Feature Extraction Algorithm Using a Correlation Coefficient Combined With the VMD and Its Application to the GPS and GRACE

To improve the reliability of the Global Positioning System (GPS) and Gravity Recovery and Climate Experiment (GRACE) feature extraction, this paper uses a correlation coefficient combined with the traditional variational mode decomposition (VMD), proposing a new correlation variational mode decomposition (CVMD). In contrast to previous studies, the CVMD denoises the sequences before feature extraction and it is the first time that be used in the GPS and GRACE. First, the correlation between the intrinsic mode function (IMF) and the original sequence is obtained to denoise the original sequence. Moreover, the algorithm reuses the VMD to obtain the IMF components with different frequencies. Then the Lomb Scargle (L-S) spectral analysis and energy density are used to obtain the trend-, seasonal, and residual items. Second, the features of the GPS and GRACE time series are extracted based on the CVMD and multidimensional ensemble empirical mode decomposition (MEEMD) to verify the availability of the CVMD. The results indicate that the CVMD is more superior to the MEEMD in feature extraction. Third, the CVMD is used to extract the trend- and seasonal terms of GPS and GRACE in the North China Plain (NCP). The conclusions are as follows: (1) the seasonal items of GRACE are used to correct the GPS sequences, and the average reduction of the weighted root mean square (WRMS) of each GPS station is 0.69, which demonstrates a strong consistency between the seasonal terms of the GPS sequence and GRACE sequence; (2) during 2003-2015, the mean slope of vertical displacements is 0.20 ± 0.07 mm / yr, and the uplift rate increases substantially (1.66 ± 0.62 mm / yr) after 2013. Then, the temporal and spatial relationship between rainfall and crustal load-deformation in the NCP is analyzed, and it is found that the crustal load-deformation is primarily related to rainfall, while human activities play a leading role in the southwestern regions where agricultural irrigation is relatively strong.