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\begin{document}

\title{A three-dimensional numerical model of tectonic plates that develop due
to a stress-history dependent rheology}



\author[1]{Masaki Ogawa}%
\author[2]{Takehiro Miyagoshi}%
\author[3]{Masanori Kameyama}%
\affil[1]{University of Tokyo}%
\affil[2]{Institute for Research on Earth Evolution, Japan Agency for Marine-Earth Science and Technology}%
\affil[3]{Ehime University}%


\vspace{-1em}



  
  \date{June 17, 2024}


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\begin{abstract}
We present a three-dimensional numerical model of tectonic plates that
self-consistently develop in the convecting mantle. The viscosity
depends on stress-history as well as temperature. The lithosphere
develops as the upper highly viscous part of the thermal boundary layer
along the surface boundary owing to a strong dependence of the viscosity
on temperature. When the stress S exceeds a threshold Sp in the
lithosphere, however, we assumed that the viscosity drops by orders of
magnitude and keeps the low value, even when S is reduced below Sp,
provided that S remains higher than the other threshold Sm (\textless{}
Sp). Sp corresponds to the rupture strength of the tectonic plates,
while Sm to that at plate margins. The viscosity is a two-valued
function of the stress S in the range of (Sm, Sp), and which of the two
values the lithosphere chooses is determined by whether or not S has
exceeded Sp in the past. When the model parameters are tuned so that the
stress in the lithosphere stays in the range, the lithosphere is rifted
into several highly viscous pieces, or tectonic plates, separated by
narrow plate margins where the viscosity takes the lower value, and the
tectonic plates rigidly and stably move and occasionally rotate for
several hundred million years or longer. (See the planform of the plate
motion shown in the figure. The arrows show the velocity, while the
color shows the relative viscosity on the surface.) Because of the
rather stable plate motion, the heat flow decreases with the distance
from the spreading centers L in their vicinity as 1/sqrt(L), and the
secondary convection occurs beneath the plates in the form of
two-dimensional rolls with their axes aligned with the direction of
plate motions.%
\end{abstract}%



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