A review of empirical orthogonal function (EOF) with an emphasis on the co-seismic crustal deformation analysis

An automatic, transparent, and regular way to investigate and analyze the spatiotemporal variations in a large, unstructured, and high-dimensional data set is highly desirable in almost every area of knowledge. In light of this, the present study concentrates on a versatile spatiotemporal technique, empirical orthogonal function (EOF), and provides a thorough review of the EOF method with an emphasis on the co-seismic crustal deformation analysis. For this, (i) we provide a mathematical description of the EOF method that decomposes a coherent space–time data set into individual spatial patterns and associated time scales; (ii) we highlight the strength of the EOF method and its several extensions in dealing with correlated data variables, intermittent data gaps, and nonlinear relations among data features; (iii) we discuss prominent applications of the innovative data-summarization EOF method in diverse fields, such as crustal deformation analysis, pattern hunting in climate and atmospheric sciences, reconstruction of gappy data, and ionospheric total electron content (TEC) modeling; and (iv) finally, we implement the EOF method to demonstrate its efficacy in the 3-D co-seismic pattern identification caused by the 2016, $$M_\mathrm{w}$$ M w 7.8, Kaikoura earthquake of New Zealand. As a self-organizing approach, the EOF method not only uncovers the unique dynamic patterns hidden behind the data set, but also is capable of recovering the missing values in a large-volume data set .