Gaetano Festa

Spectral Element Analysis in Seismology

We present a review of the application of the spectral-element method to regional and global seismology. This technique is a high-order variational method that allows one to compute accurate synthetic seismograms in three-dimensional heterogeneous Earth models with deformed geometry. We first recall the strong and weak forms of the seismic wave equation with a particular emphasis set on fluid regions. We then discuss in detail how the conditions that hold on the boundaries, including coupling boundaries, are honored. We briefly outline the spectral-element discretization procedure and present the time-marching algorithm that makes use of the diagonal structure of the mass matrix. We show examples that illustrate the capabilities of the method and its interest in the context of the computation of three-dimensional synthetic seismograms.

Earthquake early warning system in southern Italy: Methodologies and performance evaluation

We investigate the effect of extended faulting processes and heterogeneous wave propagation on the early warning system capability to predict the peak ground velocity (PGV) from moderate to large earthquakes occurring in the southern Apennines (Italy). Simulated time histories at the early warning network have been used to retrieve early estimates of source parameters and to predict the PGV, following an evolutionary, probabilistic approach. The system performance is measured through the Effective Lead-Time (ELT), i.e., the time interval between the arrival of the first S-wave and the time at which the probability to observe the true PGV value within one standard deviation becomes stationary, and the Probability of Prediction Error (PPE), which provides a measure of PGV prediction error. The regional maps of ELT and PPE show a significant variability around the fault up to large distances, thus indicating that the systems capability to accurately predict the observed peak ground motion strongly depends on distance and azimuth from the fault.

PML Absorbing Boundaries

It has been previously demonstrated that no reflection is generated when elastic (or electromagnetic) waves enter a region with Perfectly Matching Layer (PML) absorbing conditions in a continuous medium. The practical application of PMLs, however, is in numerical modeling, where the medium is discretized by either a finite-element or a finite-difference scheme thus introducing a reduced amount of reflection. In such a case what is the practical and quantitative efficiency of PML absorbing boundaries? Assuming a regular spatial mesh, we start by evaluating analytically the reflection of body waves introduced by the discrete transition toward PML properties, under variable angle of incidence and wavelength. We then extend our evaluation with numerical tests for both body and Rayleigh waves. Surprisingly enough, the absorption remains equally efficient at wavelengths far larger than the PML thickness itself. As a consequence, the PML thickness can be kept minimal even for studies involving relatively low frequencies, and no rescaling with model size is required. Another pleasant feature is that it is all the more efficient at shallow angles of incidence. Finally, we show through numerical examples that a major advantage of using PMLs is their efficiency in absorbing Rayleigh waves at the free surface, a point where more classical methods perform rather poorly. Although previous authors essentially limited the description of their discrete implementation to 2D, we develop to some level of detail a 3D finite-difference scheme for PMLs and provide numerical examples.

Influence of the rupture initiation on the intersonic transition : Crack-like versus pulse-like modes

We numerically investigate the supershear transition of inplane rupture under slip weakening friction and tectonic loading, using a non-smooth spectral element method. Nucleation of the rupture in the vicinity of an initial stress concentration is consistently solved together with the dynamic propagation. Nucleation is shown to influence the transition to the supershear propagation and, depending upon the initiation process and the level of the stress out of the nucleating asperity, crack-like or pulse-like solutions can be selected in the intersonic regime. Pulses are triggered by dynamic unloading of the traction ahead of the Rayleigh wave and tend to become metastable. The asymptotic numerical solution is always a crack propagating close to P wave speed. The rupture front and the arrest velocities are numerically characterized. We argue that the nucleation phase introduces a trade-off with the state of the stress, in determining the distance at which supershear appears.

Early magnitude and potential damage zone estimates for the great Mw 9 Tohoku-Oki earthquake

The Mw 9.0, 2011 Tohoku-Oki earthquake has reopened the discussion among the scientific community about the effectiveness of earthquake early warning for large events. A well-known problem with real-time procedures is the parameter saturation, which may lead to magnitude underestimation for large earthquakes. Here we measure the initial peak ground displacement and the predominant period by progressively expanding the time window and distance range, to provide consistent magnitude estimates (M = 8.4) and a rapid prediction of the potential damage area. This information would have been available 35 s after the first P-wave detection and could have been refined in the successive 20 s using data from more distant stations. We show the suitability of the existing regression relationships between early warning parameters and magnitude, provided that an appropriate P-wave time window is used for parameter estimation. We interpret the magnitude under-estimation as a combined effect of high-pass filtering and frequency dependence of the main radiating source during the rupture process.

The Earthquake‐Source Inversion Validation (SIV) Project

Finite-fault earthquake source inversions infer the (time-dependent) displacement on the rupture surface from geophysical data. The resulting earthquake source models document the complexity of the rupture process. However, multiple source models for the same earthquake, obtained by different research teams, often exhibit remarkable dissimilarities. To address the uncertainties in earthquake-source inversion methods and to understand strengths and weaknesses of the various approaches used, the Source Inversion Validation (SIV) project conducts a set of forward-modeling exercises and inversion benchmarks. In this article, we describe the SIV strategy, the initial benchmarks, and current SIV results. Furthermore, we apply statistical tools for quantitative waveform comparison and for investigating source-model (dis)similarities that enable us to rank the solutions, and to identify particularly promising source inversion approaches. All SIV exercises (with related data and descriptions) and statistical comparison tools are available via an online collaboration platform, and we encourage source modelers to use the SIV benchmarks for developing and testing new methods. We envision that the SIV efforts will lead to new developments for tackling the earthquake-source imaging problem.

Twin ruptures grew to build up the giant 2011 Tohoku, Japan, earthquake.

The 2011 Tohoku megathrust earthquake had an unexpected size for the region. To image the earthquake rupture in detail, we applied a novel backprojection technique to waveforms from local accelerometer networks. The earthquake began as a small-size twin rupture, slowly propagating mainly updip and triggering the break of a larger-size asperity at shallower depths, resulting in up to 50 m slip and causing high-amplitude tsunami waves. For a long time the rupture remained in a 100–150 km wide slab segment delimited by oceanic fractures, before propagating further to the southwest. The occurrence of large slip at shallow depths likely favored the propagation across contiguous slab segments and contributed to build up a giant earthquake. The lateral variations in the slab geometry may act as geometrical or mechanical barriers finally controlling the earthquake rupture nucleation, evolution and arrest.

Evidence for a difference in rupture initiation between small and large earthquakes

The process of earthquake rupture nucleation and propagation has been investigated through laboratory experiments and theoretical modelling, but a limited number of observations exist at the scale of earthquake fault zones. Distinct models have been proposed, and whether the magnitude can be predicted while the rupture is ongoing represents an unsolved question. Here we show that the evolution of P-wave peak displacement with time is informative regarding the early stage of the rupture process and can be used as a proxy for the final size of the rupture. For the analysed earthquake set, we found a rapid initial increase of the peak displacement for small events and a slower growth for large earthquakes. Our results indicate that earthquakes occurring in a region with a large critical slip distance have a greater likelihood of growing into a large rupture than those originating in a region with a smaller slip-weakening distance.

Anatomy of a microearthquake sequence on an active normal fault

The analysis of similar earthquakes, such as events in a seismic sequence, is an effective tool with which to monitor and study source processes and to understand the mechanical and dynamic states of active fault systems. We are observing seismicity that is primarily concentrated in very limited regions along the 1980 Irpinia earthquake fault zone in Southern Italy, which is a complex system characterised by extensional stress regime. These zones of weakness produce repeated earthquakes and swarm-like microearthquake sequences, which are concentrated in a few specific zones of the fault system. In this study, we focused on a sequence that occurred along the main fault segment of the 1980 Irpinia earthquake to understand its characteristics and its relation to the loading-unloading mechanisms of the fault system.

A Local Magnitude Scale for Southern Italy

local magnitude scale has been defined for southern Italy, in the area monitored by the recently installed Irpinia Seismic Network. Waveforms recorded from more than 100 events of small magnitude are processed to extract synthetic Wood–Anderson traces. Assuming a general description of peak-displacement scaling with the distance, by means of linear and logarithmic contributions, a global exploration of the parameter space is performed by a grid-search method with the aim of investigating the correlation between the two decay contributions and seeking for a physical solution of the problem. Assuming an L2 norm, we found M=logA+1.79 log R - 0.58 yielding an error on the single estimation smaller than 0.2, at least when the hypocenter location is accurate. Station corrections are investigated through the station residuals, referring to the average value of the magnitude. Using a z test, we found that some stations exhibit a correction term significantly different from 0. The use of the peak acceleration and peak velocity as indicators of the magnitude is also investigated.