S43E-01 INVITED
Dynamic Earthquake Source Models – From Idealizations to Complexity with Interaction between Scales
Earthquakes are complex (fractal) phenomena occurring in a complex medium on a complex (fractal) fault
network with dynamic interactions between the smallest and largest length scales.
The first dynamic model of an earthquake source (Kostrov, 1964) was a growing crack, in which rupture
velocity is determined such that energy flux into the singular crack tip equals prescribed fracture energy. The
singular crack tip could be generalized to a finite cohesive zone in which slip grows to a critical value, D_c.
The motivation of this popular slip-weakening model was to have a continuous solution that could be
calculated numerically. Growth of the large-scale solution depends on the behavior in the small cohesive
zone, which remains elusive to observation. Laboratory observations of friction on prepared surfaces led to
the rate-state friction law. The observed characteristic length scale, L, was proportional to the grit size
used to grind the surface, that is, to the wavelength at which the surface becomes rough. Natural faults,
however, are rough at all scales, so that the characteristic length, L, of the rate-state friction law is
undefined.
Inversions of observed ground motion reveal slip functions with self-similar irregularity, but the inversions are
incapable of revealing the smaller scale processes that produce the fractal character.
A more realistic model might start by representing the fault as a pair of rough surfaces in contact, each
surface having self-similar deviation from planarity. The large-scale solution will depend on variations at
length scales smaller than the slip, which is typically 10-4 times the rupture length. Reality is likely even
more complex than that, involving interaction of faults and cracks of all orientations, forming a fractal network.
Slip can occur at a triple junction of faults with different orientations, but each increment of slip increases the
geometric incompatibility and makes the junction a stronger barrier. After a number of events, fresh fracture
must occur to create a new junction. The large-scale solution depends on small-scale incompatibility at the
junction.
Understanding the interaction between different scales is an enormous challenge, both observationally and
computationally.
S43E-02
Off-Fault Plasticity Influence on Rupture Dynamics and Ground Motions
A fractured medium, such as a damage zone surrounding a fault, cannot behave fully elastically, but rather plastically. We perform 2D and 3D dynamic rupture simulations in such a medium, inside which the shear stresses are bounded. We computed the 2D in-plane, anti-plane, and, for the first time, more realistic 3D geometries. Some general features hold in all cases. Compared to the full elasto-dynamic case, the slip velocity is now bounded, the rupture speed is slightly decreased, and the overall final slip shape shows differences. The energy lost outside the fault increases linearly with the rupture propagation length. This energy is dissipated close to the crack tip, and hence has a lot of consequences on the energy balance of the rupture. We show that the rupture cannot break barriers as easily as a pure elastic crack does, favoring the spontaneous arrest of the rupture. The plasticity stabilizes the rupture instability, scaling the fracture energy with the growing size of the crack.Taking this phenomenon into account for earthquakes should lead to reduce the spatial variability of the fracture energy, that is usually needed to stop the rupture. We also show that the plasticity reduces the high frequency content of ground motions. Close to the fault, it does reduce the peak ground velocity and peak ground acceleration by several tens of percents.
S43E-03
Numerical Model for the Effect of Off-Fault Damage on Dynamic Rupture
Real earthquake faults are surrounded by fractured zones whose effect on earthquake rupture is investigated using a micro-mechanics based damage constitutive description, for the off-fault material, with friction on the fault governed by coulomb like slip weakening law. The micro-mechanics based damage model is an extension of the Ashby and Sammis (1990) formulation. The model was tested with a series of dynamic photoelasticity experiments of a dynamic shear rupture along a frictional interface bounded on one side by an intact material and on the other side by a damaged material of the same or different undamaged elastic properties. The main effect of off-fault damage is that it introduces an anelastic asymmetry in rupture propagation. On the side of the rupture where damage is in tension the bulk damage effects dominate over the local elastic effects leading to reduction in rupture velocity or in some cases complete termination. On the compressional side damage has little effect on the rupture and the local elastic effect dominates.
S43E-04 INVITED
Some Characteristics of Supershear Ruptures
Recent studies show that earthquake faults may rupture at speeds exceeding the shear wave velocity of rocks. We report that fault segments where supershear rupture has been observed display some specific charcateristics. The most striking one is the simple linear geometry of the surface breaks along these segments. Another remarkable characteristic of supershear segments is that the surface slip which is observed is almost pure strike-slip. These segments are also characterized by a specific pattern of aftershocks: The fault plane itself is remarkably quiet after the earthquake, while aftershocks cluster off the fault, on secondary structures that seem to be activated by the supershear rupture. The post-earthquake quiescence of the fault shows that friction is relatively uniform over supershear segments, whereas the activation of off-fault structures is explained by the shock wave radiation which produces high stresses over a wide zone surrounding the fault.
S43E-05
Effects of supershear rupture speed on the high-frequency content of S waves investigated using spontaneous dynamic rupture models and isochrone theory
The problem of the rupture propagation at speeds greater that shear wave velocity has received the increasing interest of theoretical and numerical studies, laboratory experiments and observations of real–world events. In this work we achieve three goals: (1) We demonstrate that crack tips governed by friction laws including slip–weakening, rate– and state–dependent laws, and thermal pressurization of pore fluids, propagating at super–shear speed have slip velocity functions with reduced high frequency content compared to crack tips traveling at sub–shear speeds. This is demonstrated using a fully dynamic, spontaneous, 3–D earthquake model, in which we calculate fault slip velocity at nine points (locations) distributed along a quarter–circle on the fault where the rupture is traveling at super–shear speed in the in–plane direction and sub–shear speed in the anti–plane direction. This holds for a fault governed by the linear slip–weakening constitutive equation, by slip–weakening with thermal pressurization of pore fluid and by rate– and state–dependent laws with thermal pressurization. The same is also true even assuming a highly heterogeneous initial shear stress field on the fault. (2) Using isochrone theory we derive a general expressions for the spectral characteristics and geometric spreading of two pulses arising from super–shear rupture, the well–known Mach wave, and a second lesser known pulse caused by rupture acceleration. (3) We demonstrate that the Mach cone amplification of high frequencies overwhelms the de–amplification of high frequency content in the slip velocity functions in super–shear ruptures. Consequently, when earthquake ruptures travel at super–shear speed, a net enhancement of high frequency radiation is expected, and the alleged "low" peak accelerations observed for the 2002 Denali and other large earthquakes are probably not caused by diminished high frequency content in the slip velocity function, as has been speculated.
S43E-06
Experimental Investigation of Radiated Ground Motion Due to Supershear Earthquake Ruptures
Recent theoretical and numerical investigation of supershear ruptures in 2D (Dunham and Archuleta, 2004 and Bhat et al., 2007) and in 3D (Dunham and Bhat, 2008) have shown that ground motion due to the passage of the Mach front is virtually unattenuated at large distances from the fault. In the 2D steady- state supershear rupture model, the Mach front carries the ground motion unattenuated to infinity. Bhat et al., 2007 estimate that the actual distance should be of the order of the depth of the seismogenic zone. This has been partly observed by Bouchon and Karabulut, 2008 who showed that the aftershocks cluster in a region away from the fault at distances comparable to the depth of the seismogenic zone after a supershear rupture. Numerical simulations of supershear earthquake ruptures by Aagaard and Heaton, 2004 also show that in the supershear regime the fault parallel component of particle velocity dominates over the fault normal one whereas in the sub-Rayleigh regime the opposite is true. These two results combined could be seen as distinguishing signatures of a supershear earthquake rupture. We characterize these two effects experimentally using laser interferometry to measure the off-fault particle velocity and high speed imaging of Photo elastic fringes to characterize super shear rupture in a laboratory earthquake setup (Xia et al., 2004, 2005). Ground motion attenuation is investigated by measuring the ratio of the fault normal and fault parallel particle velocities as a function of fault normal distance as a supershear rupture propagates along the fault. A complementary set of velocimeter measurements are also conducted to characterize ground motion associated with the passage a shear wave Mach front at various distances from the fault. Collectively, these experiments serve to reveal the nature of ground motion in the region surrounding a fault undergoing super shear rupture.
S43E-07 INVITED
Size Dependence of Strength in Materials with Self-organized Critical Pre- stress
Earthquakes occur at many length scales and they have slip that is spatially heterogeneous. This implies that earthquakes are a type of spontaneous failure within a material with strongly heterogeneous stress. We present two definitions of the strength of such a material 1) the first is the spatially averaged pre-stress of a region that fails (stress-based strength), and 2) the change in potential energy of a system in an event normalized by the potency of the event (work-based strength). We show that if the material has evolved into a state such that it can fail at any length scale (self-organized critical), then its stress-based strength can be derived from the spatial power spectrum of the pre-stress. Furthermore, the stress-based strength of the material must decrease with increasing length scale of the failure event. We describe a simple spring-block- slider model with velocity weakening friction that demonstrates these principles. We show that the work- based strength of this system has a stronger length scale dependence than the work-based strength. The key physics in this system is that slip is localized into slip pulses with chaotic behavior.
S43E-08
Accounting for Gouge-Scale Strain Localization in Dynamic Earthquake Ruptures
We study the impact of gouge-scale shear strain localization in models of fault-scale earthquake ruptures. We account for strain localization using Shear Transformation Zone (STZ) Theory, a continuum approximation for plastic deformation in amorphous materials. STZ Theory ties fault weakening to an effective disorder temperature. While the effective temperature is distinct from thermal temperature, it will evolve in a similar manner and we include shear heating, diffusion, and relaxation terms in its governing partial differential equation. Strain localization is incorporated into the dynamic rupture model by resolving the effective temperature dynamics on a spatial grid spanning the width of the fault zone. This approach differs from the common practice of modeling fault dynamics with a slip-weakening or rate and state friction law, as the STZ law dynamically chooses how to distribute shear strain at the gouge scale. Localization of slip alters the spontaneous propagation of elastodynamic ruptures. Ruptures where strain localizes exhibit larger peak slip rates and stress drops, decreased shear stress at which supershear rupture can occur, and ruptures can propagate with lower initial shear stresses as self-healing pulses. Our results indicate that accounting for physical processes that occur at small scales can measurably change the propagation of earthquakes at the fault scale.