1 Introduction

Coupling between processes within the earth’s crust and the troposphere over regions of seismic activity is known for a long time (Nagata 1976), and that anomalous variations within the ionosphere are observed several days/hours before strong earthquakes (e.g., Yamazaki and Rikitake 1970; Smith and Johnston 1976; Zhu 1976; Honkura 1985).

Sasai (1980, 1983) studied the tectonomagnetic field based on the linear piezomagnetic effect. He showed magnetic changes due to stress force. Chen et al. (1999) proved the statistical significance of the magnetic precursors on the background of day-to-day ionospheric variability for magnitudes larger than 5. They also concluded that the precursors were observed 5 days before the seismic shock, and that the probability of the precursor’s identification increases with the magnitude of future event. Liu et al. (2004) studied pre-earthquake ionospheric anomalies using GPS signals and claimed that within 5 days prior to 16 of the 20 M ≥ 6.0 earthquakes (80% success rate), these precursors could be observed. Similar observations were made for example by Yen et al. (2004) for the 1999 Chi-chi M7.3 earthquake and by Johnston et al. (2006) for Seismomagnetic effects from the long-awaited 28 September 2004 M6.0 Parkfield earthquake.

Liu et al. (2000) used critical plasma frequency as index of ionospheric anomalies, for F2, measured by ionospheric sounding instruments (ionosondes), corresponding to the maximum electron density of the ionospheric F layer (160–400 km in altitude). They found that this index significantly decreased locally during afternoons within a few days before M ≥ 6 earthquakes occurred.

Several mechanisms have been evoked to explain the lithosphere–atmosphere–ionosphere coupling. One is the chemical influence of emanations from the Earth’s crust (radon, noble gases, and metallic aerosols) on the boundary layer of the atmosphere; these emanations change the conductivity of the layer, and as a consequence, modify the atmospheric electric field value within the active area (e.g., Pulinets et al. 1999). It has also been proposed that pre-seismic electric fields on the ground can be generated actively by plastic deformations during the slow cooperative build-up of stress (Freund 2000; Freund and Sornette 2007), but these currents prior to ionospheric anomalies have not yet been observed (Kamogawa 2006). Geomagnetic external disturbances like geomagnetic storms and cloud-to-ground lightning have also been proposed as a mean to trigger seismicity (e.g., Sobolev and Zakrzhevskaya 2003). Duma (1996, 1999) focused on the involvement of the regular diurnal variations of the Earth’s magnetic field, known as Sq-variations in this process and Duma and Ruzhin (2003) attempted to quantify the forces which resulted from the interaction between the induced Sq-variation currents in the Earth’s lithosphere and the regional Earth’s magnetic to assess its possible influence on the tectonic stress field and, as a consequence, on seismic activity. They claim that Lorentz forces due to the interaction between the conductive lithosphere and the external field superimpose the tectonic stress field creating a so-called ‘Magneto-Seismic Effect’ that can efficiently trigger seismic activity, including strong earthquakes (Duma 2005).

In this paper, we study the seismically active Suez–Sinai area (see Fig. 1 for location). The region is dominated by the active boundary between the African and the Arabian plates that are separating one from the other along the Red Sea rift. Sinai Peninsula can be considered a sub-plate that accommodates the main motion of the Aqaba left-lateral transform fault (Le Pichon and Gaulier 1988) with the supposed extensional motion of the Suez Gulf (Jackson et al. 1988) and the opening of the Red Sea (Ben-Menahem et al. 1976). The seismicity of the region (see Fig. 1) indicates that the Gulf of Aqaba is presently the more active segment of the plate boundary.

Fig. 1
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Location of the study area

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In this area, seismic monitoring started in 1899 with the installation of a seismological station in Egypt (HLW), but most instrumental events have small magnitudes, with only two instrumental events with M > 6 in the Dead Sea Transform fault (July 11, 1927 and November 22, 1995). Magnetic observations from Misallat observatory are available at World Data Centre for Geomagnetism since 1960.

As both seismic and magnetic data are available, we check the existence of a temporal and spatial relationship between ionospheric magnetic disturbances and seismicity, and we can evaluate the Sq-affects along with the diurnal magnetic variations corresponding to the seismic activities. This mechanism was proposed by Duma (1999) and Duma and Ruzhin (2003) as a trigger of earthquake activity.

2 Comparison between Sq- and earthquake activity

2.1 Diurnal and long-term comparison

The diurnal magnetic variations, Sq, also called “magnetic quiet-day solar daily variations” (Chapman and Bartels 1940) are generated in the Earth’s ionosphere, mainly by solar radiation and tidal forces. It can be computed by removing the absolute values of the horizontal magnetic field from the mean values of the horizontal magnetic component H along the daytime. This procedure was applied to the continuous magnetic data available at three Geomagnetic Observatories close to the study area: Misallat in Egypt and Bar Gyora and Amatsia in Israel. Their geographic latitudes are 29.515 N, 31.723 N, and 31.550 N, respectively.

Considering the seismicity of the study area, the seismic catalogue includes a group of about 34,559 seismic events with magnitudes ranging from >1 to <8 for which magnitudes have been computed by NRIAG along more than 100 years. From this dataset, we produced a 3 h running mean using local time for the three observatories in Local Time.

The comparison between average magnetic data and average seismic data is shown in Fig. 2a–c for each of the three observatories. It shows that earthquake occurrence and Sq depend on Local Time in the same way, as suggested before, pointing to the existence of a general relation between time-dependent earthquake activity and regional Sq-variation. Maximum values for the number of earthquake events are slightly lesser than the corresponding maximum of Sq, between 10 and 15 Local Time, whereas the minimum values are found between 0 and 5.

Fig. 2
figure 2

Correlation of a mean diurnal variation of the magnetic component (H) with 3 h mean values seismic activities for a Misallat, b Amatsia, and c Bar Gyora geomagnetic observatories

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We can even emphasize the existence of magnetic signals related with seismic activity, if we consider the 2004 magnetic year from Misallat geomagnetic observatory, which is considered the year of small seismic activity, according to the Egyptian Seismic network records, and we compute the average value of the magnetic field removing the effect of the seismic active periods with a simple average of ±2 weeks around the minor earthquakes. We can also retain only the seismically active periods and produce the complementary 3 h average magnetic field. Results shown in Fig. 3 indicate that deduced magnetic variations outside the seismic active periods are similar to the baseline for Misallat Geomagnetic Observatory, thus confirming that seismic activity increases the magnetic field variation.

Fig. 3
figure 3

The magnetic field variations for mean value of 1 year to the magnetic component (H) from Misallat geomagnetic observatory once during normal variations, and the other after removing 3 weeks before and after the Earthquake from the magnetic data

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2.2 The magnetic signal as a seismic precursor

In a number of situations, it is possible to identify a sharp magnetic signal 24 h before a large earthquake. This signal appears often as an increase in the magnetic field (Δh) reaching several tenths of nT more than normal daily variation.

One example is the 23 June 2001 M w8.4 earthquake that took place near the coast of Peru, whose epicenter was located at 16°15′S and 73°40′W. It caused an increase in ΔH of approximately 20 nT at Huancayo Geomagnetic Observatory on the preceding day, 22 June 2001 (cf. Fig. 4). Another example is the 2 November 2002 earthquake occurred in Sumatra, Indonesia, with M w7.4. Its epicenter was located at 3°24′N and 96°18′E. ΔH reached 15 nT at Tonghai Geomagnetic Observatory the preceding day, 1 November 2002 (cf. Fig. 5). Similar situations were observed for the 5 September 2004 M w7.4 earthquake of Honshu and the 15 November 2006 M w8.3 earthquake at Kuril Islands causing in both cases an increase of near 15 nT at Kakioka Geomagnetic Observatory (cf. Figs. 6, 7).

Fig. 4
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23-June Earthquake, 2001, near coast of Peru of M = 8.4 showed the magnetic signal before the Earthquake

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Fig. 5
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2-November Earthquake, Sumatra, Indonesia, 2002 of M = 7.4 showed the magnetic signal before the Earthquake

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Fig. 6
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5-September Earthquake, near the south coast of Honshu, Japan with magnitude 7.4, showed the magnetic signal before the Earthquake

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Fig. 7
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15-November Earthquake, 2006, Kuril Islands of Magnitude = 8.3, showed the magnetic signal before the Earthquake

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In our study area, we must refer the M5.3 earthquake that took place on the Red Sea on the 20 August 2004, which caused an increase in the magnetic field by approximately 25 nT, at Misallat (Fig. 8).

Fig. 8
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20-August Earthquake, Egypt, 2004 of M = 5.3 showed the magnetic signal before the Earthquake

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In all these cases, there is a consistent magnetic signal that can be detected 24 h before the earthquake.

2.3 How far does the correlation go?

The maximum distance for the above-described relationship can be determined if we compare the observations corresponding to a large event for a set of magnetic observatories at increasing distances, in what concerns the diurnal correlation and the long-term correlation. To do so, we analyzed magnetic data from five different observatories: Misallat, Bar Gyora, Amatsia, Qsaybeh, and Istanbul-Kandilli.

In analyzing what concerns the diurnal correlation, we can verify (cf. Fig. 9) that the similarity between magnetic and earthquake data is observed for the first four observatories, whereas in the case of Istanbul-Kandilli, this similarity vanished. In this case, we have an empiric determination of about 1,400 km as the maximum distance.

Fig. 9
figure 9

Ideal case for determining the diameter of the detected magnetic signal before the Earthquakes from a Misallat-Egypt, b Bargayora-Israel, c Qsaybeh-Lebanon, and d Kandilli-Istanbul, Turkey for long-period correlation

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If we focus on a specific event like the 20 August 2004 M5.3 Aqaba earthquake (cf. Fig. 10), we get a similar conclusion as the increase in the magnetic field the day before is observed up to Qsaybeh geomagnetic observatory, thus corresponding to a maximum distance of about 600 km.

Fig. 10
figure 10

Tracing the diameter of the magnetic signal due to 20-August Earthquake, Egypt, 2004 of M = 5.3

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To look for other cases where the earthquakes have larger magnitudes and where we can hypothesize that the distance affected is larger, we considered three complementary cases. The first one is the M w8.3 15 November 2006 earthquake at Kuril Islands, whose epicenter was located at 46°60′N 153°23′E, and where the magnetic signal can be detected at Kakioka geomagnetic Observatory, thus corresponding to a distance of about 1,200 km (cf. Fig. 11). The second one is M w8.7 28 March 2005 earthquake, Northern Sumatra, Indonesia with epicenter 2°07′N 97°01′E, whose signal can be detected at Guangzhou geomagnetic observatory located at 23°09′N, 113°34′E, which indicates a distance of about 2,300 km (cf. Fig. 12). The third one is the M w7.9 3 November 2002 earthquake that took place in Alaska at 63°51.4′N, 147°45′W, and whose signal becomes weak at Sitka geomagnetic observatory (57°06′N and 135°33′W), thus corresponding to a distance of about 700 km (cf. Fig. 13).

Fig. 11
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Tracing the diameter of the magnetic signal due to 15-November, 2006, Kuril Islands of Magnitude = 8.3

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Fig. 12
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Tracing the diameter of the magnetic signal due to 28-March, 2005, Northern Summatra, Indonesia of Magnitude = 8.7

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Fig. 13
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Tracing the diameter of the magnetic signal due to 3-November, 2002, Alaska of Magnitude = 7.9

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From all the above observations, we can conclude that the anomalous variations of the magnetic field that take place about 1 day before the strong earthquakes are observed up to a distance that is dependent on the magnitude of earthquake.

3 The algorithm of the method

In our algorithm, we present a simple formula for the calculation of the magnetic disturbance due to static radial magnetic dipole induced for example by piezomagnetic effects at the epicenter E (Fig. 14). The observation point is P at the angle epicentral distance γ (e.g., 83°). The triangle OEP we suppose to draw in the plane of great circle radius a connected the points EP and the center O. Then the distance of the EP is \( R = \left( {2a^{2} - 2a^{2} \cos \gamma } \right)^{1/2} = a\left[ {2\left( {1 - \cos \gamma } \right)} \right]^{1/2} \) and \( \sin \gamma = \left( {1 - \cos^{2} \gamma } \right)^{1/2} \).

Fig. 14
figure 14

A schematic shows the magnetic field due to static radial magnetic dipole at the epicenter of the earthquake

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It is known that \( \cos \gamma = \cos \vartheta \cos \vartheta_{0} + \sin \vartheta \sin \vartheta_{0} \cos \left( {\varphi - \varphi_{0} } \right) \). The magnetic potential at the point P will be:

$$ U\left( P \right) = {\frac{{\mu_{0} }}{4\pi }}\,{\frac{{m\cos \vartheta_{m} }}{{R^{2} }}} $$
(1)

where \( \vartheta_{m} \) is the angle reckoned by magnetic moment m and segment EP.

Using triangle geometry formulae, we see that \( \vartheta_{m} = \pi - \beta \) so, \( \cos \vartheta_{m} = - \cos \beta \). The sinus theorem gives \( R/\sin \gamma = a/\sin \beta \), \( \sin \beta = \left( {a/R} \right)\;\sin \gamma \), and \( \cos \beta = \left[ {1 - \left( {a/R} \right)^{2} \sin^{2} \gamma } \right]^{1/2} \).

Then, we have more complicated formula for \( U\left( P \right) \):

$$ U\left( P \right) = - {\frac{{\mu_{0} m}}{4\pi }}\;{\frac{{\left[ {1 - \left( {a/R} \right)^{2} \sin^{2} \gamma } \right]^{1/2} }}{{2a^{2} \left( {1 - \cos \gamma } \right)}}} $$
(2)

Using expressions for \( \cos \gamma \) and \( \sin \gamma \), we can calculate components of the magnetic disturbance due to m at the point P, \( \Updelta X = a^{ - 1} \partial U/\partial \vartheta , \Updelta Y = - \left( {a\sin \vartheta^{ - 1} } \right)\partial U/\partial \varphi \) and ΔZ = ∂U/∂a.

The formula for modulus of the disturbance due to magnetic dipole ΔB = μ0 m/R 3 (Tesla) is used for the calculation of ΔH.

The torque acts on the ambient magnetic field, T is the magnetic moment that affects the magnetic field H. It can be expressed as:

$$ {\text{T }}\left( {\text{in Joules}} \right) = m \times H $$
(3)

We calculated the magnetic moment and the torque parameters related to the earthquakes. The results are listed in Table 1.

Table 1 Magnetic and the torque parameters related to the earthquakes
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A statistical calculation for several major earthquakes (<5 magnitudes) was studied in detail to model the final results. The results (cf. Fig. 15; Table 2) agree with the results calculated by the algorithm. They show that if we have Δh of 15 nT, then we can expect earthquake with magnitude 5.3 Richter, which generates energy of 6.927 E + 12 Joules in an area of 550 km diameter. It can be concluded that there is an electromagnetic coupling that occurs between the processes within the earth’s crust and the troposphere over the regions of seismic activity and anomalous variations within the ionosphere several days/hours before the strong earthquakes. These emanations change the conductivity of the layer and, as a consequence, modify the atmospheric electric field and hence the magnetic field values within the active area.

Fig. 15
figure 15

Curves model illustrate the relation between Earthquake’s magnitude, Δh, and radius of the traced magnetic signal

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Table 2 Relationship between the distance of the earthquake’s epicenter, magnitude, distance, and the magnetic signal
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4 Discussion and conclusions

In this study, we investigated the relationship between the diurnal and the long-term variations of the magnetic field with seismic activity within a study area encompassing the Sinai sub-plate. Diurnal and long-term Sq-magnetic variation showed a good correlation with seismic activity. In order to show that changes in the magnetic field are due to seismic activities, mean values of 1 year from the Misallat geomagnetic were selected and ±3 weeks before and after the earthquakes has been removed from the magnetic data. The comparison between the Sq-variation during the seismic active periods and the Sq-variation during seismic quiet periods shows that both the phenomena are related.

We also studied the magnetic field variations for several days before and/or after the major earthquakes occurred along the last 26 years. The investigation showed a clear magnetic signal 1 day before the occurrence of a major earthquake. We also compared the magnitude of the earthquake to come with the maximum distance until which it is possible to identify the magnetic signal, and we concluded that it is a function of the earthquake magnitude. This conclusion was extended to a larger number of events for major earthquakes to obtain a relationship between earthquake magnitude, distance, and maximum Δh. These results show a good agreement with the conclusions of Duma and Ruzhin (2003) for small magnitude earthquakes (M5–M6) and differ in the case of larger magnitude earthquakes, mainly because large magnitude earthquakes generate larger quantity of energy more than estimated by Duma and Ruzhin (2003).