Advancing the Frontiers of Earthquake Science

Statistical seismology has been emerging as a new discipline at the interface between earthquake physics, earthquake statistics, hazard assessment, and society. A workshop in Italy was sponsored by the Italian Istituto Nazionale di Geofisica e Vulcanologia (INGV), the Swiss Federal Institute of Technology Zurich (ETH), and the Japanese Institute of Statistical Mathematics (ISM), to discuss the state of the art and future directions. Conference participants discussed how to use available tools and techniques of statistical seismology to advance earthquake science. Building increasingly accurate timedependent earthquake forecast models at various spatial and temporal scales is widely recognized as an important challenge, and various such models were presented and discussed at the workshop. Exploiting time dependence for hazard assessment requires us to develop a detailed understanding of the behavior of regional fault systems and corresponding earthquake catalogs spanning decades. We can no longer analyze individual faults or earthquake sequences in isolation

Portfolio Selection with Probabilistic Utility, Bayesian Statistics, and Markov Chain Monte Carlo

We propose a novel portfolio selection approach that manages to ease some of the problems that characterise standard expected utility maximisation. The optimal portfolio is no longer defined as the extremum of a suitably chosen utility function: the latter, instead, is reinterpreted as the logarithm of a probability distribution for optimal portfolios and the selected portfolio is defined as the expected value with respect to this distribution. A further theoretical aspect is the adoption of a Bayesian inference framework. We find that this approach has several attractive features, when comparing it to the standard maximisation of expected utility. We remove the over-pronounced sensitivity on external parameters that plague optimisation procedures and obtain a natural and self consistent way to account for uncertainty in knowledge and for personal views. We test the proposed method against traditional expected utility maximisation, using artificial data to simulate finite-sample behaviour, and find superior performance of our procedure. All numerical integrals are carried out by using Markov Chain Monte Carlo, where the chains are generated by an adapted version of Hybrid Monte Carlo. We present numerical results for a portfolio of eight assets using historical time series running from January 1988 to January 2002.Bayesian Statistics, Estimation Risk, Finite Sample, Markov Chain Monte Carlo, Portfolio Selection

3D dynamic simulations of spontaneous rupture propagation governed by different constitutive laws with rake rotation allowed

In this work we present a 3D Finite Difference numerical method to model the dynamic spontaneous propagation of an earthquake rupture on planar faults in an elastic half-space. We implement the Traction-at-Split-Nodes fault boundary condition for a system of faults, either vertical or oblique, using different constitutive laws. We can adopt both a slip-weakening law to prescribe the traction evolution within the breakdown zone or rate- and state-dependent friction laws, which involve the choice of an evolution relation for the state variable. Our numerical procedure allows the use of oblique and heterogeneous distribution of initial stress and allows the rake rotation. This implies that the two components of slip velocity and total dynamic traction are coupled together to satisfy, in norm, the adopted constitutive law. The simulations presented in this study show that the rupture acceleration to super-shear crack speeds occurs along the direction of the imposed initial stress; the rupture front velocity along the perpendicular direction is slower than that along the pre-stress direction. Depending on the position on the fault plane the orientation of instantaneous total dynamic traction can change with time with respect to the imposed initial stress direction. These temporal rake rotations depend on the amplitude of initial stress and on its distribution on the fault plane. They also depend on the curvature and direction of the rupture front with respect to the imposed initial stress direction: this explains why rake rotations are mostly located near the rupture front and within the cohesive zone

Near-field propagation of tsunamis from megathrust earthquakes

We investigate controls on tsunami generation and propagation in the near-field of great megathrust earthquakes using a series of numerical simulations of subduction and tsunamigenesis on the Sumatran forearc. The Sunda megathrust here is advanced in its seismic cycle and may be ready for another great earthquake. We calculate the seafloor displacements and tsunami wave heights for about 100 complex earthquake ruptures whose synthesis was informed by reference to geodetic and stress accumulation studies. Remarkably, results show that, for any near-field location: (1) the timing of tsunami inundation is independent of slip-distribution on the earthquake or even of its magnitude, and (2) the maximum wave height is directly proportional to the vertical coseismic displacement experienced at that location. Both observations are explained by the dominance of long wavelength crustal flexure in near-field tsunamigenesis. The results show, for the first time, that a single estimate of vertical coseismic displacement might provide a reliable short-term forecast of the maximum height of tsunami waves

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