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首页> 外文期刊>Journal of applied statistics >A continuous-time HMM approach to modeling the magnitude-frequency distribution of earthquakes
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A continuous-time HMM approach to modeling the magnitude-frequency distribution of earthquakes

机译：连续时间HMM方法模拟地震震级-频率分布

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摘要

The magnitude-frequency distribution (MFD) of earthquake is a fundamental statistic in seismology. The so-called b-value in the MFD is of particular interest in geophysics. A continuous time hidden Markov model (HMM) is proposed for characterizing the variability of b-values. The HMM-based approach to modeling the MFD has some appealing properties over the widely used sliding-window approach. Often, large variability appears in the estimation of b-value due to window size tuning, which may cause difficulties in interpretation of b-value heterogeneities. Continuous-time hidden Markov models (CT-HMMs) are widely applied in various fields. It bears some advantages over its discrete time counterpart in that it can characterize heterogeneities appearing in time series in a finer time scale, particularly for highly irregularly-spaced time series, such as earthquake occurrences. We demonstrate an expectation-maximization algorithm for the estimation of general exponential family CT-HMM. In parallel with discrete-time hidden Markov models, we develop a continuous time version of Viterbi algorithm to retrieve the overall optimal path of the latent Markov chain. The methods are applied to New Zealand deep earthquakes. Before the analysis, we first assess the completeness of catalogue events to assure the analysis is not biased by missing data. The estimation of b-value is stable over the selection of magnitude thresholds, which is ideal for the interpretation of b-value variability.
机译：地震的幅频分布是地震学中的一项基本统计数据。 MFD中的所谓b值在地球物理学中特别受关注。提出了一种连续时间隐马尔可夫模型（HMM）来表征b值的变异性。与广泛使用的滑动窗口方法相比，基于HMM的MFD建模方法具有一些吸引人的特性。通常，由于窗口大小调整，在b值的估计中会出现较大的可变性，这可能会导致b值异质性解释方面的困难。连续时间隐马尔可夫模型（CT-HMM）广泛应用于各个领域。与离散时间相对物相比，它具有一些优势，因为它可以在更精细的时间尺度上表征时间序列中出现的异质性，特别是对于高度不规则间隔的时间序列，例如地震发生。我们展示了一种期望最大化算法，用于估计一般指数族CT-HMM。与离散时间隐马尔可夫模型并行，我们开发了维特比算法的连续时间版本，以检索潜在马尔可夫链的整体最优路径。该方法适用于新西兰深地震。在分析之前，我们首先评估目录事件的完整性，以确保分析不会因缺少数据而产生偏差。 b值的估计在选择幅度阈值时是稳定的，这对于b值变异性的解释是理想的。

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