Three dimensional empirical mode decomposition analysis apparatus, method and article manufacture

摘要

An apparatus, article of manufacture, and method of physical phenomena analysis. In particular the physical phenomena may include any varying three-dimensional (3D) physical phenomena such as time varying polar ice flows, for example. A linear trend line and a modeled seasonal cycle may be removed from the representation of the 3D phenomenon to keep subsequent matrix operations within machine capabilities. The representation is passed through a Hilbert transform to convert the data into complex form. A spatial variable is separated from the complex representation by producing a time based covariance matrix. The temporal parts of the principal components are produced by applying Singular Value Decomposition (SVD). Based on the rapidity with which the eigenvalues decay, the first 3-10 complex principal components (CPCs) are selected for Empirical Mode Decomposition (EMD) into intrinsic modes. The intrinsic modes produced are selected in order to filter the intrinsic modes with either a high-pass, low-pass or band-pass filter. The spatial part of the CPCs (multiplied by the appropriate eigenvalues) is reconstructed by multiplying the unfiltered temporal part into the original data. Finally, a filtered time series may be reconstructed from the first 3-10 filtered complex PCs. The reconstructed filtered time series may be displayed for checking. Thus, a valid intercomparison of various data sequences on an intrinsic mode-by-mode basis is permitted to enhance greatly the ability to establish teleconnections between various geophysical variables.