ENVIRONMENT AND ENERGY

Much of what one refers to as geological activity of the Earth arises from convective processes within the Earth’s mantle that transport heat from the deep interior of our planet to the surface. One of the major challenges in the geosciences is to constrain the distribution and magnitude of the resulting vast forces that drive plate tectonics. Mantle flow also provides boundary conditions - thermal and mechanical - to other key elements of the Earth system (e.g., geodesy, geodynamo/geomagnetism). This makes fluid dynamic studies of the mantle essential to our understanding of how the entire planet works. In a long-term effort, scientists at the Ludwig-Maximilians-Universität München strive for improved computational models of the Earth's deep interior. To assess the quality of the models against Earth observations (e.g., geologic information) they run inverse models to track mantle flow back into the past.

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].

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.