Revisiting force balance on subduction zones: the missing bridge to numerical simulations

Subduction zone geodynamics have been a primary area of focus since the early days of plate tectonics theory. Initial approaches using analytical solutions sought to understand the fundamental driving forces, moment balances, and energetics governing oceanic plate subduction. Despite the limitations of scarce geophysical imaging, limited geological sampling, and emerging numerical techniques, these studies provided the foundations of modern geodynamics. As numerical techniques improved, power-law rheologies and complex geological processes were integrated into various codes. These provided more realistic simulations to understand a wide variety of regions on Earth, but they are rarely presented in the context of classical physical approaches. Nowadays, a unique opportunity exists to revisit these classical frameworks, aided by improved subducting slab imaging, an excellent geological record, and a deeper understanding of slab dynamics across active and ancient subduction zones.

In this work, a simplified but physically transparent framework is developed to revisit the force/moment balance, energetic conditions, and dissipation analyses governing slab dynamics. For this purpose, three representative slab geometries (steep, normal, and flat) were selected based on their dip below 40 km depth, where slab behavior is dominated by internal negative buoyancy and viscous lifting forces from the mantle. Slab pull was estimated by varying density contrasts and thickness, while viscous forces were derived from semi-analytical Stokes flow solutions to resolve pressure distributions along the slab surface. Gravitational potential energy changes were calculated to test whether internal density variations (e.g., eclogitization) and crustal thickening from oceanic plateaus drive changes in geometry.

Results show that mantle wedge suction can counteract slab weight in a flat subduction setting, while increased density from eclogitization destabilizes flat slabs and promotes steepening, linking moment balance and buoyancy to the global diversity of slab dips. Total energy dissipation is mainly controlled by mantle wedge flow, with low-angle and flat subduction representing the most dissipative configurations. Once moment balance allows, these tend to evolve toward steeper, more energetically stable states. Slab flattening occurs with increased buoyancy, higher convergence velocities, and greater mantle viscosities, producing flattening within 10–30 Myr. Conversely, reduced buoyancy, slower convergence, and lower viscosities favor steepening and slab rollback on comparable or shorter timescales of 5–10 Myr. This integrated and physically transparent analysis is consistent with the development of arc magmas on western margins of the Americas and provides a clear perspective to explain the diverse slab morphologies observed on Earth.