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

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

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 (Dc). 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 Dc 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 infer the traction time history

Dependence of slip weakening distance (Dc) on final slip during dynamic rupture of earthquakes

In this study we aim to understand the dependence of the critical slip weakening distance (Dc) on the final slip (Dtot) during the propagation of a dynamic rupture and the consistency of their inferred correlation. To achieve this goal we have performed a series of numerical tests suitably designed to validate the adopted numerical procedure and to verify the actual capability in measuring Dc. We have retrieved two kinematic rupture histories from spontaneous dynamic rupture models governed by a slip weakening law in which a constant Dc distribution on the fault plane as well as a constant Dc / Dtot ratio are assumed, respectively. The slip velocity and the shear traction time histories represent the synthetic “real” target data which we aim to reproduce. We use a 3-D traction-at-split nodes numerical procedure to image the dynamic traction evolution by assuming our modeled slip velocity as a boundary condition on the fault plane. We assume a regularized Yoffe function as source time function in our modeling attempts and we measure the critical slip weakening distance from the inferred traction versus slip curves at each point on the fault. We compare the inferred values with those of the target dynamic models. Our numerical tests show that fitting the slip velocity functions of the target models at each point on the fault plane is not enough to retrieve good traction evolution curves and to obtain reliable measures of Dc. We find that the estimation of Dc is very sensitive to any small variation of the slip velocity function. An artificial correlation between Dc/Dtot is obtained when a fixed shape of slip velocity is assumed on the fault (i.e., constant rise time and constant time for positive acceleration) which differs from that of the target model. We point out that the estimation of fracture energy (breakdown work) on the fault is not affected by biases in measuring Dc

Modeling the dynamic rupture propagation on heterogeneous faults with rate- and state-dependent friction

We investigate the effects of non-uniform distribution of constitutive parameters on the dynamic propagation of an earthquake rupture. We use a 2D finite difference numerical method and we assume that the dynamic rupture propagation is governed by a rate- and state-dependent constitutive law. We first discuss the results of several numerical experiments performed with different values of the constitutive parameters a (to account for the direct effect of friction), b (controlling the friction evolution) and L (the characteristic length-scale parameter) to simulate the dynamic rupture propagation on homogeneous faults. Spontaneous dynamic ruptures can be simulated on velocity weakening (a < b) fault patches: our results point out the dependence of the traction and slip velocity evolution on the adopted constitutive parameters. We therefore model the dynamic rupture propagation on heterogeneous faults. We use in this study the characterization of different frictional regimes proposed by Boatwright and Cocco (1996) based on different values of the constitutive parameters a, b and L. Our numerical simulations show that the heterogeneities of the L parameter affect the dynamic rupture propagation, control the peak slip velocity and weakly modify the dynamic stress drop and the rupture velocity. Moreover, a barrier can be simulated through a large contrast of L parameter. The heterogeneity of a and b parameters affects the dynamic rupture propagation in a more complex way. A velocity strengthening area (a > b) can arrest a dynamic rupture, but can be driven to an instability if suddenly loaded by the dynamic rupture front. Our simulations provide a picture of the complex interactions between fault patches having different frictional properties and illustrate how the traction and slip velocity evolutions are modified during the propagation on heterogeneous faults. These results involve interesting implications for slip duration and fracture energy

Rupture process of the 2007 Niigata-ken Chuetsu-oki earthquake by non-linear joint inversion of strong motion and GPS data

We image the rupture history of the 2007 Niigata-ken Chuestu-oki (Japan) earthquake by a nonlinear joint inversion of strong motion and GPS data, retrieving peak slip velocity, rupture time, rise time and slip direction. The inferred rupture model contains two asperities; a small patch near the nucleation and a larger one located 10÷15 km to the south-west. The maximum slip ranges between 2.0 and 2.5 m and the total seismic moment is 1.6×1019 Nm. The inferred rupture history is characterized by rupture acceleration and directivity effects, which are stable features of the inverted models. These features as well as the source-to-receiver geometry are discussed to interpret the high peak ground motions observed (PGA is 1200 gals) at the Kashiwazaki-Kariwa nuclear power plant (KKNPP), situated on the hanging-wall of the causative fault. Despite the evident source effects, predicted PGV underestimates the observed values at KKNPP by nearly a factor of 10

Tsunami generation in Stromboli island and impact on the south-east Tyrrhenian coasts

Stromboli is one of the most active volcanoes in the Aeolian island arc in south Tyrrhenian sea, Italy. In the last 100 years the most relevant volcanic eruptions have beenaccompanied by local tsunamis, that have caused damage and casualties. In some cases the direct mechanism of local tsunami generation is clear, i.e. pyroclastic flows entering the sea. In some others it is uncertain and some speculation concerning the collapse of the eruptive column on the sea surface or the failure of some underwater mass can be made. But the ordinary activity is unlikely to generate large regional tsunamis. These can be produced by the lateral collapse of the volcanic cone that geomorphological and volcanological&nbsp; investigations have proven to have occurred repeatedly in the recent history of the volcano, with return period in the order of some thousands of years. The last episode is dated to less than 5 ka BP, and left the Sciara del Fuoco scar on the north-west flank of Stromboli.</p> <p style='line-height: 20px;'>Based on previous studies, the possible collapse of the nortwestern sector of Stromboli and the consequent generation and propagation of a tsunami are explored. The impact on Stromboli and on the other islands of the Aeolian archipelago is estimated, as well as the impact on the coast of Sicily and the Tyrrhenian coasts of Calabria. The simulation is carried out by means of a double model: a Lagrangian block model to compute the motion of the collapsing mass, and a finite-element hydrodynamic model to compute the evolution of the tsunami. Two distinct tsunami simulations are carried out, one on a very fine grid around the source region to evaluate the tsunami near Stromboli, and one utilising a coarser grid covering the whole south-east Tyrrhenian sea to compute the tsunami propagation toward Sicily and Calabria. It is found that a huge-volume collapse of the north-western flank of the Stromboli cone is capable of producing a regional tsunami which is catastrophic at the source and devastating on long stretches of Tyrrhenian coasts, but particularly in the neighbouring islands of Panarea and Salina, and along the Calabria coasts around Capo Vaticano

Local thermodynamical equilibrium and the beta frame for a quantum relativistic fluid

We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics in flat spacetime in a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. We show that the appropriate definition of local equilibrium naturally leads to the introduction of a relativistic hydrodynamical frame in which the four-velocity vector is the one of a relativistic thermometer at equilibrium with the fluid, parallel to the inverse temperature four-vector \beta, which then becomes a primary quantity. We show that this frame is the most appropriate for the expansion of stress-energy tensor from local thermodynamical equilibrium and that therein the local laws of thermodynamics take on their simplest form. We discuss the difference between the \beta frame and Landau frame and present an instance where they differ.Comment: 22 pages, 3 figures. To appear in Eur. Phys. J.

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 do, and those that represent slip for the entire fault zone, which include the effective critical friction distance, Dcb, and the effective dynamic slip weakening distance Do. A scaling law for Dcb 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 Dcb, Do, and the slip at yield strength Da. We find that Da 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, Da scales with fault zone width and shear traction exhibits prolonged hardening before reaching a yield strength. The parameters Dcb and Do increase roughly linearly with fault zone thickness. This chapter and a companion chapter 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

The role of shear fabric in controlling breakdown processes during laboratory slow-slip events

Understanding the physical mechanisms at the origin of slow-slip events has been proven a very challenging task. In particular, little is known on the role of fault heterogeneity during slow slip. In this study, we provide evidences that fault fabric controls slip velocity time histories during slow-slip events generated in the laboratory. We performed experiments using a double-direct biaxial shear apparatus and two different fault gouges, homogeneous quartz powder, and heterogeneous anhydrite/dolomite mixture. We measure details of fault slip to resolve the slip velocity function and volumetric deformation that, coupled with an analysis of the resulting microstructure, allow us to infer the mechanical processes at play. Our results show that slow-slip events can be generated for both fault gouges when k&nbsp;~&nbsp;kc with similar values of breakdown work. The shear fabric exerts a strong influence during the coseismic breakdown stage. In quartz, where most of the slip occurs on a very localized slipping surface, the peak slip velocity is attained near the final stage of friction breakdown and therefore a relevant amount of the mechanical work is absorbed during slip acceleration. In anhydrite/dolomite mixture, the peak slip velocity is suddenly reached after a relatively small drop in friction, accompanied by fault dilation, implying that most of the mechanical work is absorbed during slip deceleration. For anhydrite/dolomite mixture these results are likely related to heterogeneous slip distribution along the observed foliation. Taken together, these observations suggest that the mechanics of slow-slip events depends on shear zone fabric

Centroid moment tensor catalog with 3D lithospheric wavespeed model. The 2016–2017 Central Apennines sequence

Moment tensor inversions of broadband velocity data are usually managed by adopting Green's functions for 1D layered seismic wave speed models. This assumption can impact on source parameter estimates in regions with complex 3D heterogeneous structures and discontinuities in rock properties. In this work, we present a new centroid moment tensor (CMT) catalog for the Amatrice-Visso-Norcia (AVN) seismic sequence based on a recently generated 3D wave speed model for the Italian lithosphere. Forward synthetic seismograms and Fréchet derivatives for CMT-3D inversions of 159 earthquakes with Mw ≥ 3.0 are simulated using a spectral-element method (SEM) code. By comparing the retrieved solutions with those from time domain moment tensor (TDMT) catalog, obtained with a 1D wave speed model calibrated for Central Apennines (Italy), we observe a remarkable degree of consistency in terms of source geometry, kinematics, and magnitude. Significant differences are found in centroid depths, which are more accurately estimated using the 3D model. Finally, we present a newly designed parameter, τ, to better quantify and compare a-posteriori the reliability of the obtained MT solutions. τ measures the goodness of fit between observed and synthetic seismograms accounting for differences in amplitude, arrival time, percentage of fitted seconds, and the usual L2-norm estimate. The CMT-3D solutions represent the first Italian CMT catalog based on a full-waveform 3D wave speed model. They provide reliable source parameters with potential implications for the structures activated during the sequence. The developed approach can be readily applied to more complex Italian regions where 1D models are underperforming and not representative of the area