# Global High-Resolution Earth Models - Generation and Assessment

**Principal Investigator:** Hans-Peter Bunge, Geophysics Section, Department of Earth and Environmental Sciences, Ludwig-Maximilians-Universität München (Germany)

**HPC Platform:** SuperMUC of LRZ

**Date published:** September 2018

**LRZ Project ID:** pr48ca

**Introduction**

Earth’s mantle, although solid on short time scales, can flow like a very viscous fluid over the course of geologic eras. Heat coming from the underlying core and internal heat production due to radioactive decay are large enough to set the mantle in vigorous convection. Mantle convection drives the motion of tectonic plates and dictates the long-term evolution of the Earth: it controls the distribution of continents and oceans and their topographic elevation; it determines the formation of mountain ranges, shallow seas and land bridges between continents; and it is the cause of Earth’s seismicity and volcanic activity. As such, it has a broad impact on many aspects of the Earth system, ranging from its oceanic and atmospheric circulation to its climate, from its hydrosphere to the erosion and deposition of sediments, from the location and abundance of natural resources to the evolution of life. As such, mantle convection is one of the main research areas at the Geophysics section of the Ludwig-Maximilians-Universität München [1].

*Fig. 01: First mantle flow retrodictions for geodynamically plausible, compressible, high resolution Earth models with ~670 million finite elements, going back in time to the mid-Paleogene [3]. The visualization shows the time evolution of one of the four retrodiction models (top: temperature variations, middle: asthenospheric flow velocity, and bottom: the induced surface topography). The retrodictions produce a spatially and temporally highly variable asthenosphere flow with faster than plate velocities, and a history of dynamic topography characterized by local doming events, in agreement with considerations on plate driving forces, and regional scale uplifts reported in the geologic literature.* © LMU München

**Results and Methods**

In an earlier study, we showed that, although mantle convection at earth-like vigor is a chaotic process, one can constrain its flow history back in time for periods comparable to a mantle overturn, i.e. ≈100 million years, if knowledge of the surface velocity field and estimates on the present-day heterogeneity state are available [2]. Such “retrodictions”, which involve the solution of a geodynamic inverse problem through the adjoint method, are a promising tool to improve our understanding of deep Earth processes, and to link uncertain geodynamic modeling parameters to geologic observables. We have now performed the first mantle flow retrodictions for geodynamically plausible, compressible, high resolution Earth models with ≈670 million finite elements, going back in time to the Mid Paleogene [3].

The geodynamic inverse problem aims at finding the (unknown) state of the mantle some time in the past that naturally evolves into its (known) present-day state. The adjoint method minimizes the difference between the observed present-day mantle structure and the prediction of a geodynamic model by refining the initial condition in the past through an iterative method. Each iteration requires the solution forward in time of the equations that govern mantle convection, which are based on first-principle conservation laws of physics, and the solution backward in time of a set of adjoint equations, which are derived from the forward equations.

One of the appealing aspects of the adjoint method is the similarity of the forward and adjoint equations. They can thus be solved by the same numerical code with only slight modifications. For this project we used the parallel finite element code TERRA, modified to solve the forward and adjoint equations for compressible Earth models [4]. In order to simulate mantle convection at earth-like vigor, a sufficiently high resolution is needed. This is obtained by dividing the volume of the mantle into ≈670 million finite elements, for a maximum grid spacing of ≈11 km at Earth’s surface. An adjoint iteration for this model over 40 Ma requires between 75 and 150 thousand CPU-hours, equivalent to 36 to 72 hours of computation using 2048 CPUs. The initial condition is optimally recovered after 5 to 10 iterations, leading to a total of about a million CPU-hours per retrodiction. We have chosen to retrodict past mantle flow for four scenarios, combining two different estimates for the present-day state of the Earth’s mantle with two different viscosity profiles for the geodynamic model. Retrodictions of mantle evolution for these four scenarios were performed for the last 40 Ma of geologic history (i.e., back to the mid-Paleogene). We then investigated the related implications in terms of dynamic topography [3] and changes in the the shape of the Earth’s gravitational potential field induced by mantle circulation [5]. We found that the retrodicted history of mantle convection and dynamic topography in our simulations is sensitive to the assumptions about the present-day mantle state and its viscosity, suggesting that mantle flow retrodictions obtained from adjoint modeling can provide powerful constraints on the assumptions of structural and rheologic parameters of Earth models. In particular, this can be achieved by comparing their predicted dynamic topography evolution to constraints gleaned from the geologic record.

Furthermore, we assessed the signal retrievability of the modeled geoid rates by current and future satellite gravity missions using closed-loop numerical simulations, with different satellite gravity retrieval mission assumptions [5]. Temporal gravity signals induced by deep Earth’s processes are commonly thought to lie below the observational threshold of satellite gravity missions, as one assumes them to be small in amplitude and restricted to the longest spatial and temporal scales. However, the fast rates of surface uplift and subsidence in the retrodiction models of the mantle, and the geologic observations of epeirogenic movements provide evidence for the contrary. The modeled deep Earth signal, on the order of 5 μm/year at spatial scales of 1000 km, is on the edge of detectability by current gravimetry satellite missions, but coming into the range of detectability in future temporal gravity field solutions, suggesting the use of satellite gravity data to validate geodynamic Earth models. Importantly, the application of forward modeled dynamic mantle signals, which can be linked to geologic observables and are thus independently testable, seems to be essential for improved de-aliasing and signal separation in future gravity missions.

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*mp4 Video, Animation of the 3-D model - This animated sequence is part of a simulation carried out on SuperMUC and depicts the evolution of the mantle over the past 200 million years. The visualization illustrates how dynamic processes in the Earth’s interior affect the planet’s surface. Not only does it show the continents from different perspectives, it also portrays the convection currents that are driven by temperature differences within the mantle. In this case, the regions shown in red correspond to the hot and rising rock, while the colder, sinking regions are depicted in blue. The animation starts at present day and shows the mantle evolution backward in time. *

*© LRZ/LMU, M. Wiedemann & B. Schuberth*

*(NOTE: Should an error-message be displayed, please refresh your browser window!)*

**On-going Research/Outlook**

After these first successful retrodictions, we now plan to use this powerful methodology to systematically investigate the parameter space of mantle convection – in particular, various pressure and temperature-dependent viscosities – by checking the predicted changes in surface dynamic topography against the geologic record. In addition, a variety of seismic tomographic models, mineralogies and chemical compositions exist that we can use in different combinations as proxy for the present-day thermodynamic state of the mantle, for which many tens of simulations need to be run in the next years.

**Project Team**

Hans-Peter Bunge (PI), Lorenzo Colli, Siavash Ghelichkhan, Bernhard Schuberth *(all: Geophyics Section, Department for Earth and Environmental Sciences, Ludwig-Maximilians-Universität München)*

**References**

[1] www.geophysik.uni-muenchen.de

[2] L. Colli, H.-P. Bunge, and B. S. A. Schuberth. 2015. On retrodictions of global mantle flow with assimilated surface velocities. Geophysical Research Letters 42, 8341–8348. DOI: https://doi.org/10.1002/2015gl066001

[3] L. Colli, S. Ghelichkhan, H.-P. Bunge and J. Oeser. 2017. Retrodictions of Mid Paleogene mantle flow and dynamic topography in the Atlantic region from compressible high resolution adjoint mantle convection models: Sensitivity to deep mantle viscosity and tomographic input model. Gondwana Research 53, 252–272. DOI: https://doi.org/10.1016/j.gr.2017.04.027

[4] S. Ghelichkhan and H.-P. Bunge. 2016. The compressible adjoint equations in geodynamics: derivation and numerical assessment. Int J Geomath 7, 1–30. DOI: https://doi.org/10.1007/s13137-016-0080-5

[5] S. Ghelichkhan, M. Murböck, L. Colli, R. Pail and H.-P. Bunge. 2017. On the observability of epeirogenic movement in current and future gravity missions. Gondwana Research 53, 273–284. DOI: https://doi.org/10.1016/j.gr.2017.04.016

**Scientific Contact:**

Dr. Bernhard Schuberth

Geophysics

Dept. of Earth and Environmental Sciences

Ludwig-Maximilians-Universität München

Theresienstr. 41, D-80333 München (Germany)

e-mail: bernhard.schuberth [@] geophysik.uni-muenchen.de

http://venus.geophysik.uni-muenchen.de/~bernhard

Please see also: GCS News Flash - Earth Exhibit Comes to New York City Thanks to SuperMUC Simulations

**NOTE:** This report was first published in the book "High Performance Computing in Science and Engineering – Garching/Munich 2018":

*September 2018*