Mantle convection models featuring plate tectonic behavior: An overview of methods and progress

Arguably, the presence of plate-tectonic-type surface motion for periods that endure over hundreds of millions of years is the primary feature a mantle convection model must possess in order to be considered Earth-like. From the early days of mantle dynamics modeling, research has been dedicated to understanding how mantle convection produces the first order observations of plate tectonics as well as how the plates and deep mantle interact. Fledgling studies of the effect of plates on the mantle recognized the ability of imposed plate-scale surface motion to influence global temperatures and heat flux and organize convective planform. Later studies featuring model plates with dynamically determined velocities discovered that the interaction between convection and the plates could result in cyclic plate motion patterns and other time-dependent behavior that was not manifested in systems in which dynamic plates were absent. Focussing on different aspects of system realism (with respect to terrestrial mantle convection) has spawned multiple approaches for modeling convection with dynamic integrated plates. In broadest terms, the two main approaches can be categorized as rheological modeling methods and methods utilizing evolving surface boundary conditions. Over the past dozen years, studies focussing on the former approach have steadily made progress in modeling the self-generation of plate tectonics from convection dynamics. Continual advances have been encouraging, and a consensus is beginning to form regarding the necessary requirements for obtaining the primary elements of plate-like surface motion. However, despite significant progress, the generation of plates over long periods has not yet been modeled with Earth-like convective vigor. In contrast, models utilizing dynamically determined boundary conditions to achieve plate-like surface motion have relatively little difficulty with emulating terrestrial convective vigor or simulations of billions of years. Instead, their weakness is more fundamental; they can only provide insight into the reciprocating dynamics of the mantle and plates once the existence of the plates is assumed and they cannot model any aspects of the dynamics responsible for the origin of the plates. This paper briefly reviews the evolution of mantle convection models featuring plates and examines the progress that has been made in our understanding of the feedback between the mantle and plate tectonics through the use of both rheological and boundary condition modeling methods. Common findings, recent advances and unbridged problems are identified and discussed.

Research highlights
► The history of incorporating plates in mantle convection models is reviewed.
► Two main modeling approaches are considered.
► Boundary condition methods are compared to rheological plate modeling methods.
► Self-consistent plate generation models are compared to force-balance models.
► Particular emphasis is placed on the findings of the past decade.