An adequate characterization of the temporal features of background seismicity, namely after removal of temporally and spatially clustered events (e.g. aftershocks), is a key element in several studies aimed at earthquake forecasting and seismic hazard assessment. In order to investigate the features of background seismicity component, we analyse the rate of background events, that is the rate of main/independent earthquakes as identified by Nearest Neighbour (NN) and Stochastic Declustering (SD) methods. The use of two different declustering methods, which are based on diverse statistical and physical assumptions, allows us to assess whether the identified features depend on the specific definition of background events. In this study, we carry out an in depth analysis of the time changes of background seismicity rate in Northeastern Italy, by means of continuous-time Hidden Markov Models, a stochastic tool that can be used to assess heterogeneity in the temporal pattern of seismicity rates. Specifically, we aim at understanding if the analysed time series can be better described by a homogeneous Poisson model, with unique constant rate, or by a switched Poisson model (i.e. linked to some systematic changes in earthquakes occurrence rates) or whether a basically different model is required. The analysis performed based on Markov modulated Poisson process, and according to Bayesian Information Criterion, shows that a switched Poisson process with three states is the best model describing the background rate identified by SD and NN approaches. The capability of adopted methodology in identifying seismicity rate changes, as well as the sensitivity of the method against the minimum magnitude threshold of analysis, have been verified by applying the method to synthetic catalogues with known properties, namely Poissonian time series with different rates prescribed in specific time intervals. The obtained results suggest that a Poisson model with multiple rates can be used to properly describe background seismicity in Northeastern Italy.

在针对地震预报和地震危险性评估的多项研究中，充分表征背景地震活动的时间特征，即去除时空聚集的事件（例如余震）之后，是一个关键要素。为了调查背景地震活动分量的特征，我们分析了背景事件的发生率，即通过最近邻居（NN）和随机聚类（SD）方法确定的主要/独立地震的发生率。基于不同的统计和物理假设，使用两种不同的去聚类方法，使我们能够评估所识别的特征是否取决于背景事件的特定定义。在这项研究中，我们对意大利东北部地区背景地震活动率的时间变化进行了深入分析，通过连续时间隐马尔可夫模型，这是一种随机工具，可用于评估地震发生率的时间模式中的异质性。具体来说，我们旨在了解是否可以通过均一的泊松模型（具有唯一的恒定速率）或转换的泊松模型（即与地震发生率的某些系统性变化相关联）更好地描述分析的时间序列，或者是否可以使用基本不同的模型是必须的。基于马尔可夫调制泊松过程并根据贝叶斯信息准则进行的分析表明，具有三种状态的切换泊松过程是描述SD和NN方法识别的背景速率的最佳模型。所采用方法论确定地震烈度变化的能力，通过将该方法应用于具有已知属性的合成目录，即具有特定时间间隔中规定的不同速率的泊松时间序列，已验证了该方法以及针对最小分析阈值的灵敏度。获得的结果表明，具有多个比率的泊松模型可用于正确描述意大利东北部的背景地震活动。