Normal Morlet wavelet transform and its application to the Earth's polar motion

摘要

The normal Morlet wavelet transform (NMWT), which is a mathematical method for harmonic analysis, is defined in this study by resorting to L 1 normalization continuous wavelet transform and a normalized simplified Morlet wavelet. The NMWT of a complex time signal enables direct recognition and extraction of the harmonic components of the signal without an inverse transform. We demonstrate theoretically and numerically the benefit of the NMWT in the harmonic analysis. A NMWT analysis of the observed polar motion data shows that except for the prograde annual wobble (PAW), the interseasonal wobbles including the retrograde annual wobble (RAW) became less significant in amplitude by at least 70% after the 1970s, manifesting the accuracy improvement in the polar motion observation. This NMWT analysis proves that the observed Chandler wobble possesses only one instantaneous period at any time point within the 20th century and such instantaneous period is slightly variable around 433.08 days with a standard deviation of 1.57 days from 1950 to 2000. Using the NMWT analysis, we show that at the prograde and retrograde annual scales, the atmospheric pressure and the oceanic current play the most significant and stable role in polar motion excitation. The atmosphere and ocean can explain the phases of the PAW with 15 days discrepancy but only 70% of the amplitude of the PAW. However, they can explain the RAW with less than 10 days in phase discrepancy and less than 10% in amplitude discrepancy. This study reveals that the ocean always reduces the atmospheric effects on the annual polar motion.