Geomagnetic Kp Index and Earthquakes

In the ionosphere, the solar winds generate electrical currents. On the Earth surface, these currents cause magnetic field fluctuations. These fluctuations, penetrating the Earth interior, induce the electrical currents J, and, in the presence of the Earth magnetic field B, generate electromagnetic force, known as Lorentz force F = J × B. To study the relation of earthquakes and the Lorentz force, acting at the near onset times of strong earthquakes, we examine the Kp index, a logarithmic measure of the magnetic field deviation. The time varying Kp index gives us J, which in turn determines F. The variations of the Kp index were stacked by aligning their central times to the times of main earthquake shocks. This stacking method has been a popular and powerful tool in image processing, because it lifts up only the geomagnetic effect like carving a relief. The Lorentz force tilts the subtle force balance in the earth crust towards triggering the release of stress strain energy, initiating an earthquake in a similar way as a mountain climber’s step can trigger the avalanches. The internal dynamics, however, are highly statistical. Conventional statistical methods are used in combination with a newly devised method, which compares the time sequences of hypothetical random earthquakes to real ones. We find that the distinctive patterns of the Kp surges often strongly correlate to the onset of earthquake. This correlation depends on the seismic regions and the magnitudes of earthquakes. The stronger the earthquake is, more closely the Kp surge is associated. The statistical significance of nearly 100% is obtained for the Kp variations, synchronizing with more earthquakes in the Pacific Rim region. In parallel with the data analysis the historical studies are reviewed. The solar activities have been considered to influence the earthquake occurrences and the relation of the two has been studied extensively in the recent years as well as in the past century. A comprehensive list of publications is created with the brief introductions for each in the last chapter. *Retired. How to cite this paper: Urata, N., Duma, G. and Freund, F. (2018) Geomagnetic Kp Index and Earthquakes. Open Journal of Earthquake Research, 7, 39-52. https://doi.org/10.4236/ojer.2018.71003 Received: January 16, 2018 Accepted: February 9, 2018 Published: February 12, 2018 Copyright © 2018 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access


Observations
Kp index is a complex average of the measurements by 13 magnetic observatories around the world.Kp records of almost one hundred years are available.The index goes from 0 to 9 in 1/3 increment reported 8 times a day in 3 hour intervals.The Kp index quantifies the global deviations of the magnetic field from the usual diurnal variations.Here we report on three major seismic events of M ≥ 6 in 2016 and 2017.In all three cases, as Figure 1 attests, the earthquakes struck at times of strong global magnetic disturbances, during periods of elevated or high Kp values.Figure 1(a) shows that the Kumamoto earthquake in Japan on April

Methods and Results
To visually compare the Kp indices and earthquakes, we stacked intervals of the  [3], H, Z, F: horizontal, vertical and total component, respectively, D: magnetic declination (angle of H versus geographic north, east is positive); the magnetic storm starts with a SSC pulse, "First hit" marks the Kumamoto earthquake time.Open Journal of Earthquake Research Kp variations over ±28 days before and after earthquakes.Figure 3(a) (averaged among the earthquakes at each time instance) plot the Kp variations, centered to the time of the earthquake for 4666 events of M ≥ 6, period 1932-2016, in the Pacific Rim region, longitude of 120˚ -160˚E and 70˚ -130˚W.
The average Kp in Figure 3(a) has the following features.
• During the last 12 to 14 days before the earthquakes, "period A" (marked in red), the Kp indices consistently display a broad but large surge of 0.15 (2.15 ~ 2.3), and during the last 2 days before and 2 days after the earthquakes, "period B" (marked in blue), the Kp indices consistently surge by 0.1 units In addition, since the Kp index is logarithmic, we downloaded the linear ap indices, in nano-Tesla units, from the same observatory [2] and stacked them as shown in Figure 3(b).In both cases the time series are dominated by peaks and valleys that are common to both.In both cases the A-B Maxima patterns stand out above the background.For the statistical analysis, we preferentially use the Kp index because the frequency histograms of the Kp values conform better to a normal distribution, which is a requirement for the subsequent statistical analysis.
The standard deviation of the Kp index is shown in Figure 3(c) (standard deviation among all 4666 earthquakes at each time instance).The mean of the standard deviation is σ E = 1.45.Notably this mean is the most critical number which gauges how each Kp index for each earthquake deviates from their average.The figures of Kp plots and the statistical parameters are described in more details in Table 1.
Table 1.Descriptions of the curves in Figure 3(a), Figure 3(c) and the statistical values σ A and σ E .

X-Axis (days)
days before and after EQ −28 Note: Kp values shown in the table are not the actual ones.

Statistical Evaluation
First an order estimate is made.The standard deviation of the Kp variation is σ E = 1.45 for the Pacific Rim region with n = 4,666 earthquakes.The deviation of the Kp of n earthquakes average is σ E / n = 1.45/ 4666 = 0.021.The peak-to-valley variation, shown in Figure 3(a) is 0.15.Using the half of the variation 0.075, the cumulative probability at Z factor, Z = 0.075/0.021, is 99.98%, hence this variation is concluded to be outside of the statistical deviation with 99.98% probability.
Next, a conventional statistical study is performed and its result is described in Appendix.The study verifies that the Kp index before the earthquake shows a Open Journal of Earthquake Research surge which is statistically significant, implying that the Kp surge is related to and synchronizes with the earthquakes.
For a further analysis, 54 sequences, each consisting of 4,666 hypothetical earthquakes, were generated and a hypothesis test was performed.Hypothesis (null): The Kp variation has nothing to do with the earthquakes occurrence.
Hence the sequence of the real earthquakes should show a variation, which is within the variations of the sequences of the hypothetical ones.Figure 5 gives the result.The black solid line is the statistical distribution of σ (standard deviation) of 54 sequences of hypothetical earthquakes (4,666 earthquakes/sequence).
The black line is almost same as the red line, which is the normal distribution.
The most significant finding is the blue dotted line, σ of the real earthquake sequence, which is clearly separated from the distribution area of the hypothetical earthquake sequences.Thus, the null hypothesis is rejected, and the evidence of Kp surges, relating to the earthquake onsets, is confirmed.
A similar result is shown in Figure 6 for the Mediterranean-Asian region (10˚ -100˚E, 0˚ -50˚N).The blue dotted line, showing the σ of the real earthquake sequence, is now closer to the distribution peak of the hypothetical earthquake sequences.Yet, the blue line is still about 2σ away from the peak, indicating 4% ~ 5% probability of no-difference (insignificance).Therefore, we conclude with 4% ~ 5% risk that statistically the real sequence is outside of the hypothetical sequences.It is to be noted that, if the Kp surge had nothing to do with earthquake onset, the blue dotted line would move to the left and falls on top of the peak area.

Lack of Precision of Kp Index
Kp index is a historical index of nearly a hundred years of records.Its draw-back is the increments; 0.0, 0.33, 0.67, 1.0, •••, 8.0, 8.33, 8.67, 9.0, consisting of only 28 sparse ticks.However, the final Kp variation curve is a stack of the curves of thousands of earthquakes.When we use the effect of n , i.e. central limit theorem, the resolution with the 0.33 step improves to 0.005 for the case of n = 4666, assuring the adequate resolution for detecting the Kp surges.The fine ripples, for example, seen in Figure 3(a), may reflect this sparseness problem.

Effect of Aftershocks and Mega Earthquakes
Numerous strong aftershocks may falsify the results obtained by the method of stacking the temporal Kp signals.Aftershock activity is solely caused by the main shock and follows this shock by a specific temporal attenuation law.Thus, it cannot be correlated with solar induced Kp values.In order to keep this influence small, we used a seismic data set of larger magnitude earthquakes, M ≥ 6.7, as a threshold which is not often exceeded by aftershocks within a few days after the main shock.We stacked the Kp plots of 1092 earthquakes of M ≥ 6.7 for the entire Earth for the period 1932-2016.The result is shown in Figure 7.A very

The 2011 Tohoku Earthquake and Tsunami
Another significant result was obtained by plotting the Kp sequence for the strongest and most devastating earthquake in the recent decade.

Analysis Summary
The

Review of Historical Studies
Aristotle, the Greek philosopher, described that earthquakes occur more frequently during the night than during the day [4].Starting at the beginning of the 20th century, studies were performed to determine whether the time sequences of earthquakes follow any systematic pattern.After many studies it became evident that the seismicity exhibits distinct diurnal as well as seasonal cycles in many different earthquake zones [5]- [13].
Such cycles of seismic activity can only be attributed to solar influence.Consequently, studies were done to model such solar-terrestrial effects.The powerful electric current vortices in the ionosphere, generated by solar radiation, and the associated magnetic field variations are assumed to be the essential source for the effect.Due to the penetration of those magnetic field variations into the electrically conductive Earth's lithosphere, and associated electric "telluric" currents, additional mechanical forces are generated in seismic rupture zones [14] [15] [16].Another observation that supports the theory of solar influence is the clustering of earthquakes in 11-year cycles in accordance with the solar cycles [17]- [23].
In this overall context, several recent studies focused on the cycles of the solar polar magnetic field, which manifest themselves in solar flare activity.A high degree of statistical significance was shown for a correlation of those polar field oscillations and the occurrence of strong earthquakes [24] [25].Similarly, it has been stated that, during the Maunder solar minima, the strongest earthquakes and most violent volcanic eruptions took place during transition phases of the heliospheric magnetic field [26].

Figure 2
Figure2shows the plot of the geomagnetic data relative to the Kumamoto earthquake in Figure1(a), recorded at the geomagnetic observatory in Kanoya, Japan, over four days prior to the event.The storm intensity is shown in detail.It took a sharp downward turn about 2 hrs before the quake.It then turned up rapidly, marked as "First hit" in Figure2(d), coinciding with the onset of the Kumamoto earthquake on April 14 2016 at 12:26 UT.Inspired by this coincidence as well as similar cases such as in the 1995 Great Hanshin earthquake of January 17 1995, also known as the Kobe earthquake, and the 2011 Tohoku Earthquake, we analyzed the seismic data of thousands of earthquakes of M ≥ 6 in relation to the variations of the Kp index from 1932 to 2016 (USGS Earthquake Catalogue[1] GFZ Potsdam WDC data, Kp index[2]).

Figure 2 .
Figure 2. (a), (b), (c), (d) for11, 12, 13, 14 April 2016  The diurnal variations of the geomagnetic fields for the last 4 days before the Kumamoto earthquake on April 14 2016, observed at the Kanoya Observatory, and catalogued at Kakioka Magnetic Observatory data[3], H, Z, F: horizontal, vertical and total component, respectively, D: magnetic declination (angle of H versus geographic north, east is positive); the magnetic storm starts with a SSC pulse, "First hit" marks the Kumamoto earthquake time.

( 2 .
Figure 3. (a) Time Variations of the average of the Kp index for 28 days before and after the earthquakes, 4666 events in the Pacific Rim region.(b) Time Variations of the ap index, (c) Time Variations of the standard deviations of Kp.

Figure 4 (
Figure 4(a) and Figure 4(b) show the Kp variations around the 4,666 earthquakes, based on randomly selected times with random intervals.We thereby create hypothetical earthquakes and look at the Kp signals in the window of ±28 days around the earthquake times.For a visual comparison, the A-B Maxima plot from Figure 3(a) is attached at the bottom of Figure 4.Note that the intervals

Figure 4 .
Figure 4. (a) and (b) Variations of the average Kp index when the times of earthquake onsets are randomly selected (hypothetical earthquake sequences), comparing with the variations for the actual earthquake sequence, re-plot of Figure 3(a).

Figure 5 .
Figure 5. Probability of the standard deviations of the Kp variations of 54 sequences (4,666 hypothetical quakes/sequence).Note: The standard deviation of 0.031 for the real quake sequence in the Pacific Rim region.

Figure 6 .
Figure 6.Probability of the standard deviations of the Kp variations of 54 sequences (1,200 hypothetical quakes/sequence).Note that the standard deviation is 0.046 for the sequence of the real earthquakes in the Mediterranean-trans-Asiatic zone.
Standard deviation (std) of the Kp variations 54 sequences(1200 hypothetical earthquakes/sequence) Normal Distribution Real quakes Open Journal of Earthquake Research similar pattern as shown previously in Figure3(a) appears again.To prove the statistical significance, the data of thousands of earthquakes are needed.Surprisingly, mega earthquakes of M ≥ 8 show the same A-B Maxima even though only around 50 such earthquakes occurred in the time window considered.These mega earthquakes coincide highly with Kp surges, compared to the M6 level earthquakes.

Figure 7 .
Figure 7. Kp curve showing the A-B Maxima again, synchronizing with 1092 global earthquakes of magnitude M ≥ 6.7, aftershocks mostly removed.

Figure 8 .
Figure 8. Kp variations of the single 2011 Tohoku earthquake and Tsunami in Japan.
Figure 8 shows the ±28 day Kp plot of the Tohoku earthquake, occurred on March 11 2011 at 14:46 JST, 5:46 UTC.The Kp variation is stunningly similar to that previously shown in Figure 3(a), the averaged Kp over many earthquakes in the Pacific Rim region.The implication of the similarity is profound and deserving of the future research that could cast light on the geomagnetic field disturbances being a factor for triggering of mega-earthquakes.The autocorrelation and FFT analysis was also performed.In addition to the dominant 27 ~ 28 day period associated with the Sun rotation, a distinctive 10-day periodicity was found in the Kp variations.
distinct patterns found in the Kp fluctuations prior to earthquakes indicate Open Journal of Earthquake Research synchronization of the geomagnetic surges and the seismicity.We called this pattern A-B Maxima.Maxima A occurs 8 ~ 10 days before earthquakes and lasts for few days.Maxima B occurs right before or during earthquakes.