Modeling dynamic rupture in a 3D earthquake fault model (original) (raw)
Related papers
Influence of friction and fault geometry on earthquake rupture
Journal of Geophysical Research, 2000
We investigate the impact of variations in the friction and geometry on models of fault dynamics. We focus primarily on a three-dimensional continuum model with scalar displacements. Slip occurs on an embedded two-dimensional planar interface. Friction is characterized by a two-parameter rate and state law, incorporating a characteristic length for weakening, a characteristic time for healing, and a velocity-weakening steady state. As the friction parameters are varied, there is a crossover from narrow, self-healing slip pulses to crack-like solutions that heal in response to edge effects. For repeated ruptures the crack-like regime exhibits periodic or aperiodic systemwide events. The self-healing regime exhibits dynamical complexity and a broad distribution of rupture areas. The behavior can also change from periodicity or quasi-periodicity to dynamical complexity as the total fault size or the length-to-width ratio is increased. Our results for the continuum model agree qualitatively with analogous results obtained for a one-dimensional Burridõe-Knopoff model in which radiation effects are approximated by viscous dissipation. context of a three-dimensional continuum model and a one-dimensional Burridge-Knopoff model. In our studies, dynamical complexity refers to observations of a
Geophysical Journal International, 1981
In this paper we set up and simulate numerically a scalar analogue for a rupturing seismic fault plane in a three-dimensional space. The scalar analogue bears the same relation to the full vector elastic system as an SH (anti-plane strain) system bears to a P-SV (plane strain) system in two dimensions. The fault plane is embedded in a whole space of homogeneous material and behaves like a frictional surface. We allow zones of rupture to propagate out at the wave speed in various ways within the fault plane. In some cases the region of slip propagates around unbreakable obstacles within the fault. The resulting far-field pulse shapes and spectra are computed. Mathematically we set up an integral equation for the displacement on the fault. As in earlier work which addressed the two-dimensional problem the integral equation has a non-integrable kernel, but a discretized version of this function may be found numerically from the discrete version of the wave operator and a stable explicit numerical scheme is obtained.
Sensitivity of 3D rupture dynamics to fault geometry and friction parameters
We scale the various parameters de ning a 3D fault model (i.e. characteristic distance and time of a state friction law, size and aspect ratio of the fault, medium impedance) and derive two dimensionless parameters governing the typical dynamics of the fault through single or multiple ruptures. The di erent faulting regimes are illustrated by a series of numerical simulations. As the parameters are varied the model crosses over from a regime which exhibits narrow, self-healing slip pulses, to one which exhibits broad, crack-like solutions that only heal in response to edge e ects. In the crack-like regime we observe periodic systemwide events. For self-healing pulses, the system exhibits self-roughening which leads to dynamical complexity. The behavior also changes from periodicity o r quasi-periodicity t o m o re complex time sequences as the total fault size or the length to width ratio are increased. Our results are in good qualitative agreement with analogous results which we obtain for a one dimensional Burridge{Knopo model, where the variations in the sti ness of the transverse spring are related to variations in the width of an equivalent two dimensional fault, and radiation e ects are approximated by viscous dissipation.
Nucleation of rupture under slip dependent friction law: Simple models of fault zone
Journal of Geophysical Research: Solid Earth, 2002
The initiation of frictional instability is investigated for simple models of fault zone using a linearized perturbation analysis. The fault interface is assumed to obey a linear slip‐weakening law. The fault is initially prestressed uniformly at the sliding threshold. In the case of antiplane shear between two homogeneous linearly elastic media, space‐time and spectral solutions are obtained and shown to be consistent. The nucleation is characterized by (1) a long‐wavelength unstable spectrum bounded by a critical wave number; (2) an exponential growth of the unstable modes; and (3) an induced off‐fault deformation that remains trapped within a bounded zone in the vicinity of the fault. These phenomena are characterized in terms of the elastic parameters of the surrounding medium and a nucleation length that results from the coupling between the frictional interface and the bulk elasticity. These results are extended to other geometries within the same formalism and implications fo...
Slip on wavy frictional faults: Is the 3rd dimension a sticking point?
Journal of Structural Geology
The formulation for the 3D triangular displacement discontinuity boundary element method with frictional constraints is described in detail. Its accuracy in comparison to analytical solutions is then quantified. We show how this can be used to approximate stress intensity factors at the crack tips. Using this method, we go on to quantify how slip is reduced on fault surfaces with topography, where the asperities are approximated as a sinusoidal waveform, i.e. corrugations. We use stress boundary conditions (compressive) orientated such that frictional contacts shear. We show that slip reductions relative to planar faults for 2D line and 3D penny-shaped crack models are comparable within 10% when slip is perpendicular to the corrugations. Using the 3D model, we then show how slip is reduced more when corrugation wavelengths are doubled compared to the reduction due to corrugation 2 alignment with the slip direction. When slip is parallel with the corrugation alignment we show that reducing the out-of-plane stress, from the normal traction acting on the fault when planar to that resolved on a perpendicular plane, has the same effect as halving the length of the corrugation waveform in terms of slip reduction for a given amplitude. 'corrugations'. As the study of Ritz and Pollard (2012) is 2D, fracture walls shear perpendicular to the asperities on the fracture faces. The boundary conditions are set such that the two principal stresses driving shearing are both compressive, and the ratio between these is calculated empirically, based
Effective friction law for small-scale fault heterogeneity in 3D dynamic rupture
Journal of Geophysical Research, 2011
We address the problem of modeling dynamic rupture on multiscale heterogeneous faults in 3D. Under the assumption of slip-weakening friction, we numerically construct effective friction laws that integrate the effects of small-scale heterogeneity during the rupture. This homogenization process is based on the description of the initial phase of the rupture by the dominant unstable spectral mode. Its dynamics is influenced by the geometry of the fault, the static friction heterogeneities and the friction law. We first define a periodic small-scale heterogeneous model, introducing heterogeneity in the distribution of the static friction coefficient. We then describe a method for constructing this effective friction law. Applying this new law homogeneously on the fault permits to reproduce the dynamic evolution of the heterogeneous fault. Furthermore, we show that the effective friction law can be used to replace small-scale heterogeneities in two-scale heterogeneous models, while preserving their effects. We study three kinds of two-scale models, with growing complexity: first periodic at both scales, then periodic only at small scale, and finally irregular at both scales. This homogenization method can be adapted to the case where the heterogeneity is introduced in the initial stress rather than in the static friction value. Finally, we show in a simple example that the effective friction law permits to reproduce the transition between subshear and supershear rupture propagation, originally produced by heterogeneities on the fault.
We estimate the critical slip-weakening distance on earthquake faults by using a new approach, which is independent of the estimate of fracture energy or radiated seismic energy. The approach is to find a physically based relation between the breakdown time of shear stress T b , the time of peak slip-velocity T pv , and the slip-weakening distance D c , from the time histories of shear stress, slip, and slip velocity at each point on the fault, which can be obtained from dynamic rupture calculations using a simple slip-weakening friction law. Numerical calculations are carried out for a dynamic shear crack propagating either spontaneously or at a fixed rupture velocity on a vertical fault located in a 3D half-space and a more realistic horizontally layered structure, with finite-difference schemes. The results show that T pv is well correlated with T b for faults even with a heterogeneous stress-drop distribution, except at locations near strong barriers and the fault edges. We also investigate this relation for different types of slip-weakening behavior.
Dynamic Rupture in a 3-D Particle-based Simulation of a Rough Planar Fault
Pure and Applied Geophysics, 2006
An appreciation of the physical mechanisms which cause observed seismicity complexity is fundamental to the understanding of the temporal behaviour of faults and single slip events. Numerical simulation of fault slip can provide insights into fault processes by allowing exploration of parameter spaces which influence microscopic and macroscopic physics of processes which may lead towards an answer to those questions. Particle-based models such as the Lattice Solid Model have been used previously for the simulation of stick-slip dynamics of faults, although mainly in two dimensions. Recent increases in the power of computers and the ability to use the power of parallel computer systems have made it possible to extend particle-based fault simulations to three dimensions. In this paper a particlebased numerical model of a rough planar fault embedded between two elastic blocks in three dimensions is presented. A very simple friction law without any rate dependency and no spatial heterogeneity in the intrinsic coefficient of friction is used in the model. To simulate earthquake dynamics the model is sheared in a direction parallel to the fault plane with a constant velocity at the driving edges. Spontaneous slip occurs on the fault when the shear stress is large enough to overcome the frictional forces on the fault. Slip events with a wide range of event sizes are observed. Investigation of the temporal evolution and spatial distribution of slip during each event shows a high degree of variability between the events. In some of the larger events highly complex slip patterns are observed.
Mechanics and interpretations of fault slip
Earthquakes: Radiated Energy and the Physics of Faulting, 2006
Profiles of fault slip reflect the redistribution of strain energy associated with faulting. Real slip profiles typically are irregular and commonly are drawn as piecewise linear, although the data permit other interpretations. In a linear elastic body, stress singularities would occur at the ends of profile segments along which slip varies linearly, and strain incompatibilities would occur where the third derivative of the slip is discontinuous: concentrated fracturing (energy sinks) along a fault should arise there. Elastic solutions for interacting faults with uniform strengths yield slip profiles consistent with the first-order shapes of many observed slip profiles, including those with near-linear tapers, which are difficult to explain by on-fault effects. Slip data collected and analyzed in conjunction with information on both along-fault fracturing and neighboring faults can lead to improved insight into how faults slip, propagate, and dissipate energy.. IntRoduCtIon Slip, the relative displacement of the walls of a fault, defines faulting, provides a quantitative measure of a fault's mechanical behavior, and manifests the redistribution of strain energy in an earthquake [e.g., Scholz, 2002]. Slip typically is irregular along fault traces both for single earthquakes and for cumulative fault slip [e.g., dawers et al., 993; nicol et al., 996 and references therein; Shipton and Cowie, 200; Aydin and Kalafat, 2002; d'Alessio and Martel, 2005]. Slip profiles commonly are interpreted as piecewise linear, especially near fault trace tips, with line segments connecting, passing through, or enveloping discrete slip data [e.g., Peacock and Sanderson, 994; Manighetti et al., 200]. In addition, slip distributions commonly are presented or analyzed without accounting for fault interaction, even though the distance between faults commonly is much less than the fault trace length and fault interaction could be expected [Segall and Pollard, 980]. We compare observations of slip to theoretical predictions involving one, two, or three faults to assess what slip profiles might reveal about fault mechanics, fracturing accompanying slip (energy sinks), and fault interaction. In particular, we address near-linear tapers in slip along interacting faults, and profiles with flat midsections ("quasi-elliptical profiles"), topics not addressed explicitly by other mechanics studies [Willemse et al., 996; Willemse, 997; Crider and Pollard, 998; Maerten et al., 999; 2002]. 2. obSERvAtIonS of SlIP We consider the extensive data of Manighetti et al. [200, 2004], who compiled cumulative slip profiles from 255 normal faults along active rifts of East Africa (fig.). they classified the profiles into eight sets (fig. 2) and emphasized their piecewise linear character: 72% have long, roughly linear portions, ~60% taper nearly linearly towards a fault trace end, and ~5% have roughly flat tops. the spacing of the subparallel fault traces is generally small relative to the trace length. these profiles reflect slip accumulation over millions of years but resemble slip distributions during single earthquakes [see also Schwartz and Coppersmith, 984]. 3. MEChAnICAl ModElS We model slip (D) along faults idealized as two-dimensional shear fractures in infinite, uniform, isotropic, isother-title Geophysical Monograph Series
2011
We explore experimentally and theoretically how fault edges may affect earthquake and slip dynamics, as faults are intrinsically heterogeneous with common occurrences of jogs, edges and steps. In the presented experiments and accompanying theoretical model, shear loads are applied to the edge of one of two flat blocks in frictional contact that form a fault analog. We show that slip occurs via a sequence of rapid rupture events that initiate from the loading edge and are arrested after propagating a finite distance. This event succession extends the slip size, transfers the applied shear across the block, and causes progressively larger changes of the contact area along the contact surface. This sequence of events dynamically forms a hard asperity near the loading edge and largely reduces the contact area beyond. These sequences of rapid events culminate in slow slip events that precede a major, unarrested slip event along the entire contact surface. We show that the 1998 M5.0 Sendai and 1995 Off-Etorofu Earthquake sequences may correspond to this scenario. Our work demonstrates, qualitatively, how a simple deviation from uniform shear loading can significantly affect both earthquake nucleation processes and how fault complexity develops.