General Solution Scaling Relations in Linear Elastic Dynamic Rupture Models

Abstract Dynamic rupture models have been widely used to enhance our understanding of earthquake processes and associated hazards. A commonly held insight among modelers is that if the initial stress, rheological parameters, and space and time coordinates are scaled by certain factors in a specific manner, the solution will scale accordingly and remain similar. While this principle has been applied in numerical simulations, particularly to optimize parameter studies and interpret results through non‐dimensionalization, its general applicability to more complex modeling scenarios has not been rigorously established. In this study, we provide a proof of the generality of solution scaling in linear elastic dynamic rupture problems using a boundary integral equation formulation. We demonstrate how dynamic rupture solutions, including slip and traction evolution, scale with initial stress, fault rheology parameters, space and time coordinates, and elastic medium properties. The proof holds under arbitrary complexity in fault geometry and medium velocity structure, as well as with heterogeneous on‐fault rheology parameters, provided that solution uniqueness is satisfied. We consider four types of fault rheology: linear slip‐weakening, rate‐and‐state friction, linear time‐weakening, and general composite rheology with different slip rate dependencies at different slip rates. Our results have practical implications for the design of large‐scale simulation campaigns and for interpreting laboratory dynamic rupture experiments. More broadly, our work provides theoretical support for widely used scaling practices in the dynamic rupture modeling community by establishing a mathematical foundation.