Significance test and precision analysis of Morlet wavelet: Application to studying periodic variation of earthquake activity and geomagnetic field

Firstly analyzed the signal with random noise by using Morlet wavelet transformation and tested significance level of the resulted period components, then studied the relationship between signal periods, the time length of observational data and wavelet transformation precision. As a test example we analyzed sunspot activity, which has relatively stable activity cycles. The result shows that the precision analysis and significance test used in this paper are feasible for studying periodicity of geophysical activity. Finally, this method is applied to analyzing global seismicity period，and the periods of global seismicity and their precision are given. Result of this study indicates that, when analyzing geophysical data with Morlet wavelet, researchers can acquire more objective periods and their precision from the signals with noise by combining precision estimation and significance test.