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DISS. ETH NO. 20567




A dissertation submitted to



for the degree of

Doctor of Sciences

presented by


Diplom Physikerin, Technische Universit¨t Dresden, Germany a 06 July, 1983 German accepted on the recommendation of Prof. Dr. Domenico Giardini ETH Z¨rich u Referent Dr. Luis A. Dalguer ETH Z¨rich u Korreferent Prof. Dr. Jean-Paul Ampuero California Institute of Technology Korreferent Prof. Dr. P. Martin Mai King Abdullah University of Science and Technology Korreferent ´ Prof. Dr. Raul Madariaga Ecole Normale Sup´rior e Korreferent i Abstract This dissertation concerns complexities in earthquake source dynamics and the resulting implications for seismic ground motion. Its findings are based on numerical and analytical investigations that are validated by comparison with seismic observations. The core of this work is a comprehensive set of 2D in-plane dynamic rupture simulations with a spectral element method incorporating faults. The fault rheology is governed by a velocity-and-state-dependent friction law, utilising severe velocity-weakening at high slip rates and a homogeneous initial stress state. Seismological observations, laboratory experiments, and theoretical models indicate that earthquakes can operate in different manners. We classify a diversity of rupture styles based on their stability (decaying, steady, or growing), rupture speed (subshear or supershear), healing properties (cracks or pulses), and complexity (simple or multiple fronts). Such rupture styles and their transitions depend on the state of stress and on the strength of the fault, and their identification in earthquake observations may inform about rheological parameters along active fault zones. We study the alteration of macroscopic rupture properties by off-fault energy dissipation into plastic deformation, which may be triggered by high stress concentrations at earthquake rupture fronts. Investigating in detail the energy balance and equation of motion of self-similar pulse-like ruptures, we are able to define quantitative relations between off-fault energy dissipation and macroscopic source properties. These findings contribute to a self-consistent theoretical framework for the study of the earthquake energy balance based on observable earthquake source parameters.

The emanated seismic wave fields contain signatures of rupture styles and plasticity in near-field seismograms and source spectra. The asymmetrically induced plastic strain fields result in characteristic damage patterns off the fault and contribute to the total seismic moment. Identifying the diversity of rupture patterns in real earthquakes poses an interesting observational challenge. The long-term perspective of this work is to provide physical constraints with respect to the source of earthquakes applicable in strong ground motion prediction, seismic hazard analysis, and source inversion methods.


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Natural earthquakes surround us day after day. In Switzerland alone, 500seismic events are recorded annually. Statistically speaking, only about 10 of these excite strong enough shaking to be felt. Globally, only about 10 earthquakes exceeding magnitude 7 are recorded every year. Many of these Big Ones occur in sparsely populated regions or in the middle of oceans, and unless a tsunami is triggered, they pass by unnoticed by most of the Earth’s population. Nonetheless, the relatively rare, highly destructive Black Swan events, striking unpredictably and with catastrophic consequences for human life and property, challenge humanity worldwide. Recent large earthquakes dramatically illustrated our limited state of knowledge on what causes earthquakes and how they operate. For example, the catastrophic Tohoku-Oki earthquake (Mw 9.0) in March 2011 broke across fault areas formerly considered to be separated by (modestly) locked seismic barriers, that is, segments of fault surface that are assumed to be resistant to slip because of geometrical or structural heterogeneities. Likewise unexpected, the intraplate 2012 Sumatra earthquake (Mw 8.6) was the largest strike-slip earthquake recorded so far. With the anticipated further increase in population density and infrastructure the vulnerability of modern societies is increasing alongside. Rapidly developing communication networks enhance the Subjective Seismic Hazard, i.e. the personal feeling of being at risk. Consequently, trying to add to our 2 1 Introduction Figure 1.1: The 2.5-km-deep San Andreas Fault Observatory at Depth, or SAFOD.

Figure courtesy of USGS.

current scientific understanding of earthquakes seems more important than ever.

1.1 Thesis Objective and Importance Relating strong ground motion predictions and seismic hazard analysis to fault rheology and continuum mechanics is a key challenge for seismologists.

The complexity of natural geological settings, the multiple factors affecting ground motion (source, wave path, and site effects), the inaccessibility of insitu observations from several kilometers deep in the seismogenic zone, and the naturally limited amount of large, strongly radiating, crustal earthquakes impede a detailed knowledge of the dynamics of natural earthquakes. Nevertheless, with the increasingly dense seismic (and other) instrumentation (e.g.

the San Andreas Fault Observatory in Southern California at Depth, sketched in Fig. 1.1), recent well-recorded large earthquakes (e.g. the 1999 Chi-Chi (Mw 7.6) and the 2011 Tohoku-Oki (Mw 9.0) earthquakes) and the resulting gain of near-source data, the observational resolution of source complexities becomes feasible.

Earthquakes and the faults upon which they occur interact over a wide range of spatio-temporal scales (e.g. Ben-Zion, 2008). Spatial scales span hundreds of kilometers over which seismic waves propagate and interact with large scale fault (network) geometries, non-linear rheologies, fluid and heat transport.

On the other hand, the forces upon crack initiation and propagation along frictional rock interfaces act on atomic dimensions. The seismic cycle enfoldGeophysical Background ing the collective earthquake behavior operates on timescales ranging from tens of years up to hundreds of thousands of years, whereas single ruptures strike during time intervals of seconds. Thus, the ambitious task of implementing “physics” into earthquake source modeling, prompts the substantial question: What are the first-order physical processes that are relevant at a given spatio-temporal scale to justify the (most often computational) cost of their inclusion?

This thesis focuses on understanding the complex dynamics at a singular earthquake source level. Understanding what drives the dynamic processes during an earthquake requires an integrative view of the physics of rock fracture, rupture propagation, and emanated seismic radiation. The herein relevant spatio-temporal scales are sensitive to the fault rheology, frictional properties, and stress and strength conditions of the fault. This work contributes numerical and analytical insights towards a deeper understanding of the coseismic processes on natural faults. It also contributes towards bridging the (scaling) gap between rupture dynamic simulation and seismic observations by analysing the variability of exemplary radiated seismic wave fields.

The modelled source complexities and the plastic energy dissipation affect the resulting, potentially destructive seismic ground motion.

Accounting for features of dynamic rupture may be helpful in understanding seismic observations, as for example a re-activation of slip, observed in some source models of the Chi-Chi and of the Tohoku earthquake (Lee et al., 2006, 2011), radiation pattern asymmetries (e.g. Oglesby, 2000) and neareld seismogramms (e.g. Ellsworth et al., 2004). In the long term, these insights may contribute to a physical framework applicable in seismic hazard assessment.

1.2 Geophysical Background

A (crustal) earthquake is defined as the sudden release of slowly (at rates of cm/year) accumulated tectonic stress along a pre-existing frictionally weak discontinuity, termed a fault zone. Global seismicity patterns reveal a strong correlation between plate boundaries and fault zones and the presence of intercontinental fault zones, indicating that earthquakes often - but not exclusively - occur at tectonic plate boundaries.

During interseismic periods, which denote the time delay between earthquake occurrence, faults are considered to be “sticking”, storing energy associated with the elastic deformation of the adjacent tectonic plates. Once rock fracture initiates as local (frictional) instability (Dieterich, 1978; Lapusta and 4 1 Introduction Figure 1.2: Evolution of friction with shear displacement during a velocity-stepping experiment of Niemeijer et al. (2010).

Rice, 2003; Rice, 1983) the naturally often kinked and branched fault interface (re-)ruptures, thereby accumulating a permanent offset, or “slip, between both sides of the fault interface. The propagation of the dislocation is, amongst many other factors, governed by a constitutive relation, the friction law. The resulting displacement along the fault, which may be described by a slip-velocity function of a certain duration, is related to a drop in shear stress.

Despite the apparent simplicity of this constitutive behavior, the earthquake induced slip patterns and the slip rate history along the fault are highly nonlinear. For example, two antithetic models currently endeavour to explain the earthquake initiation process. In the cascade model, nucleation initiation only occurs on a small localized area within the fault plane, which triggers successively larger ruptures. This model predicts an equivalent origin of both, small and large earthquakes and thus, eliminates the possibility of finding a measurable earthquake pre-cursor for early warning assessment.

On the other hand, seismic observations frequently reveal an accumulation of quasi-static slip leading up to large earthquakes, as recently for the 2011 Mw 9.0 Tohoku-Oki earthquake (Kato et al., 2012). The “pre-slip” model assumes nucleation occurs in the form of slow, “quiet” pre-slip, i.e. beneath the (current) detection level of seismic observations, until the such weakened fault breaks. The implication of this model is that a larger area of pre-slip leads to a seismic event with larger seismic moment.

Nevertheless, even if we record an earthquake with a dense network of seismic instrumentation, only the source processes active at the onset of detectable fault slip are resolved. Observational insights on the controlling mechanisms

1.2 Geophysical Background of nucleation may thus result from utilising monitoring instrumentation situated in the vicinity of active faults which experience earthquakes.

Numerical simulations of singular earthquakes often artificially nucleate rupture in a prescribed overstressed or weak patch on the fault, that resembles some laboratory procedures applying explosive wires for the same purpose.

As also thematised in this work, artificial earthquake nucleation may have a strong impact on dynamic rupture (e.g. Ampuero and Rubin, 2008; Rubin and Ampuero, 2005). The implication of mechanically consistent nucleation procedures, however, implies additional complexity and computational cost (e.g. Ripperger et al., 2008).

In theoretical models of earthquake nucleation the specific rock frictional properties determine the smallest possible earthquake size, i.e. the critical nucleation size. The appropriate form of the constitutive law which describes the relationship between fault stress and slip along a fault plane, is topic of intense debate. Such a constitutive law should unify all observables associated with fault zones in the earth, e.g.the partially non-linear effects on and off natural fault zones including thermal pressurization of fluids trapped in rock pores, the existence of granular gouge material instead of a clean, solid rock interface and off-fault damage and plastic deformation. In reality, fault constitutive behavior is poorly constrained. The proposed constitutive laws have been shown to not only control earthquake nucleation, but also the style of singular rupture propagation, the occurrence of stable sliding (“creep”), as well as foreshock and aftershock distributions in the seismic cycle.

Laboratory experiments have provided invaluable insights into rock mechanics (e.g. Brace and Byerlee, 1966; Ohnaka, 1987; Ohnaka and Mogi, 1982;

Ruina, 1983). Shear loading axial and rotary setups measuring the displacement and frictional resistance during fracture of realistic fault samples are becoming capable of reproducing close to seismogenic conditions, requiring high pressures (in the order of MPa) and temperatures (hundreds of K), coseismic slip rates (m/s), and incorporation of the effects of fluid-content in the host rock (e.g. di Toro et al., 2005; Niemeijer et al., 2010).

At high slip rates, non-linear physical weakening processes, e.g. thermal pressurization of pore fluids, are thought to cause an observed extra-ordinary decrease of effective friction. Experimental results motivate empirically derived constitutive relations. These are frequently enhanced via the ad-hoc inclusion of theoretical ingredients from rock mechanics. However, the validation of the such derived relations is difficult. The developed friction laws differ in correlating weakening of tractions on the fault surface to the slipped distance (slip-weakening law), the particle velocity on the fault (rate-dependent) 6 1 Introduction Figure 1.3: Variation of rupture style in experimental setups of Lu et al. (2007);

Xia et al. (2004).

and/or the history of the microstructural contacts (state-dependent).

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