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Authors:  Tinti, Elisa^{*} 
Title:  THE MECHANICS OF SEISMIC SOURCE: DYNAMICALLY CONSISTENT MODELS OF EARTHQUAKE RUPTURE 
Issue Date:  2005 
Keywords:  Earthquake 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 2D 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 nonuniform 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 2D inplane
crack obeying to either slip weakening (SW) or rate and statedependent 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 elastodynamic 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 slipweakening behavior. In order to
remove its singularity we apply a convolution with a triangular function and
obtain a regularized source time function called “regularized 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 3D 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. 
Appears in Collections:  Theses 04.06.03. Earthquake source and dynamics

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