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Authors: Tinti, Elisa 
Issue Date: 2005
Keywords: Earthquake dynamics
Subject Classification04. Solid Earth::04.06. Seismology::04.06.03. Earthquake source and dynamics 
Abstract: In the first chapter we review the theoretical modeling of a dynamic rupture propagation governed by friction processes. We introduce two of the most commonly used constitutive laws in the literature: slip weakening law and rate and state law. We present the analytical expressions of these frictions laws and we discuss the different competing physical mechanisms which contribute to dynamic fault weakening during earthquakes. In particular, we describe the dynamic traction and the slip velocity evolution within the cohesive zone during a 2-D inplane dynamic rupture using rate and state dependent constitutive laws. In the second chapter we show how the rate and state constitutive laws allow a quantitative description of the dynamic rupture growth. These modeling results help understanding the physical interpretation of the breakdown process and the weakening mechanisms. We compare the time histories of slip velocity, state variable and total dynamic traction to investigate the temporal evolution of slip acceleration and stress drop during the breakdown time. Because the adopted analytical expression for the state variable evolution controls the slip velocity time histories, we test different evolution laws to investigate slip duration and the healing mechanisms. We will discuss how the direct effect of friction and the friction behavior at high slip rates affect the weakening and healing mechanisms. In the third chapter we investigate the effects of non-uniform distribution of constitutive parameters of rate and state laws on the 2D dynamic rupture propagations. We use the characterization of different frictional regimes proposed by Boatwright and Cocco (1996), which is based on different values of the constitutive parameters a, b and L (these are the parameters defining rate and state constitutive laws). The results involve interesting implications for slip duration and fracture energy. In the fourth chapter we check the possibility to constrain and to estimate the critical slip weakening distance from slip velocity functions, following a recent idea of Mikumo et al.(2003). Because of the poor knowledge of the scaling relation between dynamic parameters inferred from laboratory experiments and from real faults, it is still open to debate the actual dimensions of physical parameters characterizing the seismic source. Particularly, the range of real Dc values is still unknown. We model the dynamic propagation of a 2-D in-plane crack obeying to either slip weakening (SW) or rate- and state-dependent friction laws (R&S). Therefore we compare the value of slip weakening distance (Dc), adopted or estimated from the traction versus slip curves, with the critical slip distance measured as the slip at the time of peak slip velocity (D' c). In the fifth chapter we compute the temporal evolution of traction by solving the elasto-dynamic equation and by using the slip velocity history as aboundary condition on the fault plane. We employ a 3D finite difference algorithm. In this chapter we do not consider a fully dynamic model because we do not assume any constitutive law, but we infer the dynamic parameters and the traction evolution from kinematic models. We use different source time functions to derive a suite of kinematic source models to image the spatial distribution of dynamic and breakdown stress drop, strength excess and critical slip weakening distance (Dc). Therefore we compare the inferred dynamic parameters trying to answer the following questions: Can we constrain the actual values of fundamental dynamic parameters from kinematic models? If the kinematic slip velocity histories affect the inferred dynamic parameters, is it still possible to constrain the dynamic source parameters of real earthquakes? We suggest that source time functions compatible with earthquake dynamics have to be used to infer the traction time history. For this reason, we propose a new source time function to be used in kinematic modelling of ground motion time histories, which is consistent with dynamic propagation of earthquake ruptures and makes feasible the dynamic interpretation of kinematic slip models. This function is derived from a source time function first proposed by Yoffe (1951), which yields a traction evolution showing a slip-weakening behavior. In order to remove its singularity we apply a convolution with a triangular function and obtain a regularized source time function called ‚Äúregularized Yoffe'' function. Using this analytical function we examine the relation between kinematic parameters, such as peak slip velocities and slip duration, and dynamic parameters, such as slip weakening distance and breakdown stress drop. In the sixth chapter we estimate fracture energy on extended faults for several recent earthquakes (having moment magnitudes between 5.6 and 7.2) by retrieving dynamic traction evolution at each point on the fault plane from slip history imaged by inverting ground motion waveforms. We define the breakdown work (Wb) as the excess of work over some minimum traction level achieved during slip. Wb is equivalent to "seismological" fracture energy (G) in previous investigations. We employ a 3-D finite difference algorithm to compute the dynamic traction evolution in the time domain during the earthquake rupture. We estimate Wb by calculating the scalar product between dynamic traction and slip velocity vectors. Finally we compare our inferred values with geologic surface energies.
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