Diverse preseismic creep behavior realized with various state-evolution laws: insight from dynamic earthquake cycle simulations

Abstract Understanding the preseismic behavior of faults before large earthquakes is crucial. Previous quasistatic and quasidynamic modeling of nucleation with rate- and state-dependent friction (RSF) has reported diverse preseismic creep behaviors depending on the choice of a state-evolution law. However, a dynamic earthquake cycle simulation (ECS), which yields a more realistic solution, exhibits different results. Thus far, preseismic behavior in the dynamic ECS has been examined only for the aging law (AG). In this study, we investigated it for a linear RSF fault embedded in a two-dimensional linearly elastic infinite medium using a series of state-evolution laws. With AG and the Nagata law (NGT), the preseismic moment rate $$\text{d}M/\text{d}t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>d</mml:mtext> <mml:mi>M</mml:mi> <mml:mo>/</mml:mo> <mml:mtext>d</mml:mtext> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> was inversely proportional to the time-to-failure $${t}_{\text{f}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>t</mml:mi> <mml:mtext>f</mml:mtext> </mml:msub> </mml:math> in the final stage of nucleation, where the acceleration of a compact patch occurred. In contrast, the modified slip law (MSL) exhibited an approximately $${t}_{\text{f}}^{-0.9}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>t</mml:mi> <mml:mrow> <mml:mtext>f</mml:mtext> </mml:mrow> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.9</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> acceleration. The measure of uniformity of the slip rate distribution $${V}_{\text{ave}}/{V}_{\text{max}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>ave</mml:mtext> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>max</mml:mtext> </mml:msub> </mml:mrow> </mml:math> decreased before the final stage in all cases. Subsequently, AG and NGT showed a nearly constant $${V}_{\text{ave}}/{V}_{\text{max}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>ave</mml:mtext> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>max</mml:mtext> </mml:msub> </mml:mrow> </mml:math> , whereas $${V}_{\text{ave}}/{V}_{\text{max}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>ave</mml:mtext> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>max</mml:mtext> </mml:msub> </mml:mrow> </mml:math> kept decreasing for MSL. The transition in the acceleration and localization behavior with AG and NGT can be explained by the decrease in similarity to the slip law and convergence to the constant-weakening limit. The creep front for AG migrated deeper into the seismogenic patch with acceleration. For NGT and MSL, the migration behavior is influenced by the occasional switchback of the slow rupture, where said front propagates backward from the creep front. This switchback caused a longer creeping region at the onset of the earthquake. The critical crack length derived from the energy criterion approximated the simulated nucleation size well regardless of the occurrence of switchback. The differences and similarities between the simulation results and foreshock activities before large earthquakes were discussed. Graphical Abstract