Elisa Tinti

A Kinematic Source-Time Function Compatible with Earthquake Dynamics

We propose a new source-time function, to be used in kinematic modeling 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 the regularized Yoffe function. We propose a parameterization of this slip-velocity time function through the final slip, its duration, and the duration of the positive slip acceleration ( Tacc ). Using this analytical function, we examined the relation between kinematic parameters, such as peak slip velocity and slip duration, and dynamic parameters, such as slip-weakening distance and breakdown-stress drop. The obtained scaling relations are consistent with those proposed by Ohnaka and Yamashita (1989) from laboratory experiments. This shows that the proposed source-time function suitably represents dynamic rupture propagation with finite slip-weakening distances.

Real-Time Determination of Seismic Moment Tensor for the Italian Region

This work has been funded by the 2005–2007 DPC-S4 and 2008–2010 DPC-S3 Italian Civil Protection contracts.

Slip heterogeneity and directivity of the ML 6.0, 2016, Amatrice earthquake estimated with rapid finite-fault inversion

On 24 August 2016 a magnitude ML 6.0 occurred in the Central Apennines (Italy) between Amatrice and Norcia causing nearly 300 fatalities. The main shock ruptured a NNW-SSE striking, WSW dipping normal fault. We invert waveforms from 26 three-component strong motion accelerometers, filtered between 0.02 and 0.5 Hz, within 45 km from the fault. The inferred slip distribution is heterogeneous and characterized by two shallow slip patches updip and NW from the hypocenter, respectively. The rupture history shows bilateral propagation and a relatively high rupture velocity (3.1 km/s). The imaged rupture history produced evident directivity effects both N-NW and SE of the hypocenter, explaining near-source peak ground motions. Fault dimensions and peak slip values are large for a moderate-magnitude earthquake. The retrieved rupture model fits the recorded ground velocities up to 1 Hz, corroborating the effects of rupture directivity and slip heterogeneity on ground shaking and damage pattern.

The dependence of traction evolution on the earthquake source time function adopted in kinematic rupture models

[1] We compute the temporal evolution of traction by solving the elasto-dynamic equation and by using the slip velocity history as a boundary condition on the fault plane. 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 (D c ). Our results show that the source time functions, adopted in kinematic source models, affect the inferred dynamic parameters. The critical slip weakening distance, characterizing the constitutive relation, ranges between 30% and 80% of the total slip. The ratio between D c and total slip depends on the adopted source time functions and, in these applications, is nearly constant over the fault. We propose that source time functions compatible with earthquake dynamics should be used to inter the traction time history.

On the mechanical work absorbed on faults during earthquake ruptures

In this paper we attempt to reconcile a theoretical understanding of the earthquake energy balance with current geologic understanding of fault zones, with seismological estimates of fracture energy on faults, and with geological measurements of surface energy in fault gouges. In particular, we discuss the mechanical work absorbed on the fault plane during the propagation of a dynamic earthquake rupture. We show that, for realistic fault zone models, all the mechanical work is converted in frictional work defined as the irreversible work against frictional stresses. We note that the γ eff of Kostrov and Das (1988) is zero for cracks lacking stress singularities, and thus does not contribute to the work done on real faults. Fault shear tractions and slip velocities inferred seismologically are phenomenological variables at the macroscopic scale. We define the macroscopic frictional work and we discuss how it is partitioned into surface energy and heat (the latter includes real heat as well as plastic deformation and the radiation damping of Kostrov and Das). Tinti et al. (2005) defined and measured breakdown work for recent earthquakes, which is the excess of work over some minimum stress level associated with the dynamic fault weakening. The comparison between geologic measurements of surface energy and breakdown work revealed that 1-10% of breakdown work went into the creation of fresh fracture surfaces (surface energy) in large earthquakes, and the remainder went into heat. We also point out that in a realistic fault zone model the transition between heat and surface energy can lie anywhere below the slip weakening curve.

Chapter 6 The Critical Slip Distance for Seismic and Aseismic Fault Zones of Finite Width

We present a conceptual model for the effective critical friction distance for fault zones of finite width. A numerical model with 1D elasticity is used to investigate implications of the model for shear traction evolution during dynamic and quasi-static slip. The model includes elastofrictional interaction of multiple, parallel slip surfaces, which obey rate and state friction laws with either Ruina (slip) or Dieterich (time) state evolution. A range of slip acceleration histories is investigated by imposing perturbations in slip velocity at the fault zone boundary and using radiation damping to solve the equations of motion. The model extends concepts developed for friction of bare surfaces, including the critical friction distance L , to fault zones of finite width containing wear and gouge materials. We distinguish between parameters that apply to a single frictional surface, including L and the dynamic slip weakening distance d o , and those that represent slip for the entire fault zone, which include the effective critical friction distance, D cb , and the effective dynamic slip weakening distance D o . A scaling law for D cb is proposed in terms of L and the fault zone width. Earthquake source parameters depend on net slip across a fault zone and thus scale with D cb , D o , and the slip at yield strength D a . We find that D a decreases with increasing velocity jump size for friction evolution via the Ruina law, whereas it is independent of slip acceleration rate for the Dieterich law. For both laws, D a scales with fault zone width and shear traction exhibits prolonged hardening before reaching a yield strength. The parameters D cb and D o increase roughly linearly with fault zone thickness. This chapter and Chapter 7 in the volume discuss the problem of reconciling laboratory measurements of the critical friction distance with theoretical and field-based estimates of the effective dynamic slip weakening distance.

Precursory changes in seismic velocity for the spectrum of earthquake failure modes

Temporal changes in seismic velocity during the earthquake cycle have the potential to illuminate physical processes associated with fault weakening and connections between the range of fault slip behaviors including slow earthquakes, tremor and low frequency earthquakes1. Laboratory and theoretical studies predict changes in seismic velocity prior to earthquake failure2, however tectonic faults fail in a spectrum of modes and little is known about precursors for those modes3. Here we show that precursory changes of wave speed occur in laboratory faults for the complete spectrum of failure modes observed for tectonic faults. We systematically altered the stiffness of the loading system to reproduce the transition from slow to fast stick-slip and monitored ultrasonic wave speed during frictional sliding. We find systematic variations of elastic properties during the seismic cycle for both slow and fast earthquakes indicating similar physical mechanisms during rupture nucleation. Our data show that accelerated fault creep causes reduction of seismic velocity and elastic moduli during the preparatory phase preceding failure, which suggests that real time monitoring of active faults may be a means to detect earthquake precursors.

Chapter 7 Scaling of Slip Weakening Distance with Final Slip during Dynamic Earthquake Rupture

We discuss physical models for the characteristic slip weakening distance Dc of earthquake rupture with particular focus on scaling relations between Dc and other earthquake source parameters. We use inversions of seismic data to investigate the breakdown process, dynamic weakening, and measurement of Dc. We discuss limitations of such measurements. For studies of breakdown processes and slip weakening it is important to analyze time intervals shorter than the slip duration and those for which slip velocity is well resolved. We analyze the relationship between Dc and the parameters and , which are defined as the slip at the peak slip velocity and the peak traction, respectively. We discuss approximations and limitations associated with inferring the critical slip weakening distance from c D′ a D c D′ . Current methods and available seismic data introduce potential biases in estimates of Dc and its scaling with seismic slip due to the limited frequency bandwidth considered during typical kinematic inversions. Many published studies infer erroneous scaling between Dc and final slip due to inherent limitations, implicit assumptions, and poor resolution of the seismic inversions. We suggest that physical interpretations of Dc based on its measurement for dynamic earthquake rupture should be done with caution and the aid of accurate numerical simulations. Seismic data alone cannot, in general, be used to infer physical processes associated with Dc although the estimation of breakdown work is reliable. We emphasize that the parameters Tacc and peak slip velocity contain the same dynamic information as Dc and breakdown stress drop. This further demonstrates that inadequate resolution and limited frequency bandwidth impede to constrain dynamic rupture parameters. Cocco et al. Scaling of dynamic slip weakening distance p. 1

On the evolution of elastic properties during laboratory stick-slip experiments spanning the transition from slow slip to dynamic rupture

The physical mechanisms governing slow earthquakes remain unknown, as does the relationship between slow and regular earthquakes. To investigate the mechanism(s) of slow earthquakes and related quasi-dynamic modes of fault slip we performed laboratory experiments on simulated fault gouge in the double direct shear configuration. We reproduced the full spectrum of slip behavior, from slow to fast stick slip, by altering the elastic stiffness of the loading apparatus (k) to match the critical rheologic stiffness of fault gouge (kc). Our experiments show an evolution from stable sliding, when k > kc, to quasi-dynamic transients when k ~ kc, to dynamic instabilities when k < kc. To evaluate the microphysical processes of fault weakening we monitored variations of elastic properties. We find systematic changes in P wave velocity (Vp) for laboratory seismic cycles. During the coseismic stress drop, seismic velocity drops abruptly, consistent with observations on natural faults. In the preparatory phase preceding failure, we find that accelerated fault creep causes a Vp reduction for the complete spectrum of slip behaviors. Our results suggest that the mechanics of slow and fast ruptures share key features and that they can occur on same faults, depending on frictional properties. In agreement with seismic surveys on tectonic faults our data show that their state of stress can be monitored by Vp changes during the seismic cycle. The observed reduction in Vp during the earthquake preparatory phase suggests that if similar mechanisms are confirmed in nature high-resolution monitoring of fault zone properties may be a promising avenue for reliable detection of earthquake precursors.

Complex Fault Geometry and Rupture Dynamics of the MW 6.5, 30 October 2016, Central Italy Earthquake

We study the October 30th 2016 Norcia earthquake (MW 6.5) to retrieve the rupture history by jointly inverting seismograms and coseismic GPS displacements obtained by dense local networks. The adopted fault geometry consists of a main normal fault striking N155°and dipping 47° belonging to the Mt. Vettore-Mt. Bove fault system (VBFS) and a secondary fault plane striking N210° and dipping 36° to the NW. The coseismic rupture initiated on the VBFS and propagated with similar rupture velocity on both fault planes. Up-dip from the nucleation point, two main slip patches have been imaged on these fault segments, both characterized by similar peak-slip values (~3 m) and rupture times (~3 s). After the breakage of the two main slip patches, coseismic rupture further propagated southeastward along the VBFS, rupturing again the same fault portion that slipped during the August 24th earthquake. The retrieved coseismic slip distribution is consistent with the observed surface breakages and the deformation pattern inferred from InSAR measurements. Our results show that three different fault systems were activated during the October 30th earthquake. The composite rupture model inferred in this study provides evidences that also a deep portion of the NNE-trending section of the Olevano-Antrodoco-Sibillini (OAS) thrust broke co-seismically, implying the kinematic inversion of a thrust ramp. The obtained rupture history indicates that, in this sector of the Apennines, compressional structures inherited from past tectonics can alternatively segment boundaries of NW-trending active normal faults or break co-seismically during moderate-to-large magnitude earthquakes.