Tavares and Azevedo [1] showed in their article, that there existed a correlation between the solar cycles and the earthquake activity. In their study they used both ancient records, as well as recent seismicity between 1950 and 2010. According to them, a possible link between solar activity and earthquake occurrence is the magnetic field of the earth, that is being changed in shape corresponding to the solar cycles and thus exerts a pressure on the earth’s crust. This study tries to test their results by means of correlation and cointegration, not only using recent solar and earthquake data, but also taking measurements of the Earth’s magnetic field strength into account. The results presented in this work show no clear connection between the seismicity and the 11-year solar cycles. The data rather indicates an anti-periodicity. It is not excluded, that few strong CME events can influence the triggering of earthquake events, however, this effect is presumably small and plays only a minor roll in the faulting process.
The issue of a link between the solar activity and the occurrence of earthquakes is still not quite understood. There are several theories, e.g. Tavares and Azevedo [
This work concentrates more on the actual relationship between earthquakes and solar activity and treats the effects causing the correlation only in the aspect of geomagnetic field strength variations. The approx. 11-year solar cycles, represented by the amount of Sunspots are correlated with the magnetic field strength on three different places (Colombia, Germany and Alaska), so to see, if the field shows the same long-term periodicity. Furthermore different types of earthquake data are used to check the results from Tavares and Azevedo [
All data mentioned in this section are available as daily and yearly means of the respective values.
The International Sunspot Number, provided by the SIDC in Belgium [
Some of these ejections are directed towards the earth, called magnetic storms that cause e.g. the Northern Lights but also drastically compress the magnetosphere on the day-side of the earth and stretch it on the nightside [
Regarding the seismic activity, the worldwide ANSS catalogue [
The worldwide ANSS catalogue is created by merging the master earthquake catalogues from contributing ANSS member institutions and then removing duplicate events, or non-unique solutions for the same event. For the study period the catalogue contains 39,343 events with the mentioned characteristics.
For comparison concerning large events also the Centennial earthquake catalogue, which is regarded complete down to magnitude 6.5 between the 1930’s and today, is used [
As Tavares and Azevedo [
Finally, in the attempt to prove Tavares and Azevedo [
Especially the data from Fúquene at the beginning of the observation period (starting 1955) shows errors or missing values. In all three time series the data is revised and corrected for such flaws. However, as the goal of this study is to find the 11-year cycles of the solar activity, minor errors in the range of days in the appearance of the curves are not expected to influence the results.
The standard cross-correlation method is adopted to find patterns in the occurrence of Earthquakes that resemble the 11 year solar cycles. Thus, the results have to show significantly higher correlation coefficients than the null-hypothesis (cross-correlation of the Sunspot Index with a random time series). The standard numerical cross-correlation function of two vectors x and y of length N is given by:
For comparison, the series x and y are normalized before using cross-correlation, so that their autocorrelations at zero lag (m = 0) is identically to 1.0. Moreover, possible trends were removed before applying the algorithm. The cross-correlation has also the characteristic of showing common periodicities in the correlated series, for example in the three magnetic field strength variations.
The cointegration method is a statistical method mostly used in economics to find dependencies in two or more time series. The basic concept can be expressed in the following manner (Definition from Sørensen [
The two time series y t and x t are cointegrated if there exists a parameter α such that
is a stationary process.
This definition applies to I(1) processes for and, which means they are integrated of the order 1, thus becoming stationary after differentiation. One also says the process has a unit root, i.e.
for a = 1 (3)
This is the equation of a random walk, so that at every time point the value of depends on the value before and a random term. A standard unit root test would be e.g. testing the Null-Hypothesis of a = 1 (unit-root) versus a < 1 (stationary). For a = 1, the time series is nonstationary and will be drifting from its initial value with increasing standard deviation. The series and are cointegrated if they are both following such a random walk, but having a common trend, i.e. they don’t drift away too far from each other, such that there is always a relationship between the variables as in Equation (2).
The cointegration relationship is also valid for processes of higher order I(p) and there are methods to test cointegration for more than two variables, for example the Engle-Granger Cointegration Test, used in this article [
After calculating the regression, the residuals are tested for a unit-root.
The big advantage of cointegration testing is that normal regression for uncorrelated traces can, in the case of random walks, yield results showing a correlation between the time series where in fact there is none. This phenomenon is called spurious regression.
It becomes quite clear, that none of the series used shows a significant positive correlation. However, it seems like there is a negative correlation especially pronounced for the worldwide ANSS catalogue, which plots
at exactly zero time lag with a coefficient of almost –0.4 (mean random + one standard deviation ≈ ±0.3). It is quite noticeable, that there seems to be stronger negative correlation. The picture changes only slightly when considering time lags of up to five years (
Furthermore, common periodicity in the magnetic field strength data is found according to
Yet another approach is the comparison between the magnetic field strength and the regional earthquake data.
It shows the highest correlation for the case of Niemegk and Central Europe. The correlation coefficient is about 0.4, whereas correlation with a random earthquake profile plus one standard deviation is about 0.3. However,
As mentioned in Section 3.2, in order to adopt the cointegration method it is important, that the analysed time series have a unit root. Intuitively one already suspects the geomagnetic records to meet the criteria for
cointegrated time series. The series follow a random walk (secular variations) with some degree of individual, random freedom (magnetic storms, currents in the ionosphere...), but undoubtedly their general behaviour is linked to each other.
On the other hand, the Sunspot Number does not show those random walk characteristics, resembling a stationary process with a rather strict periodicity. Also the earthquake occurrence is stationary, following (in a basic model) a Poisson Distribution.
The test statistics show indeed a cointegration relation between the three magnetic field strength records. The graph for the Residuals ut in
where are the records from the observatories, constant factors and c is a constant that shifts the curve to zero mean.
Applying the cointegration with the Sunspot data, although it contains no unit root, results either in an associated factor of α almost zero, or, in the case of SSN = yt in Equation (4), in the residuals being identically to the Index. Although this is not exactly a valid test, this could mean that Sunspot Number and magnetic field strength (in a relation of year-long cycles) are independent. If there was a common trend or cyclicality the curve form of the Sunspot Index wouldn’t appear in the Residuals.
As the earthquake data is linked to the same problem, further cointegration testing is omitted.
First of all it’s notably that the geomagnetic field strength does not show a clear correlation with solar activity (
the data used in this study. During solar maxima the number of magnetic storms increases considerably, yet, those are effects, typically in the range of hours to few days. Hence, the long-term magnetic field strength is not expected to be influenced strongly by these disturbances. The correlation between field strength and regional earthquake events doesn’t resolve this issue (
The cointegration analysis including the Sunspot Number, yields the same result, as the residuals resemble the variations in solar activity. This could mean that there is no direct link between the two values, i.e. no cointegration, although the results cannot be seen as proof, as the basic prerequisite condition of a unit root has been ignored.
Although the three geomagnetic observations are cointegrated, the approx. 20 year periodicity in
Concerning the earthquake data, there also seems to be no strong relation between their occurrence and the solar activity (
Tavares and Azevedo [
Their observations are backed by observations during the last 50 years, similar to this study. The last maximum (around 2000), earthquakes seem to have occurred more frequently on different tectonic plates. This result, however, is not universal for all parts of the earth and not during all of the 5 maxima between 1950 and 2005. Their observations during the modern period seems exclusively based on graphical comparison and not one number is shown in this part. Also, the comparison of occurrence during the two historic minima vs. the whole time period are hardly statistically robust, as there are only small deviations from a normal pattern observed. Those effects could probably as well be explained by natural random behaviour.
The results of this work rather contradict the observations from Tavares and Azevedo [
The influence of the solar activity on earthquakes proves to be an elusive phenomenon. Magnetic storms caused by CMEs are supposed not only to affect modern technology such as GPS, but also the solid Earth’s crust, triggering earthquakes. As such events happen considerably more frequently during solar Sunspot Maxima, it is of interest, whether earthquake occurrence resembles these cycles.
This study doubts the results presented by Tavares and Azevedo [
We want to thank the Colombian National University and the University of Potsdam, for making this project possible. For providing the data we express our thanks to the Geomagnetic Observatory in Fúquene (Instituto Geográfico Agustín Codazzi—IGAC), Niemegk (GFZ Potsdam) and College (USGS), as well as the NCEDC, the SIDC and the USGS.