Spatial-temporal Analysis of Earthquake Catalogs using Point Processes

该项目的目的是开发和应用描述地震目录的统计技术，主要侧重于时空标记点过程模型和密切相关的物体，如镶嵌和分支过程。地震学应用的目标是拟合、评估和改进模型，如流行病余震序列(ETAS)模型，这些模型可用于描述地震目录，特别是地震断层的几何和时空结构，并彻底调查地震参数记录中的错误及其对地震推断(如地震危险性估计和模型参数的标准误差)的影响。除了开发新的有用的随机模型外，主要的统计目标是将评估方法，特别是通过重新缩放和细化的点过程残差分析，扩展到时空标记点过程以及镶嵌和分支过程等其他类型的模型的情况，并开发残差的平稳性检验，这些检验在检测偏离空间均质性和时空震级分离性方面具有强大的作用。该项目有可能对这些潜在破坏性事件的准备和应对产生非常直接的社会影响。地震危险性评估是对在特定时间间隔内某一地区至少发生一定规模地震的可能性进行量化，这对于土木工程、防震和应对系统以及确定地震保险费是至关重要的，而地震保险费反过来又会影响政府的政策和财产估值。为了更准确地估计地震危险性，本项目中描述的地震模式的时空模型的改进是必要的。此外，分析地震目录中的错误及其对地震危险性估计的影响对于公众和科学界正确认识地震预报中的不确定性至关重要。本项目开发的统计工具对其他应用程序也很有用。特别是，时空标记点过程模型对于描述地震以外的其他自然现象的发生非常重要，例如野火、疾病流行、飓风等。

The aim of this project is the development and application of statistical techniques for describing earthquake catalogs, focusing primarily on spatial-temporal marked point process models and closely related objects such as tessellations and branching processes. The goals of the seismological application are the fitting, assessment, and improvement of models such as the epidemic-type aftershock sequence (ETAS) model, which are useful for describing earthquake catalogs, especially the geometric and spatial-temporal structure of earthquake faults, and the thorough investigation of errors in records of earthquake parameters and their impact on seismological inferences such as estimates of seismic hazard and standard errors for model parameters. In addition to the development of new useful stochastic models, the main statistical goals are the extension of assessment methods, especially point process residual analyses via rescaling and thinning, to the case of spatial-temporal marked point processes as well as other types of models such as tessellations and branching processes, and the development of tests for stationarity in the residuals that are powerful in the detection of departures from spatial homogeneity and from the assumption of spatial-temporal-magnitude separability.Major earthquakes are catastrophic events that can cause numerous injuries, loss of lives, and billions of dollars in damages to public and private property. This project has the potential for very direct societal impact on the preparation for and response toward these potentially devastating occurrences. Seismic hazard estimation, defined as the quantification of the likelihood of an earthquake of at least a given size occurring in a certain region within a given time interval, is crucial to civil engineering, earthquake preparedness and response systems, and the determination of earthquake premiums which in turn influence governmental policy and property valuation. The refinement of spatial-temporal models for earthquake patterns described in this project is necessary for more precise estimation of seismic hazard..Further, the analysis of errors in earthquake catalogs and their impact on seismic hazard estimates is critical in order for proper awareness of uncertainties in earthquake forecasts among the public and scientific community. The statistical tools developed in this project are useful for other applications as well. In particular, spatial-temporal marked point process models are important for describing the occurrences of other natural phenomena besides earthquakes, such as wildfires, disease epidemics, hurricanes, and many others.