Quantitative Analysis and Scaling Relationship in 2D and 3D Numerical Modeling of Mantle Plume-Lithosphere Interaction

Mantle plume constitutes a crucial component in geodynamics, linking the deep interior of the Earth to the surficial tectonic plate. Numerical simulation holds significant importance in exploring plume dynamics and its interaction with the overlying lithosphere. Although the 3D model can more effectively capture the geometric characteristics of the plume, the 2D simulation demonstrates remarkable computational efficiency in large-scale and high-resolution situations, especially when complex geological processes are in play. As a result, both 2D and 3D models have been widely utilized in previous numerical research endeavors. Nevertheless, with the same parameters, these two types of models may produce distinct outcomes. The key issue then becomes how to establish the scaling relationship between the 2D and 3D models. In this regard, we conduct a systematic comparison of the 2D and 3D mantle plume evolution within two different scenarios. In the first scenario where there is only a plume head, for the 2D plume to align with the 3D model, it should possess a relatively smaller diameter (ranging from 65% to 100%) and a lower temperature (decreased by 10 - 50 K). In the second scenario where there is a continuous plume tail, the 2D plume tail needs to have a much smaller diameter (ranging from 30% to 45%) yet a slightly higher temperature (increased by 20 - 100 K) to approximate the 3D result. Further analytical investigations reveal that such differences are mainly governed by the conservation of area in the 2D case versus the conservation of volume in the 3D case for plume materials. These numerical and analytical findings establish quantitative relationships between the 2D and 3D plume models, which offer a theoretical basis not only for interpreting previous models but also for guiding future studies.