Determination of constitutive relations of fault slip based on seismic wave analysis

Constitutive laws define the boundary conditions on fault plane and govern many aspects of earthquake failure. Although several constitutive laws have been formulated based on laboratory rock experiments and applied to theoretical studies in various fields, no actual relation during a natural earthquake has been determined. The 1995 Kobe earthquake is suitable for detailed kinematic analysis, and this enables the first evaluation of constitutive relations for a natural earthquake. In this study, we determine spatiotemporal slip distribution on an assumed fault plane of the 1995 Kobe earthquake by waveform inversion and then solve elastodynamic equations using a finite difference method to determine the stress distribution and constitutive relations on the fault plane. An inversion method based on Bayes theorem is employed to obtain a spatiotemporal slip distribution, and enables us to ensure the objective uniqueness of the solution with numerous parameters and smoothing constraints. This slip distribution is then used as part of the boundary condition in the finite difference calculation The time histories of slip and shear stress obtained then provide a constitutive relation at each point on the fault plane. They show slip weakening relations almost everywhere on the fault plane, while slip rate dependency is not clear. The slip weakening behavior has a clear depth dependency indicating that the slip weakening rate (d tau/du) is smaller in the shallow crust than that in the deep crust. This may be associated with the paucity of shallow seismicity observed in the source region of this earthquake as reported for many mature fault systems.