Stochastic models for earthquake occurrence

The complexity of seismogenesis requires the development of stochastic models, the application of which aims to improve our understanding on the seismic process and the associated underlying process. Semi Markov models are introduced for estimating the expected number of earthquake occurrences with the classification of the model states based on earthquake magnitudes. The instantaneous earthquake occurrence rate between the model states as well as the total earthquake occurrence rate can be calculated. Seismotectonic characteristic of the study area, incorporated in the model as important component of the model, increase the consistency between the model and the process of earthquake generation and support a classification that integrates magnitudes and style of faulting, thus being more effective for the seismic hazard assessment. For revealing the stress field underlying the earthquake generation, which is not accessible to direct observation, the hidden Markov models (HMMs) are engaged. The HMMs consider that the states correspond to levels of the stress field and its application aim to reveal these states. Different number of states may be examined, dependent upon the organization of observations, and the HMMs are capable to reveal the number of stress levels as well as the way in which these levels are associated with the occurrence of certain earthquakes. Even better results are obtained via the application of hidden semi–Markov models (HSMMs) considering that the stress field constitutes the hidden process and which, compared with HMMs, allow any arbitrary distribution for the sojourn times. The investigation of the interactions between adjacent areas is accomplished by means of the linked stress release model (LSRM), based upon the consideration that spatio–temporal stress changes and interactions between adjacent fault segments constitute the most important component in seismic hazard assessment, as they can alter the occurrence probability of strong earthquakes onto these segments. The LSRM comprises the gradual increase of the strain energy due to continuous tectonic loading and its sudden release during the earthquake occurrence. The modeling is based on the theory of stochastic point process, and it is determined by the conditional intensity function. In an attempt to identify the most appropriate parameterization that better fits the data and describes the earthquake generation process, a constrained “m–memory” point process is introduced, the Constrained–Memory Stress Release Model (CM–SRM) implying that only the m most recent arrival times are taken into account in the conditional intensity function, for some suitable mÎN, instead of the entire history of the process. The performance of the above mentioned models application are evaluated and compared in terms of information criteria and residual analysis.