Properties of Dynamic Earthquake Ruptures With Heterogeneous Stress Drop

Earthquake rupture is a notoriously complex process, at all observable scales. We introduce a simplified semi-dynamic crack model to investigate the connection between the statistical properties of stress and those of macroscopic source parameters such as rupture size, seismic moment, apparent stress drop and radiated energy. Rupture initiation is treated consistently with nucleation on a linear slip-weakening fault, whereas rupture propagation and arrest are treated according to the Griffith criterion. The available stress drop is prescribed as a spatially correlated random field and is shown to potentially sustain a broad range of magnitudes. By decreasing the amplitude of the stress heterogeneities or increasing their correlation length the distribution of earthquake sizes presents a transition from Gutenberg- Richter to characteristic earthquake behavior. This transition is studied through a mean-field analysis. The bifurcation to characteristic earthquake behavior is sharp, reminiscent of a first-order phase transition. A lower roll-off magnitude observed in the Gutenberg-Richter regime is shown to depend on the correlation length of the available stress drop, rather than being a direct signature of the nucleation process. More generally, we highlight the possible role of the stress correlation length scale on deviations from earthquake source self-similarity. The present reduced model is a building block towards understanding the effect of structural and dynamic fault heterogeneities on the scaling of source parameters and on basic properties of seismicity

Non-equilibrium work fluctuations for oscillators in non-Markovian baths

We study work fluctuation theorems for oscillators in non-Markovian heat baths. By calculating the work distribution function for a harmonic oscillator with motion described by the generalized Langevin equation, the Jarzynski equality (JE), transient fluctuation theorem (TFT), and Crooks' theorem (CT) are shown to be exact. In addition to this derivation, numerical simulations of anharmonic oscillators indicate that the validity of these nonequilibrium theorems do not depend on the memory of the bath. We find that the JE and the CT are valid under many oscillator potentials and driving forces whereas the TFT fails when the driving force is asymmetric in time and the potential is asymmetric in position.Comment: 7 pages, 3 figure

Broad-band near-field ground motion simulations in 3-dimensional scattering media

The heterogeneous nature of Earth's crust is manifested in the scattering of propagating seismic waves. In recent years, different techniques have been developed to include such phenomenon in broad-band ground-motion calculations, either considering scattering as a semi-stochastic or purely stochastic process. In this study, we simulate broad-band (0-10Hz) ground motions with a 3-D finite-difference wave propagation solver using several 3-D media characterized by von Karman correlation functions with different correlation lengths and standard deviation values. Our goal is to investigate scattering characteristics and its influence on the seismic wavefield at short and intermediate distances from the source in terms of ground motion parameters. We also examine scattering phenomena, related to the loss of radiation pattern and the directivity breakdown. We first simulate broad-band ground motions for a point-source characterized by a classic ω2 spectrum model. Fault finiteness is then introduced by means of a Haskell-type source model presenting both subshear and super-shear rupture speed. Results indicate that scattering plays an important role in ground motion even at short distances from the source, where source effects are thought to be dominating. In particular, peak ground motion parameters can be affected even at relatively low frequencies, implying that earthquake ground-motion simulations should include scattering also for peak ground velocity (PGV) calculations. At the same time, we find a gradual loss of the source signature in the 2-5Hz frequency range, together with a distortion of the Mach cones in case of super-shear rupture. For more complex source models and truly heterogeneous Earth, these effects may occur even at lower frequencies. Our simulations suggests that von Karman correlation functions with correlation length between several hundred metres and few kilometres, Hurst exponent around 0.3 and standard deviation in the 5-10percent range reproduce the available observation

Bayesian inference of kinematic earthquake rupture parameters through fitting of strong motion data

Due to uncertainties in data and in forward modelling, the inherent limitations in data coverage and the non-linearity of the governing equation, earthquake source imaging is a problem with multiple solutions. The multiplicity of solutions can be conveniently expressed using a Bayesian approach, which allow to state inferences on model parameters in terms of probability density functions. The estimation of the posterior state of information, expressing the combination of the a priori knowledge on model parameters with the information contained in the data, is achieved in two steps. First, we explore the model space using an evolutionary algorithm to identify good data fitting regions. Secondly, using a neighbourhood algorithm and considering the entire ensemble of models found during the search stage, we compute a geometric approximation of the true posterior that is used to generate a second ensemble of models from which Bayesian inference can be performed. We apply this methodology to infer kinematic parameters of a synthetic fault rupture through fitting of strong motion data. We show how multiple rupture models are able to reproduce the observed waveforms within the same level of fit, suggesting therefore that the solution of the inversion cannot be expressed in terms of a single model but rather as a set of models which show certain statistical properties. For all model parameters we compute the posterior marginal distribution. We show how for some parameters the posterior do not follow a Gaussian distribution rendering the usual characterization in terms of mean value and standard deviation not correct. We compare the posterior marginal distributions with the ‘raw' marginal distributions computed from the ensemble of models generated by the evolutionary algorithm. We show how they are systematically different proving therefore that the search algorithm we adopt cannot be directly used to estimate uncertainties. We also analyse the stability of our inferences comparing the posterior marginals computed by different independent ensembles. The solutions provided by independent explorations are similar but not identical because each ensemble searches the model space differently resulting in different reconstructed posteriors. Our study illustrates how uncertainty estimates derive from the topology of the objective function, and how accurate and reliable resolution analysis is limited by the intrinsic difficulty of mapping the ‘true' structure of the objective functio

Sensitivity of broad-band ground-motion simulations to earthquake source and Earth structure variations: an application to the Messina Straits (Italy)

In this paper, we investigate ground-motion variability due to different faulting approximations and crustal-model parametrizations in the Messina Straits area (Southern Italy). Considering three 1-D velocity models proposed for this region and a total of 72 different source realizations, we compute broad-band (0-10 Hz) synthetics for Mw 7.0 events using a fault plane geometry recently proposed. We explore source complexity in terms of classic kinematic (constant rise-time and rupture speed) and pseudo-dynamic models (variable rise-time and rupture speed). Heterogeneous slip distributions are generated using a Von Karman autocorrelation function. Rise-time variability is related to slip, whereas rupture speed variations are connected to static stress drop. Boxcar, triangle and modified Yoffe are the adopted source time functions. We find that ground-motion variability associated to differences in crustal models is constant and becomes important at intermediate and long periods. On the other hand, source-induced ground-motion variability is negligible at long periods and strong at intermediate-short periods. Using our source-modelling approach and the three different 1-D structural models, we investigate shaking levels for the 1908 Mw 7.1 Messina earthquake adopting a recently proposed model for fault geometry and final slip. Our simulations suggest that peak levels in Messina and Reggio Calabria must have reached 0.6-0.7 g during this earthquak

Local Temperature and Universal Heat Conduction in FPU chains

It is shown numerically that for Fermi Pasta Ulam (FPU) chains with alternating masses and heat baths at slightly different temperatures at the ends, the local temperature (LT) on small scales behaves paradoxically in steady state. This expands the long established problem of equilibration of FPU chains. A well-behaved LT appears to be achieved for equal mass chains; the thermal conductivity is shown to diverge with chain length N as N^(1/3), relevant for the much debated question of the universality of one dimensional heat conduction. The reason why earlier simulations have obtained systematically higher exponents is explained.Comment: 4 pages, 3 figures, revised published versio

Universality of One-Dimensional Heat Conductivity

We show analytically that the heat conductivity of oscillator chains diverges with system size N as N^{1/3}, which is the same as for one-dimensional fluids. For long cylinders, we use the hydrodynamic equations for a crystal in one dimension. This is appropriate for stiff systems such as nanotubes, where the eventual crossover to a fluid only sets in at unrealistically large N. Despite the extra equation compared to a fluid, the scaling of the heat conductivity is unchanged. For strictly one-dimensional chains, we show that the dynamic equations are those of a fluid at all length scales even if the static order extends to very large N. The discrepancy between our results and numerical simulations on Fermi-Pasta-Ulam chains is discussed.Comment: 7 pages, 2 figure