Lagrangian systems with Lipschitz obstacle on manifolds

Lagrangian systems constrained on the closure of an open subset with Lipschitz boundary in a manifold are considered. Under suitable assumptions, the existence of infinitely many periodic solutions is proved

The Assumption of Poisson Seismic-Rate Variability in CSEP/RELM Experiments

Evaluating the performances of earthquake forecasting/prediction models is the main rationale behind some recent international efforts like the Regional Earthquake Likelihood Model (RELM) and the Collaboratory for the Study of Earthquake Predictability (CSEP). Basically, the evaluation process consists of two steps: 1) to run simultaneously all codes to forecast future seismicity in well-defined testing regions; 2) to compare the forecasts through a suite of statistical tests. The tests are based on the likelihood score and they check both the time and space performances. All these tests rely on some basic assumptions that have never been deeply discussed and analyzed. In particular, models are required to specify a rate in space-time-magnitude bins, and it is assumed that these rates are independent and characterized by Poisson uncertainty. In this work we have explored in detail these assumptions and their impact on CSEP testing procedures when applied to a widely used class of models, i.e., the Epidemic-Type Aftershock Sequence (ETAS) models. Our results show that, if an ETAS model is an accurate representation of seismicity, the same "right" model is rejected by the current CSEP testing procedures a number of times significantly higher than expected. We show that this deficiency is due to the fact that the ETAS models produce forecasts with a variability significantly higher than that of a Poisson process, invalidating one of the main assumption that stands behind the CSEP/RELM evaluation process. Certainly, this shortcoming does not negate the paramount importance of the CSEP experiments as a whole, but it does call for a specific revision of the testing procedures to allow a better understanding of the results of such experiments

On the Increase of Background Seismicity Rate during the 1997-1998 Umbria-Marche, Central Italy, Sequence: Apparent Variation or Fluid-Driven Triggering?

We investigate the temporal evolution of background seismicity rate in the Umbria-Marche sector of the northern Apennines that was struck by the 1997-98 Colfiorito seismic sequence. Specifically we apply the ETAS model to separate the background seismicity rate from the coseismic triggered rate of earthquake production. Analyzed data are extracted from the CSI1.1 catalog of Italian seismicity (1981-2002), which contains for the study area 12.163 events with ML > 1.5. The capability of the ETAS model to match the observed seismicity rate is tested by analyzing the model residuals and by applying two non-parametric statistical tests (the RUNS and the Kolmogorov-Smirnov tests) to verify the fit of residuals to Poisson hypothesis. We first apply the ETAS model to the seismicity occurred in the study area during the whole period covered by the CSI1.1 catalog. Our results show that the ETAS model does not explain the temporal evolution of seismicity in a time interval defined by change points identified from time-evolution of residuals and encompassing the Colfiorito seismic sequence. We therefore restrict our analysis to this period and analyze only those events belonging to the 1997-1998 seismic sequence. We again obtain the inadequacy of a stationary ETAS model with constant background rate to reproduce the temporal pattern of observed seismicity. We verify that the failure of ETAS model to fit the observed data is caused by the increase of the background seismicity rate associated with the repeated Colfiorito main shocks. We interpret the inferred increase of background rate as a consequence of the perturbation to the coseismic stress field caused by fluid flow and/or pore pressure relaxation. In particular we show that the transient perturbation caused by poroelastic relaxation can explain the temporal increase of background rate that therefore represents a fluid signal in the seismicity pattern

Assessing annual global M6+ seismicity forecasts

We consider a seismicity forecast experiment conducted during the last 4 yr. At the beginning of each year, three models make a 1-yr forecast of the distribution of large earthquakes everywhere on the Earth. The forecasts are generated and the observations are collected in the Collaboratory for the Study of Earthquake Predictability (CSEP). We apply CSEP likelihood measures of consistency and comparison to see how well the forecasts match the observations, and we compare results from some intuitive reference models. These results illustrate some undesirable properties of the consistency tests: the tests can be extremely sensitive to only a few earthquakes, and yet insensitive to seemingly obvious flaws—a naïve hypothesis that large earthquakes are equally likely everywhere is not always rejected. The results also suggest that one should check the assumptions of the so-called T and W comparison tests, and we illustrate some methods to do so. As an extension of model assessment, we explore strategies to combine forecasts, and we discuss the implications for operational earthquake forecasting. Finally, we make suggestions for the next generation of global seismicity forecast experiment

The ETAS model for daily forecasting of Italian seismicity in the CSEP experiment

This paper investigates the basic properties of the recent shallow seismicity in Italy through stochastic modeling and statistical methods. Assuming that the earthquakes are the realization of a stochastic point process, we model the occurrence rate density in space, time and magnitude by means of an Epidemic Type Aftershock Sequence (ETAS) model. By applying the maximum likelihood procedure, we estimates the parameters of the model that best fit the Italian instrumental catalog, recorded by the Istituto Nazionale di Geofisica e Vulcanologia (INGV) from April 16th 2005 to June 1st 2009. Then we apply the estimated model on a second independent dataset (June 1st 2009- Sep 1st 2009). We find that the model performs well on this second database, by using proper statistical tests. The model proposed in the present study is suitable for computing earthquake occurrence probability in real time and to take part in international initiatives such as the Collaboratory Study for Earthquake Predictability (CSEP). Specifically we have submitted this model for the daily forecasting of Italian seismicity above Ml4.0

The global aftershock zone

The aftershock zone of each large (M ≥ 7) earthquake extends throughout the shallows of planet Earth. Most aftershocks cluster near the mainshock rupture, but earthquakes send out shivers in the form of seismic waves, and these temporary distortions are large enough to trigger other earthquakes at global range. The aftershocks that happen at great distance from their mainshock are often superposed onto already seismically active regions, making them difficult to detect and understand. From a hazard perspective we are concerned that this dynamic process might encourage other high magnitude earthquakes, and wonder if a global alarm state is warranted after every large mainshock. From an earthquake process perspective we are curious about the physics of earthquake triggering across the magnitude spectrum. In this review we build upon past studies that examined the combined global response to mainshocks. Such compilations demonstrate significant rate increases during, and immediately after (~45 min) M N 7.0 mainshocks in all tectonic settings and ranges. However, it is difficult to find strong evidence for M N 5 rate increases during the passage of surface waves in combined global catalogs. On the other hand, recently published studies of individual large mainshocks associate M N 5 triggering at global range that is delayed by hours to days after surface wave arrivals. The longer the delay between mainshock and global aftershock, the more difficult it is to establish causation. To address these questions, we review the response to 260 M ≥ 7.0 shallow (Z ≤ 50 km) mainshocks in 21 global regions with local seismograph networks. In this way we can examine the detailed temporal and spatial response, or lack thereof, during passing seismic waves, and over the 24 h period after their passing. We see an array of responses that can involve immediate and widespread seismicity outbreaks, delayed and localized earthquake clusters, to no response at all. About 50% of the catalogs that we studied showed possible (localized delayed) remote triggering, and ~20% showed probable (instantaneous broadly distributed) remote triggering. However, in any given region, at most only about 2–3% of global mainshocks caused significant local earthquake rate increases. These rate increases are mostly composed of small magnitude events, and we do not find significant evidence of dynamically triggered M N 5 earthquakes. If we assume that the few observed M N 5 events are triggered, we find that they are not directly associated with surface wave passage, with first incidences being 9–10 h later. We note that mainshock magnitude, relative proximity, amplitude spectra, peak ground motion, and mainshock focal mechanisms are not reliable determining factors as to whether a mainshock will cause remote triggering. By elimination, azimuth, and polarization of surface waves with respect to receiver faults may be more important factors

VISTO: An open-source device to measure exposure time in psychological experiments

The study of higher cognitive processes often relies on the manipulation of bottom-up stimulus characteristics such as exposure time. While several software exist that can schedule the onset and offset time of a visual stimulus, the actual exposure time depends on several factors that are not easy to control, resulting in undesired variability within and across studies. Here we present VISTO, a simple device built on the Arduino platform that allows one to measure the exact onset and offset of a visual stimulus, and to test its synchronization with a trigger signal. The device is used to measure the profile of luminance waveforms in arbitrary analog/digital (AD) units, and the implications of these luminance profiles are discussed based on a model of information accumulation from visual exposure. Moreover, VISTO can be calibrated to match the brightness of each experimental monitor. VISTO allows for control of stimulus timing presentation, both in classical laboratory settings and in more complex settings as technology allows to use new display devices or acquisition equipment. In sum, VISTO allows one to: • measure the profile of luminance curves. • determine the exposure time of a visual stimulus. • measure the synchronization between a trigger signal and a visual stimulus