand.