Energy budget analysis of fault motion in a granular rock box simulation

Here, we present the energy budget analysis that links seismic focal mechanisms to the development of geological structures in numerical granular rock box experiments, utilizing a discrete element method simulation approach. The model simulates the horizontal shortening of a thin 3D granular rock layer on a geological-scale (100 km $\times$ 0.25 km $\times$ 2 km), with a maximum element radius of 12.5 m. This simulation reproduces the millimeter-scale fault displacements caused by the rapid and intermittent motions of elements generating elastic waves, that is, virtual earthquakes. The simulation also captures early postseismic processes occurring within several tens of seconds, during which popup structure between the active faults is uplifted. We analyzed over 190 earthquake events during the simulation, with a total shortening length of 14.72 m. The change in energy balance starts with a local fault potential drop that generates the main shock, followed by a regional potential release induced by propagated waves. Statistical analysis reveals positive correlations, ranging from linear to quadratic, between the magnitudes of energy changes and fault slip displacement. Notably, approximately 0.01 % to 60 % of the local contact potential drop in the seismogenic fault is converted into kinetic wave energy, and the efficiency of this conversion increases with the earthquake size. Our results reveal that the uplift energy of the popup structure, which considerably exceeds the wave energy by several orders of magnitude, cannot be explained solely by the local seismogenic fault potential release. Instead, off-fault regional potential release should also be taken into account. We also demonstrate the scaling law for earthquake energy and seismic moment. Our findings suggest that the inherent diversity of virtual earthquakes partially captures earthquake behaviors.