We show that biased sampling of Earth structure by body‐waves provides an additional explanation for the fact that short period body‐wave seismic velocity models are faster than long‐period free‐oscillation models (apparent dispersion). We do this by tracing a set of body‐waves used in global tomography studies through synthetic seismic models derived from mantle circulation models. The histograms of the arrival time residuals have a negative mean for all the models investigated. We interpret that this results from a predominance of rays sampling the fast structures of subduction zones due to the concentration of sources there. The interpretation successfully passes two tests; the first showed that the signal is tectonically controlled, while the second involved breaking the correlation between ray paths and structures when no bias is found. The negative mean implies that Earth as sampled by body‐waves is fast compared to an average reference Earth (e.g. as measured from free‐oscillations). This effect (and others) will need to be quantified before attenuation can be extracted from the apparent dispersion.
We propose a new approach to full seismic waveform inversion on continental and global scales. This is based on the time–frequency transform of both data and synthetic seismograms with the use of time- and frequency-dependent phase and envelope misfits. These misfits allow us to provide a complete quantification of the differences between data and synthetics while separating phase and amplitude information. The result is an efficient exploitation of waveform information that is robust and quasi-linearly related to Earth's structure. Thus, the phase and envelope misfits are usable for continental- and global-scale tomography, that is, in a scenario where the seismic wavefield is spatially undersampled and where a 3-D reference model is usually unavailable. Body waves, surface waves and interfering phases are naturally included in the analysis. We discuss and illustrate technical details of phase measurements such as the treatment of phase jumps and instability in the case of small amplitudes. The Fréchet kernels for phase and envelope misfits can be expressed in terms of their corresponding adjoint wavefields and the forward wavefield. The adjoint wavefields are uniquely determined by their respective adjoint-source time functions. We derive the adjoint-source time functions for phase and envelope misfits. The adjoint sources can be expressed as inverse time–frequency transforms of a weighted phase difference or a weighted envelope difference. In a comparative study, we establish connections between the phase and envelope misfits and the following widely used measures of seismic waveform differences: (1) cross-correlation time-shifts; (2) relative rms amplitude differences; (3) generalized seismological data functionals and (4) the L2 distance between data and synthetics used in time-domain full-waveform inversion. We illustrate the computation of Fréchet kernels for phase and envelope misfits with data from an event in the West Irian region of Indonesia, recorded on the Australian continent. The synthetic seismograms are computed for a heterogeneous 3-D velocity model of the Australian upper mantle, with a spectral-element method. The examples include P body waves, Rayleigh waves and S waves, interfering with higher-mode surface waves. All the kernels differ from the more familar kernels for cross-correlation time-shifts or relative rms amplitude differences. The differences arise from interference effects, 3-D Earth's structure and waveform dissimilarities that are due to waveform dispersion in the heterogeneous Earth.
It is well accepted that convection in the Earth’s mantle provides the torques to drive vertical and horizontal plate motions. Yet the precise nature of the interaction between flow and plates remains incomplete, because the strength of plates allows them to integrate over a presumably complex flow field in the mantle beneath – making it difficult to get a glimpse even on the recent Cenozoic mantle flow. Over the past years a pressure driven, so-called Poiseuille, flow model for upper mantle flux in the asthenosphere has gained increasing geodynamic attention – for a number of fluid dynamic arguments. This elegantly simple model makes a powerful testable prediction: Poiseuille flow induce plate motion changes should coincide with regional scale mantle convection induced elevation changes.Here I will focus on Australia, which undergoes a profound directional change from westward to northward motion in the early Cenozoic. At the same time there is evidence for early Cenozoic high dynamic topography in the western part of the continent. Thus, suggesting a high-pressure source in the upper mantle to the west of Australia. Altogether these geological and geophysical observations indicate that the separation of Australia from Antarctica was largely driven by plume push torque from the Kerguelen plume.
<p>Earth's surface moves in response to a combination of tectonic forces from the thermally convective mantle and plate boundary forces. Plate motion changes are increasingly well documented in the geologic record and they hold important constraints. However, the underlying forces that initiate such plate motion changes remain poorly understood. I have developed a novel 3-D spherical numerical scheme of mantle and lithosphere dynamics, aiming to exploit information of past plate motion changes in quantitative terms. In order to validate the models and single out those most representative of the recent tectonic evolution of Earth, model results are compared to global plate kinematic reconstructions. Additionally, over the past years a pressure driven, so-called Poiseuille flow, model for upper mantle flux in the asthenosphere has gained increasing geodynamic attention&#8211;for a number of fluid dynamic arguments. This elegantly simple model makes a powerful testable prediction: Plate motion changes should coincide with regional scale mantle convection induced elevation changes (i.e., dynamic topography). For this the histories of large scale vertical lithosphere motion recorded in the sedimentary record holds important information.</p><p>Here, I will present analytical results that help to better understand driving and resisting forces of plate tectonics &#8211; in particular the plume push force. Moreover, numerical results indicate that mantle convection plays an active role in driving plate motions through pressure driven upper mantle flow. Altogether, theoretical and observational constrains provide powerful insights for geodynamic forward and inverse models of past mantle convection.</p>
<p><span>&#160;Our results suggest that geologic maps yield geodynamically-relevant quantities, allowing one to constrain mantle-induced surface deflections of the lithosphere related to past dynamic topography.</span></p>
We present a general concept for evolutionary, collaborative, multiscale inversion of geophysical data, specifically applied to the construction of a first-generation Collaborative Seismic Earth Model. This is intended to address the limited resources of individual researchers and the often limited use of previously accumulated knowledge. Model evolution rests on a Bayesian updating scheme, simplified into a deterministic method that honors today's computational restrictions. The scheme is able to harness distributed human and computing power. It furthermore handles conflicting updates, as well as variable parameterizations of different model refinements or different inversion techniques. The first-generation Collaborative Seismic Earth Model comprises 12 refinements from full seismic waveform inversion, ranging from regional crustal- to continental-scale models. A global full-waveform inversion ensures that regional refinements translate into whole-Earth structure.
Simulating the Earth’s mantle convection at full convective vigor on planetary scales is a fundamental challenge in Geodynamics even for state of the art high-performance computing (HPC) systems. Realistic Earth mantle convection simulations can contribute a decisive link between uncertain input parameters, such as the mantle viscosity structure, and testable preconditions, such as dynamic topography. The vertical deflections predicted by such models may then be tested against history of dynamic topography from stratigraphic observations. Considering realistic Earth like Rayleigh numbers (∼ 108 ) a resolution of the thermal boundary layer of 10 − 50 km is necessary considering the volume of the Earth’s mantle. Simulating Earth’s mantle convection at this level of resolution requires solving sparse indefinite systems with more than 1012 degrees of freedom, computationally feasible only on exascale HPC systems. This is achievable only by mantle convection codes providing high degrees of parallelism and scalability. Earlier approaches with prototype frameworks using hierarchical hybrid grids (HHG) as solvers for such systems demonstrated the scalability of the underlying concept for future generations of exascale computing systems. Building up on the TerraNeo project here we report on the progress of utilizing the improved framework HyTeG (Hybrid Tetrahedral Grids) based on matrix-free multigrid solvers in combination with highly efficient parallelisation and scalability. This will allow to solve systems with more than a trillion degrees of freedom on present and future generations of exascale computing systems. We also report on the advances in developing the scalable mantle convection code TerraNeo using the HyTeG framework to realise extreme-scale mantle convection simulations with realistic, Earth like parametrisation and a resolution in the order of ∼ 1km.
S U M M A R Y Mantle convection models require an initial condition some time in the past. Because this initial condition is unknown for Earth, we cannot infer the geological evolution of mantle flow from forward mantle convection calculations even for the most recent Mesozoic and Cenozoic geological history of our planet. Here we introduce a fluid dynamic inverse problem to constrain unknown mantle flow back in time from seismic tomographic observations of the mantle and reconstructions of past plate motions using variational data assimilation. We derive the generalized inverse of mantle convection and explore the initial condition problem in high-resolution, 3-D spherical mantle circulation models for a time period of 100 Myr, roughly comparable to half a mantle overturn. We present a synthetic modelling experiment to demonstrate that mid-Cretaceous mantle structure can be inferred accurately from fluid dynamic inverse modelling, assuming present-day mantle structure is well-known, even if an initial first guess assumption about the mid-Cretaceous mantle involved only a simple 1-D radial temperature profile. We also demonstrate that convecting present-day mantle structure back in time by reversing the time-stepping of the energy equation is insufficient to model the mantle structure of the past. The difficulty arises, because such backward convection calculations ignore thermal diffusion effects, and therefore cannot account for the generation of thermal buoyancy in boundary layers as we go back in time. Inverse mantle convection modelling should make it possible to infer a number of flow parameters from observational constraints of the mantle.
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