An energy-dependent earthquake moment–frequency distribution

The magnitude–frequency distribution (MFD) of many earthquake catalogs is well described by the Gutenberg–Richter (GR) law or its tapered version (TGR). This distribution is usually extrapolated to any subsets of the space–time window covered by the catalog. However, some empirical observations and logical thoughts may raise doubts about the validity of this extrapolation. For example, according to the elastic rebound theory, we may assert that the probability of a strong shock nucleating within a short-time interval in a small area A just ruptured by another strong event should be lower than that expected by GR (or TGR): a lot of energy has already been released, and it takes time to recover to the previous state. Here, we put forward a space–time modification of the TGR, named energy-dependent TGR (TGRE) in which the corner seismic moment becomes a time-varying energy function depending on (1) the conceivable strongest shock that may nucleate in A; (2) the time elapsed since the last strong earthquake that reset the elastic energy in A to a residual value; and (3) the rate of the energy recovery, linked to the recurrence time of the fault(s) involved. The model also verifies an invariance condition: for large space–time windows, the occurrence of a strong shock does not affect significantly the whole elastic energy available, that is, the TGRE becomes the TGR. The model is simple and rooted in clearly stated assumptions. To evaluate its reliability and applicability, we apply it to the 1992 Landers sequence. As expected by TGRE, we find that the MFD close to the fault system interested by the mainshock (Mw 7.3) differs from that of earthquakes off-fault, showing a lower corner magnitude. We speculate that TGRE may be profitably used in operational earthquake forecasting and that it explains the empirical observation that the strongest aftershocks nucleate always outside the mainshock fault

How likely does an aftershock sequence conform to a single omori law behavior?

The most popular aftershock forecasting model is based on the modified Omori law (MOL), which describes the expected decay of the aftershock given the mainshock's magnitude. Although such a model is still widely used for operational purposes, it is not unusual that one or more aftershocks break the MOL behavior. In this case, the time evolution of the aftershock sequence becomes much more complicated, and it may be better described by more advanced models, which also account for the triggering capability of all aftershocks. The purpose of this work is to analyze deductively the conditions under which the mean trend of an aftershock sequence, generated by one single mainshock according to the MOL, is satisfactorily described by an inverse power law. Practically, this analysis provides the likelihood that an aftershock sequence will conform to one single MOL; that is, the likelihood of delivering reliable forecasts using a model based on a single MOL. Specifically, we analyze which conditions are present when the triggering capability of a selected aftershock significantly affects the aftershock rate caused by the mainshock. For example, we discuss the application of this scheme to sequences that either conform, or do not, to the MOL behavior, such as the Amatrice-Norcia (Italy 2016-2017), Emilia (Italy 2012), and Tohoku-Oki (Japan 2011) aftershock sequences. © 2018 Seismological Society of America. All rights reserved

A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling

In statistical seismology, the Epidemic Type Aftershocks Sequence (ETAS) model is a branching process used world-wide to forecast earthquake intensity rates and reproduce many statistical features observed in seismicity catalogs. In this paper, we describe a fractional differential equation that governs the earthquake intensity rate of the pure temporal ETAS model by using the Caputo fractional derivative and we solve it analytically. We highlight that the tools and special functions of fractional calculus simplify the classical methods employed to obtain the intensity rate and let us describe the change of solution decay for large times. We also apply and discuss the theoretical results to the Japanese catalog in the period 1965-2003

How to be fooled searching for significant variations of the b-value

An unbiased estimation of the b-value and of its variability is essential to verify empirically its physical contribution to the earthquake generation process, and the capability to improve earthquake forecasting and seismic hazard. Notwithstanding the vast literature on the b-value estimation, we note that some potential sources of bias that may lead to non-physical b-value variations are too often ignored in seismological common practice. The aim of this paper is to discuss some of them in detail, when the b-value is estimated through the popular Aki's formula. Specifically, we describe how a finite data set can lead to biased evaluations of the b-value and its uncertainty, which are caused by the correlation between the b-value and the maximum magnitude of the data set; we quantify analytically the bias on the b-value caused by the magnitude binning; we show how departures from the exponential distribution of the magnitude, caused by a truncated Gutenberg-Richter law and by catalogue incompleteness, can affect the b-value estimation and the search for statistically significant variations; we derive explicitly the statistical distribution of the magnitude affected by random symmetrical error, showing that the magnitude error does not induce any further significant bias, at least for reasonable amplitude of the measurement error. Finally, we provide some recipes to minimize the impact of these potential sources of bias

An Operational Earthquake Forecasting Experiment for Israel: Preliminary Results

Operational Earthquake Forecasting (OEF) aims to deliver timely and reliable forecasts that may help to mitigate seismic risk during earthquake sequences. In this paper, we build the first OEF system for the State of Israel, and we evaluate its reliability. This first version of the OEF system is composed of one forecasting model, which is based on a stochastic clustering Epidemic Type Earthquake Sequence (ETES) model. For every day of the forecasting time period, January 1, 2016 - November 15, 2020, the OEF-Israel system produces a weekly forecast for target earthquakes with local magnitudes greater than 4.0 and 5.5 in the entire State of Israel. Specifically, it provides space-time-dependent seismic maps of the weekly probabilities, obtained by using a fixed set of the model’s parameters, which are estimated through the maximum likelihood technique based on a learning period of about 32 years (1983–2015). According to the guidance proposed by the Collaboratory for the Study of Earthquake Predictability (CSEP), we also perform the N- and S-statistical tests to verify the reliability of the forecasts. Results show that the OEF system forecasts a number of events comparable to the observed one, and also captures quite well the spatial distribution of the real catalog with the exception of two target events that occurred in low seismicity regions

The effects of aerobic exercise on metabolic risk, insulin sensitivity and intrahepatic lipid in healthy older people from the Hertfordshire cohort study: a randomised controlled trial

Aims/hypothesis We sought to determine the effect of an aerobic exercise intervention on clustered metabolic risk and related outcomes in healthy older adults in a single-centre, explanatory randomised controlled trial.Methods Participants from the Hertfordshire Cohort Study (born 1931–1939) were randomly assigned to 36 supervised 1 h sessions on a cycle ergometer over 12 weeks or to a non-intervention control group. Randomisation and group allocation were conducted by the study co-ordinator, using a software programme. Those with prevalent diabetes, unstable ischaemic heart disease or poor mobility were excluded. All data were collected at our clinical research facility in Cambridge. Components of the metabolic syndrome were used to derive a standardised composite metabolic risk score (zMS) as the primary outcome. Trial status: closed to follow-up.Results We randomised 100 participants (50 to the intervention, 50 to the control group). Mean age was 71.4 (range 67.4–76.3) years. Overall, 96% of participants attended for follow-up measures. There were no serious adverse events. Using an intention-to-treat analysis, we saw a non-significant reduction in zMS in the exercise group compared with controls (0.07 [95% CI ?0.03, 0.17], p?=?0.19). However, the exercise group had significantly decreased weight, waist circumference and intrahepatic lipid, with increased aerobic fitness and a 68% reduction in prevalence of abnormal glucose metabolism (OR 0.32 [95% CI 0.11–0.92], p?=?0.035) compared with controls. Results were similar in per-protocol analyses.Conclusions/interpretation Enrolment in a supervised aerobic exercise intervention led to weight loss, increased fitness and improvements in some but not all metabolic outcomes. In appropriately screened older individuals, such interventions appear to be safe.<br/