Toward New Methods for modeling complex mantle dynamics
Laura Eberhard1,2, John Hernlund 1
11Earth-Life Science Institute, Tokyo Institute of Technology
2Westfälische Wilhelms-Universität Münster, Germany

Frontier of Understanding Earth‘s Interior and Dynamics
Monday, August 8, 2022 – Tuesday, August 9, 2022
Tohoku University

Approach: Modeling the Mantle as a rock rather than a fluid

Scientific Research Questions:
How does the rocky majority of the Earth’s interior move and deform to produce
plate tectonics, earthquakes, volcanic eruptions, circulate its inventory of elements
in and out and create suitable conditions for the origin and evolution of life?

The “fluid-like mantle “: A historically useful abstraction

Classic conceptual sketch of fluid-like motions in the rocky mantle that would accompany tectonic activities

Fluid-like thermal convection in the Earth’s mantle is an old idea brought into prominence by Arthur Holmes,
Felix Vening Meinesz, and others. It followed on the heels of pioneering laboratory and theoretical work on
thermal convection in fluids by Bénard, Rayleigh, Jeffreys and others. This rough analogy between themovements of the thick, rocky mantle shell of the Earth and thermal convection in ordinary fluids came to beknown as “mantle convection”.

Weakness of such a simplistic analogue
Mantle convection theory is presently based on experimental analogue study of fluids in the laboratory and innumerical models. Such an approach is easy to implement, deterministic, and reproducible, which carries benefits for scientific coherency and consistency. The critical weakness is that such a simplistic analogue is intrinsicallyincapable of capturing important behaviors of rock and explaining key observations.

The “fluid-like” conception of mantle convection supposes that sub-grain processes such as vacancy diffusion
directly scale up to ~100-1000 km, without any non-linear interactions, feedbacks, or other complexities manifestingat intermediate scales.

Idea: Stochastic Mantle Dynamics
Probability that particle moves in a given direction is a function of density relative to surrounding
particles, viscosity, coupling to neighboring particles, etc..
At each time step, the random number is generated and then the probability function applies themotion. This allows freedom to add numerous complexities, such as shear zones, hysteresis, thatare very difficult in fluid like simulations.

In reality the Earth’s mantle is way more compex…the description of solid rocks as “a fluid” has limitations inaccounting for observations bearing on the physical and chemical state of the interior.

1.Problem: Plate tectonics vs. fluid mantle convection
Observations show that fluid-like convection isa poor analogue for the observed behavior of
the crust and lithosphere.
Mantle convection models utilize unrealistic fluid-like rheologies that mimic instantaneous
aspects of plate tectonics, like stressdependent viscosity, but fail to capture therealistic temporal evolution of rock-like straindependent rheologies.
Therefore, there are inconsistencies between fluid mantle thermal convection and plate
tectonics.

Ballmer et al.
(2017)
Step 1: Reproduce simpler fluid-like behavior, convection, etc.

Step 2: Make a rigorous proof that the Monte Carlo simulation converges on the exact solution inorder to derive important parameters
Step 3: Begin adding complexities and treating the material like rocks rather than fluids
Step 4: Incorporate multi-scale effects (group movements of particles, transfer information, andother factors between scales)

2. Problem: Mixing /Preservation of Heterogeneities
Takeaway Message
Developing models that explain the complex dynamic of the mantle is most probably one of the most challenging
problems in all geophysics. However, we really need to think "outside the box” and develop some new approaches
that are better suited for approaching the question of realistic Earth rheology to better understand our planet. The
old idea of fluid-like thermal convection in the Earth’s mantle, although having some benefits, is ready for an update.

A hallmark of fluid-like thermal convection is the efficiency of mixing heterogeneities, via a process of “stretchingand folding.” In a fluid-like convection model one may vary 2 parameters: viscosity and density. Scientists tried
just about every combination of both, assigning an anomalous viscosity and/or density to compositionally distinct
material in an attempt to alter its mixing/recycling and match geochemical observations. No single model thereis satisfactorily explains all the geochemical observations.

References
Bercovici,D (2000) et al. The Relation Between Mantle Dynamics and Plate Tectonics: A PrimerHernlund,J (2019) Grand Challenge: Addressing an Inconvenient Truth About Mantle Rheology