Geomagnetic jerks as chaotic fluctuations of the Earth's magnetic field

Abstract

[1] The geomagnetic field is chaotic and can be characterized by a mean exponential time scale < t > after which it is no longer predictable. It is also ergodic, so time analyses can substitute the more difficult phase space analyses. Taking advantage of these two properties of the Earth's magnetic field, a scheme of processing global geomagnetic models in time is presented, to estimate fluctuations of the time scale t. Here considering that the capability to predict the geomagnetic field is reduced over periods of geomagnetic jerks, we propose a method to detect these events over a long time span. This approach considers that epochs characterized by relative minima of fluctuations in time scale t, i.e., those periods when a geomagnetic field is less predictable, are possible jerk occurrence dates. We analyze the last 400 years of the geomagnetic field (covered by the Gufm1 model) to detect minima of fluctuations, i.e., epochs characterized by low values of the time scale. Most of the well known jerks are confirmed through this method and a few others have been suggested. Finally, we also identify some short periods when the field is less chaotic (more predictable) than usual, naming these periods as steady state geomagnetic regime, to underline their opposite behavior with respect to jerks.

After some 350 years – zero declination again in Paris

“…Going farther back in time, there is evidence of changes in the secular variation trend, supported by measurements around the epochs: 1600, 1665, 1700, 1730, 1750, 1760, 1770, 1810, 1870, 1890, and 1900. These dates are close to those detected by Qamili et al (2012Qamili et al ( ): 1603Qamili et al ( , 1663Qamili et al ( , 1703Qamili et al ( , 1733Qamili et al ( , 1751Qamili et al ( , 1763Qamili et al ( , 1770Qamili et al ( , 1810Qamili et al ( , 1868Qamili et al ( -1870Qamili et al ( , 1888Qamili et al ( , and 1900, when analysing the temporal behaviour of the difference between predicted and actual geomagnetic field model values for successive intervals from 1600 to 1980, based on the Gufm1 geomagnetic model (Jackson et al, 2000). Let us note that here we use the term "geomagnetic jerk" for all these events; however, as noted by Mandea and Olsen (2009), we must make a distinction between geomagnetic jerks and rapid secular variation fluctuations.…”

Evidence for a new geomagnetic jerk in 2014

“…Various more or less sophisticated methods, either applied to direct measurements or to the predictions given by geomagnetic models, have been used to detect and characterize geomagnetic jerks, such as those based on wavelet analysis [e.g., Alexandrescu et al, 1996], nonlinear chaotic analysis [Qamili et al, 2013], or Slepian functions [Kim and von Frese, 2013]. However, the original and most direct way to identify jerks is by looking for V-or Λ-shaped changes in the slope of the SV of one field component at geomagnetic observatories, after averaging either on an annual or a monthly basis in order to minimize the external field contribution.…”

Investigating Dynamical Complexity of Geomagnetic Jerks Using Various Entropy Measures

“…The considered time series represent the temporal variation of the geomagnetic field recorded for more than a century . For our analysis, we have used the monthly means of the Y component of the geomagnetic field, which is the one less affected by external fields (Qamili et al, 2013). Figure 1A shows the evolution of the monthly means for both observatories, as well as their first and second derivatives (Figures 1B,C), respectively, estimated by convolution with the derivative of a 33 points Gaussian kernel with σ = 5, encompassing a 32 points window of the time series within ±3σ .…”

“…Various techniques have been applied in order to detect these events in geomagnetic field time series (Mandea et al, 2010). Usually, geomagnetic jerks are particularly visible in the eastward (Y) component of the geomagnetic field, which is supposed to be the less affected by external fields (Qamili et al, 2013). Although the phenomenon has been studied for many years, its origin is not yet fully explained.…”