Wavelet analysis of geomagnetic jerks

Master Thesis


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University of Cape Town

Geomagnetic jerks, or secular variation impulses, are abrupt changes in the slope of the first time derivative of the Earth's magnetic field. These changes occur on time scales of the order of a year. It has been demonstrated that the jerks might be more singular than previously supposed; their """"regularity"""" is closer to 1.5 than to 2. Although discovered over 30 years ago, geomagnetic jerks remain poorly understood. Their origin probably lies in the magnetohydrodynamics that is responsible for the maintenance of the Earth's magnetic field produced within the Earth's liquid and convecting core (through a so-called geo-dynamo process). A wavelet tool was programmed in MATLAB and a wavelet analysis applied to detect and characterize singular events, or jerks, in the time series made of monthly mean values of the east component of the geomagnetic field from 45 selected worldwide observatories. The analysis was first performed on various synthetic series made up of a """"main"""" signal of smooth variation intervals separated by singular events, a white noise and an """"external"""" signal made up of the sum of a few harmonic signals. Conditions, in which the singular events could be clearly isolated and their associated """"regularities"""" recovered, are highlighted. Geomagnetic jerks were detected globally in 1969, 1978, 1991 and 1999. Furthermore, geomagnetic jerks are also thought to have also occurred in 1901, 1913 and 1925, but due to the small number of observatories with long enough records to allow for detection during this period, their extent is unclear. Two further geomagnetic jerks were found to have occurred around 1937 and 1952, but due to these events not being detected by all the observatories with records covering this period, these events might not be of the same extent or origin. The results of the geomagnetic jerks detected here and the phase jumps detected in the Chandler wobble are compared and the remarkable coincidence highlighted. The spatio-temporal behaviour of jerks, for example where jerks arrive in the northern hemisphere before the southern hemisphere, is explored. Using k-means clustering, an antipodal relationship is proposed between regional trends in the time delay in the detection of geomagnetic jerks at the surface of the Earth. It is possible that this finding may shed some new light on the origin of geomagnetic jerks. The wavelet analysis was also used to investigate whether the nature of geomagnetic jerks could be classified into one of the following three categories: geomagnetic jerks are the result of some instability starting at the time of the jerk; geomagnetic jerks are the result of some continuous oscillations; that geomagnetic jerks possibly reflect a process ending at the time of the jerk. A startling pattern emerged that suggested that the 1969 jerk corresponded to an event starting at that time, the 1978 jerk corresponding to an event ending at that time, and lastly an event again starting in 1990. This implied that the 1969 and 1978 jerks might have been the result of a common phenomenon starting in 1969 and ending almost a decade later in 1978.