Abstract
In this work we present a 3D Finite Difference numerical method to model the dynamic spontaneous propagation of an earthquake rupture on planar faults in an elastic half-space. We implement the Traction-at-Split-Nodes fault boundary condition for a system of faults, either vertical or oblique, using different constitutive laws. We can adopt both a slip-weakening law to prescribe the traction evolution within the breakdown zone or rate- and state-dependent friction laws, which involve the choice of an evolution relation for the state variable. Our numerical procedure allows the use of oblique and heterogeneous distribution of initial stress and allows the rake rotation. This implies that the two components of slip velocity and total dynamic traction are coupled together to satisfy, in norm, the adopted constitutive law. The simulations presented in this study show that the rupture acceleration to super-shear crack speeds occurs along the direction of the imposed initial stress; the rupture front velocity along the perpendicular direction is slower than that along the pre-stress direction. Depending on the position on the fault plane the orientation of instantaneous total dynamic traction can change with time with respect to the imposed initial stress direction. These temporal rake rotations depend on the amplitude of initial stress and on its distribution on the fault plane. They also depend on the curvature and direction of the rupture front with respect to the imposed initial stress direction: this explains why rake rotations are mostly located near the rupture front and within the cohesive zone.
Highlights
The understanding of earthquake rupture propagation and the seismic wave generation process is an important task that has focused scientific research in recent years
In this study we present and discuss the main features and several numerical simulations performed with a fully 3D spontaneous dynamic rupture model in which the crack propagation and the dynamic traction evolution are governed by assigned constitutive laws
In fig. 9a-f we present the results of the simulation performed by using the SW law: we show the slip velocity and the total dynamic traction evolution on the fault plane at three different time steps
Summary
The understanding of earthquake rupture propagation and the seismic wave generation process is an important task that has focused scientific research in recent years. With the adoption of such a conventional-grid scheme a fault surface can be represented as by a class of split nodes, represented as disjoint grid points in contact This approach is called the Traction-at-Split-Nodes (TSN) Fault Boundary Conditions (FBC) and it has been implemented in 2D by Andrews (1973) and in 3D by Day (1977, 1982a,b), Archuleta and Day (1980), Andrews (1999). The possibility to compute fault slip, fault slip velocity and traction at the same grid point allows the specification of either slipor rate- and state-dependent constitutive laws, as we will discuss Another important assumption commonly required in numerical procedures is the choice of the amplitude and the direction of the initial stress on the fault plane. We allow both components of slip to be non zero; they are mutually coupled by the assumed constitutive relation
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