A review and new insights on the estimation of the b-valueand its uncertainty

The estimation of the b-value of the Gutenberg-Richter Law and its uncertainty is crucial in seismic hazard studies, as well as in verifying theoretical assertions, such as, for example, the universality of the Gutenberg-Richter Law. In spite of the importance of this issue, many scientific papers still adopt formulas that lead to different estimations. The aim of this paper is to review the main concepts relative to the estimation of the b-value and its uncertainty, and to provide some new analytical and numerical insights on the biases introduced by the unavoidable use of binned magnitudes, and by the measurement errors on the magnitude. It is remarked that, although corrections for binned magnitudes were suggested in the past, they are still very often neglected in the estimation of the b-value, implicitly by assuming that the magnitude is a continuous random variable. In particular, we show that: i) the assumption of continuous magnitude can lead to strong bias in the b-value estimation, and to a significant underestimation of its uncertainty, also for binning of ?M = 0.1; ii) a simple correction applied to the continuous formula causes a drastic reduction of both biases; iii) very simple formulas, until now mostly ignored, provide estimations without significant biases; iv) the effect on the bias due to the measurement errors is negligible compared to the use of binned magnitudes

A technical note on the bias in the estimation of the b-value and its uncertainty through the Least Squares technique

We investigate conceptually, analytically, and numerically the biases in the estimation of the b-value of the Gutenberg-Richter Law and of its uncertainty made through the least squares technique. The biases are introduced by the cumulation operation for the cumulative form of the Gutenberg-Richter Law, by the logarithmic transformation, and by the measurement errors on the magnitude. We find that the least squares technique, applied to the cumulative and binned form of the Gutenberg-Richter Law, produces strong bias in the b-value and its uncertainty, whose amplitudes depend on the size of the sample. Furthermore, the logarithmic transformation produces two different endemic bends in the Log(N) versus M curve. This means that this plot might produce fake significant departures from the Gutenberg-Richter Law. The effect of the measurement errors is negligible compared to those of cumulation operation and logarithmic transformation. The results obtained show that the least squares technique should never be used to determine the slope of the Gutenberg-Richter Law and its uncertainty

The influence of entrepreneurs’ immigrant status and time on the perceived likelihood of exporting

We contribute in this paper to the scant literature on the factors and conditions influencing the development of different perceptions of potential international opportunities for immigrant and native entrepreneurs in the pre-internationalization phase. Specifically, we investigate what factors influence the perceived likelihood entrepreneurs have of exporting. Building on entrepreneurial intentions and opportunity-based entrepreneurial processes, we propose a cognitive account of perceived likelihood of exporting based on entrepreneurs’ perceptions of the desirability and feasibility of export opportunities. We investigate how the immigrant status (i.e., individual characteristics) and time (i.e., contextual factors) influence the relationship between the desirability and feasibility of exporting, and entrepreneurs’ perceived likelihood of exporting. We employ an experimental design on a matched-pair sample of 108 native and immigrant entrepreneurs in domestic technology-based firms. The results are a unique account of the cognitive antecedents of the perceived likelihood of exporting under different temporal conditions, comparing immigrant and native entrepreneurs. We discuss theoretical and practical implications

BET VH: a probabilistic tool for long-term volcanic hazard assessment

In this paper we illustrate a Bayesian Event Tree to estimate Volcanic Hazard (BET VH). The procedure enables us to calculate the probability of any kind of long-term hazardous event for which we are interested, accounting for the intrinsic stochastic nature of volcanic eruptions and our limited knowledge regarding related processes. For the input, the code incorporates results from numerical models simulating the impact of hazardous volcanic phenomena on an area, and data from the eruptive history. For the output, the code provides a wide and exhaustive set of spatio-temporal probabilities of different events; these probabilities are estimated by means of a Bayesian approach that allows all uncertainties to be properly accounted for. The code is able to deal with many eruptive settings simultaneously, weighting each with its own probability of occurrence. In a companion paper, we give a detailed example of application of this tool to the Campi Flegrei caldera, in order to estimate the hazard from tephra fall

Probabilistic volcanic hazard assessment and eruption forecasting: the Bayesian Event Tree approach

The purpose of this report is to discuss in detail the importance and prerogatives of quantitative volcanic hazard assessment and to describe the main features of a Bayesian model designed to achieve this goal. Ideas, models and results come out from the work made in the framework of the INGV-DPC V4 project, and partially from the application of the technique to Campi Flegrei (V3_2) and Vesuvius (V3_4). Here, we examine in depth the practical and philosophical implications of the approach, and report only a brief summary of the technical details that can be found on the cited literature

Bayesian event tree for eruption forecasting (BET_EF) at Vesuvius, Italy: a retrospective forward application to the 1631 eruption

Reliable forecasting of the next eruption at Vesuvius is the main scientific factor in defining effective strategies to reduce volcanic risk in one of the most dangerous volcanic areas of the world. In this paper, we apply a recently developed probabilistic code for eruption forecasting to new and independent historical data related to the pre-eruptive phase of the 1631 eruption. The results obtained point out three main issues: (1) the importance of “cold” historical data (according to Guidoboni 2008) related to pre-eruptive phases for evaluating forecasting tools and possibly refining them; (2) the BET_EF code implemented for Vesuvius would have forecasted the 1631 eruption satisfactorily, marking different stages of the pre-eruptive phase; (3) the code shows that pre-eruptive signals that significantly increase the probability of eruption were likely detected more than 2 months before the event

A quantitative model for volcanic hazard assessment

Volcanic hazard assessment is a basic ingredient for risk-based decision-making in land-use planning and emergency management. Volcanic hazard is defined as the probability of any particular area being affected by a destructive volcanic event within a given period of time (Fournier d’Albe 1979). The probabilistic nature of such an important issue derives from the fact that volcanic activity is a complex process, characterized by several and usually unknown degrees of freedom that are often linked by nonlinear relationships (e.g. Bak et al. 1988). Except in sporadic cases, the result of this complexity is an intrinsic, and perhaps unavoidable, unpredictability of the time evolution of the volcanic system from a deterministic point of view

BET_EF: a probabilistic tool for long- and short-term eruption forecasting

The main purpose of this paper is to introduce a Bayesian event tree model for eruption forecasting (BET_EF). The model represents a flexible tool to provide probabilities of any specific event at which we are interested in, by merging all the relevant available information, such as theoretical models, a priori beliefs, monitoring measures, and any kind of past data. BET_EF is based on a Bayesian procedure and it relies on the fuzzy approach to manage monitoring data. The method deals with short- and long-term forecasting, therefore it can be useful in many practical aspects, as land use planning, and during volcanic emergencies. Finally, we provide the description of a free software package that provides a graphically supported computation of short- to long-term eruption forecasting, and a tutorial application to the recent MESIMEX exercise at Vesuvius

On the spatio-temporal distribution of M 7.0+ worldwide seismicity with a non-parametric statistics

The aim of this paper is to provide some constrains on the time behavior of earthquake generation mechanism, through the usage of a non-parametric statistics that leads up to the empirical estimation of the hazard function. The results indicate that the most characterizing temporal feature for large (M 7.0+) worldwide shallow earthquake occurrence is a clustering lasting few years, indicating that the probability of earthquake occurrence is higher immediately after the occurrence of an event. After that, the process becomes almost time independent, as in a Poisson process. Remarkably, this time clustering is very similar to what previously found for different spatio-magnitude windows, and it does not seem to depend on the tectonic style of the region. This may support the hypothesis of an universal law for earthquake occurrence

BET_VH: exploring the influence of natural uncertainties on long-term hazard from tephra fallout at Campi Flegrei (Italy)

In this paper, we explore the effects of the intrinsic uncertainties upon long-term volcanic hazard by analyzing tephra fall hazard at Campi Flegrei, Italy, using the BET_VH model described in Marzocchi et al. (Bull Volcanol, 2010). The results obtained show that volcanic hazard based on the weighted average of all possible eruptive settings (i.e. size classes and vent locations) is significantly different from an analysis based on a single reference setting, as commonly used in volcanic hazard practice. The long-term hazard map for tephra fall at Campi Flegrei obtained here accounts for a wide spectrum of uncertainties which are usually neglected, largely reducing the bias intrinsically introduced by the choice of a specific reference setting. We formally develop and apply a general method to recursively integrate simulations from different models which have different characteristics in terms of spatial coverage, resolution and physical details. This outcome of simulations will be eventually merged with field data through the use of the BET_VH model