The fact that electromagnetic (EM) emissions accompany every stage of some large earthquake preparations seems undebatable, although short-term earthquake prediction is still one of the most challenging targets in Earth science today (Eftaxias et al., 2003). Meanwhile, the ultra low frequency (ULF) band is of particular interest because only EM signals in the ULF range and at lower frequencies that originated in the Earth's crust can be easily recorded at the Earth's surface without significant attenuation, compared with “high” frequency emissions that might be emitted at epicenter depths at more than 10 km, even several hundreds of kilometers. Recently, an increasing number of ground-based observing ULF electromagnetic emissions related to strong earthquakes have been recorded at a distance of several, hundreds, and even several thousands of kilometers. Some notable examples include the Loma Prieta MS 7.1 earthquake on 17 October 1989 (f= 0.01–10 Hz, D= 7 km, A= 1.5 nT; Fraser-Smith et al., 1990; Bernardi et al., 1991), as well as the Spitak MS 6.9 earthquake on 7 December 1988 (f= 0.005–1 Hz, D= 200 km, A= 0.2 nT; Molchanov et al., 1992; Kopytenko et al., 1993). In addition, the geo-electric potential enhancement appeared 1–19 days before five of all six earthquakes (EQs) with a magnitude > 5, which occurred within 75 km in Japan and its duration and intensity were several minutes to 1 h with an amplitude of 0.01–0.02 mV m-1 (Uyeda et al., 2000). Qian et al. (2002) reported the observation of ULF signals generated from the Jiji earthquake on 21 September 1999 in Taiwan and recorded at many stations at distances of 300–900 km in southeast China. Similarly, Ohta et al. (2002) have reported the observation of ULF/extremely low frequency (ELF) emissions generated from the Taiwan earthquake on 21 September 1999 and recorded at Nakatsugawa station in Japan at a distance of up to 2000 km.

A more notable example reported by Li et al. (2013) is the Wenchuan MS 8.0 earthquake on 12 May 2008, a typical mid-crust, which resulted in great devastation and 69 000 deaths. This earthquake was preceded by more than 1 month of increasing anomalous ULF emissions with a climax starting on 9 May, 3 days before the Wenchuan main shock (f= 0.1–10 Hz, D= 1440 km, A= 1.3 mV m-1). More details can be seen in Sect. 4.

Many simulating rock-pressure experiments were carried out in order to understand the producing mechanism of the electromagnetic information associated with seismic activities. Laboratory experiments by Qian et al. (1996, 2003) and Hao et al. (2003) presented that electromagnetic signals are always recorded when rock samples are subjected to dynamic stresses. Shorter-period electromagnetic pulses appearing at the last stage of the experiment may be induced by instantaneous electric current of accumulated charges during the stress accelerating. The work of Freund (Freund and Wengeler, 1982; Freund, 2002, 2009, 2010; Freund and Sornette, 2007; Scoville et al., 2015) has gained a new insight into the production of current and electromagnetic signals in stressed rocks. As rocks come under stress, stresses cause slight displacements of mineral grains in the rocks, which in turn leads to the activation of peroxy defects that preferentially sit on or across grain boundaries. The peroxy breakup leads to positive holes, and the positive holes are able to flow from stressed to unstressed rock, traveling fast and far by way of a phonon-assisted electron hopping mechanism using energy levels at the upper edge of the valence band. A gabbro sample 30 cm × 15 cm × 10 cm from Shanxi, China, was used in this test and a 55 nA current has recorded about 2 s before failure, with the load being at about 30 000 lbs (∼ 13 600 kg) and the maximum spike reaches 450 nA when the main failure took place (Freund, 2009).

Up to now, no clear explanation has been given although several physical mechanisms have been proposed to interpret the generation of EM emissions and electrical currents observed either during seismic activity or in the laboratory experiments. These include the electrokinetic and magnetohydrodynamic, piezomagnetism, stress-induced variations in crustal conductivity, microfracturing, etc. (Draganov et al., 1991; Park, 1996; Fenoglio et al., 1995; Egbert, 2002; Simpson and Taflove, 2005). Whatever the physical mechanism of electromagnetic generation is, it is well established that, during rock experiments conducted under laboratory conditions, a strong electrical current is produced when rocks are stressed, especially at the stage of the main rupture.

As the development of satellite Earth observation (EO), there is an increasing amount of evidence that during some last stages of the long-term process of preparation, there could be a transfer of energy between lithosphere, atmosphere, and ionosphere, so as to introduce the concept of a lithosphere–atmosphere–ionosphere coupling (LAIC) among the three involved layers of the Earth (Pulinets et al., 1994, 2000; Hayakawa and Molchanov, 2002; Molchanov et al., 2004; Kamogawa, 2006). When we investigate electromagnetic emissions induced by an electrical current or a magnetic moment on the surface or beneath the Earth, the effect of the medium air, crustal as well as ionosphere should be taken into account since these three media consist of different conductivities and we need to consider a lithosphere–atmosphere–ionosphere electromagnetic coupling (Cummer, 2000). Several tentative LAIC models have been constructed based on ground-based and ionospheric observations prior to strong earthquakes and the investigation of the influence of external electrical field on ionospheric parameters has been developed quickly (Pulinets and Ouzounov, 2011; Pulinets and Davidenko, 2014; Sorokin and Hayakawa, 2013, 2014; Kuo et al., 2011, 2014; Namgaladze et al., 2012; Zolotov et al., 2012; Zolotov, 2015). At the same time, the ionosphere plays an important role in electromagnetic propagation at ELF and very low frequency (VLF). The ground and the ionosphere are good electrical conductors and form a spherical Earth–ionosphere waveguide (Cummer, 2000). In addition, in the controlled-source electromagnetic (CSEM) method, widely used in petroleum exploration or mining, the ionospheric influence on EM fields should be considered when the distance between a large-scale and large-power fixed source and the receiver is up to 1000 km. EM fields can be amplified in the ionosphere as it is shown when we use the analytical solution of Maxwell equations, as well as numerical ones of the “Earth–ionosphere” mode with a source on the Earth's surface or in the lower atmosphere (Fu et al., 2012; Li et al., 2010a, b, 2011; Xu et al., 2012).

Therefore, in comparison with an electromagnetic attenuation without an ionospheric effect, the point is to evaluate the ionospheric influence on the electromagnetic propagation when the distance between the epicenter and the observing location is up to 1000 km or more. Furthermore, the comparison between the observation distance reported by Li et al. (2013) (D= 1440 km) and the length of the Wenchuan earthquake main rupture L= ∼ 150 km (Zhang et al., 2009a) indicates that the length of the dipole source is not negligible. So in this paper, based on the work of Key (2009), a three-layer (Earth–air–ionosphere) physical model as well as a two-layer (Earth–air) model, containing a finite length dipole current source co-located along the fault and beneath the Earth, is introduced in Sect. 2. For specified parameters, some simulation results of the current source with and without ionospheric effects are given in Sect. 3. In Sect. 4, using assumed parameters, the simulation results for the case of the Wenchuan earthquake reported by Li et al. (2013) are presented. Discussion and conclusions are given in Sects. 5 and 6, respectively.

In order to study the electromagnetic fields emitted by a long dipole current source, the approach used here follows the magnetic vector potential formulation described in Wait (1982) and developed by Key (2009), who generalized the formulation to allow for multiple layers above the transmitter (in addition to multiple layers below). He used exponential forms for the recursions rather than hyperbolic functions in isotropic media, which consists of N layers of isotropic conductivity σi where i=1,…, N, and which uses a right-handed coordinate system with the z axis pointing down. Assuming a time-harmonic source with e-iωt time dependence, negligible magnetic permeability μ variations, and angular frequencies ω that are low enough so that displacement currents can be neglected, Maxwell's equations are ∇×E=iωB, and ∇×B=μσE+μJs. Expression Js=Iδ(r-r0) is the imposed electric dipole source at position r0 with vector moment I, and here is restricted to an infinitesimal dipole with unit moment.

Based on the model setup by Key (2009), some modifications will be done in this study in order to complete the target here. A physical model is specified. It has three layers, Earth, air, and ionosphere, which is called Earth–air–ionosphere model. Its coordinate system is denoted in Fig. 1 with z direction being downward. An x-directed dipole of a length L and a current I is placed in the bottom medium (Earth: z>0), which is homogeneous and has the electrical properties: magnetic permeability μ1, permittivity ε1, and conductivity σ1. The middle medium (air: -100km<z<0) is described by its electrical properties μ0, ε0(i.e., 8.854×10-12Faradm-1) and σ0(i.e., 10-14 S m-1). The top medium (ionosphere: z<-100 km) is characterized by electrical properties μ-1, ε-1 and σ-1(i.e., 10-5 S m-1).

As a comparison, a two-layer model (Earth–air model) including an Earth medium (z>0), as well as an air medium (z<0), is also established during the study. All the corresponding parameters described are the same as those of Earth–air–ionosphere model.

We assume that the total space is non-magnetic and that the magnetic permeability μ variations are negligible in the different layers; i.e., μ1=μ0=μ-1=4π×10-7Faradm-1. However, the ionosphere, as the electrically conducting section of the upper atmosphere, plays such an important role for the electromagnetic propagation that we set ε-1=5ε0 when an ionospheric effect on electromagnetic transmission is taken into consideration. On the other hand, we have ε1=ε0=8.854×10-12Faradm-1; i.e., ε1 is not considered as zero during all calculations. Under these conditions, the formula listed above is still suitable and more explanations about the potential formulation of a horizontal electric dipole can be found in the Appendix A of Key (2009), and related programs are available with access to the website (http://marineemlab.ucsd.edu/). The horizontal finite length dipole source can be viewed as integral for an infinitesimal horizontal dipole during related calculations.

According to these two models presented above, several free parameters must be specified in order to investigate the attenuation characteristics of the electromagnetic fields emitted by a long x-directed dipole current source. As for the parameters of the dipole current source, we select L= 150 km, the Wenchuan earthquake main rupture stage within 30 s out of 90 s (∼ 300 km) based on Zhang et al. (2009a, Fig. 1), the depth d= 19 km (Xu, 2009), the hypocenter depth of the Wenchuan case and the current is set to be I=1A temporarily. Here, the Earth is considered to be an isotropic media with an average conductivity σ1, and we assume σ1=1.0×10-3 S m-1 at this time; i.e., ρ1=103 ohm m. Furthermore, the ground conductivity depends not only on the local petrology but also on the porosity, temperature, and pressure (e.g., Wait, 1966). All these parameters are common to two models. The parameter ε-1=5ε0 is very important during the calculation in the three-layer model whereby it can potentially affect the transmission of electromagnetic waves produced by the dipole beneath the Earth, and possibly induce the Earth–atmosphere–ionosphere electromagnetic coupling.

Figure 2a–d display electric field amplitude |Ex| decay curves along the x axial direction with the frequencies f= 0.01 Hz, f= 0.1 Hz, f= 1 Hz, and f= 10 Hz for the Cartesian coordinate system up to ∼ 10 000 km on the Earth's surface.

It can be seen from Fig. 2a–d that, first, the electrical field with high frequency has a bigger attenuation although all curves for both the Earth–air model (red solid lines) and the Earth–air–ionosphere model (blue dotted lines) decay rapidly as the distance increases. Second, each group of curves run at the same level for one fixed frequency, e.g., f= 1 Hz, when an observing point is located at a relatively close distance, ∼ 300 km for f= 1 Hz (Fig. 2c) for example. That is to say, the ionospheric influence on electromagnetic field transmissions can be neglected within this range. However, this range changes for different frequencies and it becomes smaller as the operating frequency of the current source increases (e.g., more than 1000 km for f= 0.01 Hz; Fig. 2a and only ∼ 200 km for f= 10 Hz; Fig. 2d). Third, the most important result is, as the distance increases, field curves with an ionospheric effect (blue dotted lines) run along a different path from that of curves without an ionospheric effect (red solid lines) and the ionospheric lines attenuate more slowly. Now, this kind of ionospheric influence can no longer be neglected. The ionospheric difference is about 1 magnitude (× 10) for all the frequencies listed and even once up to 2 magnitudes for f= 10 Hz within the range shown in Fig. 2. For example, the ionospheric difference value shows 1 magnitude from ∼ 840 km and up to 2 magnitudes from ∼ 3700 km for f= 10 Hz (Fig. 2d).

In recent years, there has been an increasing amount of evidence that during the last stages of the long-term process of preparation, there could be a transfer of energy between the lithosphere and the above layers of the atmosphere and ionosphere, so as to introduce the concept of a LAIC among the three involved layers of the Earth system (Pulinets et al., 2000; Hayakawa and Molchanov, 2002; Molchanov et al., 2004; Pulinets and Ouzounov, 2011). On the one hand, the “energy source” is usually thought to be beneath the Earth's surface and related to tectonic activities in the lithosphere. On the other hand, numerous rock-pressure experiments and electromagnetic observations associated with seismic activities have already proved that a giant electrical current and an abrupt increase of electromagnetic signals occurs during the main rupture of stressed rocks. These phenomena happened on 9 May 2008, 3 days before the Wenchuan event, whose hypocenter is located in the mid-crust. The strong seismo-telluric current is thought to run mainly along the Longmenshan fault and electromagnetic oscillations, induced by the current and predominated by ULF frequency band, propagate up to the ionosphere and give rise to perturbations of ionospheric parameters. Some of these parameters have been investigated, such as GPS TEC and f0F2 (Yu et al., 2009; Xu et al., 2010; Akhoondzadeh et al., 2010), DEMETER satellite O+ density (Zhang et al., 2009b), electron density and electron temperature (Zeng et al., 2009), etc. Fortunately, all of these study results present a climax on 9 May 2008 and this indicates a LAIC or interaction aroused by these electromagnetic signals prior to the Wenchuan event.

Unfortunately, at present, most of the investigations put emphasis on the effect of earthquakes upon the ionosphere and few of them pay attention to an inverse problem, that is, the ionospheric influence on the electromagnetic waves passing through.

The ionosphere, as a part of the electrical conducting region of the upper atmosphere, can enhance electromagnetic fields and cause the decay as a function of distance to slow down when an observation is beyond ionospheric range, and the ionospheric effect can be up to 1–2 orders of magnitude of the electrical fields in our simply three-layer model for some specified parameters we have selected here.

Considering the Wenchuan event, the electrical signals from the lithosphere interact with the ionosphere and are at the same time enhanced, and then registered at 1440 km Gaobeidian station with the amplitude of ∼ 1.3 mV m-1. This electrical field is used to simulate the seismo-telluric current produced by the Wenchuan main rupture in an Earth–air–ionosphere model together with an Earth–air model. The results present that, the seismo-telluric currents with and without ionospheric effects must be about 5.0 × 107A and 3.7 × 108A, respectively. Compared with the expected seismo-telluric current ∼ 10–100 kA of the “Alum Rock” MW= 5.6 earthquake for an observed 30 nT pulse at 1 Hz and D= 2 km (Bortnik et al., 2010), this result is probably in a reasonable range.

However, first, the total rupture of the Longmenshan fault during the Wenchuan main shock is extremely complicated, which is comprised of tenths of rupture stages and several pauses, totaling 90 s for the whole rupture process (∼ 300 km), according to Zhang et al. (2009a). Thus, the total surface rupture ∼ 300 km is nevertheless not used here. While performing the analysis on only the primary 30 s, a main stage of the Wenchuan earthquake (out of 90 s as we have selected L= 150 km above) is expected to be representative of the majority of the rupture to generate a seismo-telluric current. Second, three media are thought of as a homogeneous isotropic medium in our models and with the same average conductivity value for each one, especially for the Wenchuan area. However, the Earth conductivity plays such an important role that it predominately affects the fluctuations of the electrical fields as shown in Fig. 6, although no one exactly knows the right conductivity of the Earth medium at the rupture depth. The value σ1=7.0×10-4 S m-1, which has been used in all analyses, is estimated when the observing frequency range f= 0.1–10 Hz and the hypocenter depth d= 19 km of the Wenchuan main event are taken into account for the skin-depth formula. One must also mention that we use f= 1 Hz in our calculations because we cannot identify the actual frequencies in the recorded analog signals. All these can probably underscore our simulation results.

While these disadvantageous selections are maybe not so important at the same time, the key point of this paper is of the ionospheric influence on electromagnetic wave propagation and our investigation attains advantageous results.

The “selectivity” or “orientation” of the electromagnetic information is a very important characteristic during seismic activities (Varotsos and Lazaridou, 1991). For a finite length dipole source of the Wenchuan earthquake, its 2-D distributions of electrical field components |Ex| and |Ey|, which are orthogonal each other, on the Earth's surface show there are strong field power areas and weak field power areas around the source as illustrated by Bortnik et al. (2010). The radiating pattern of the total |E| in this investigation is symmetric to the center circle outside of the source, which indicates a signal is always registered to anyone direction if a system is designed to measure the total field |E| or both |Ex| and |Ey| components instead of only one. This result also basically supports the practices of selectivity or orientation, the observing reality before the Wenchuan earthquake described by Li et al. (2013), for example, “compared with the EW (east–west) orientation, the electromagnetic signal is more obvious in the SN (south–north) orientation”. The selectivity effect is a complex phenomenon that may be attributed to a superposition of the following three factors: “source characteristics”, “travel path” and “inhomogeneities close to the station” (Varotsos and Lazaridou, 1991; Varotsos et al., 2005). Analytical solutions of Maxwell equations (Varotsos et al., 2000), as well as numerical ones (Sarlis et al., 1999), convince that selectivity results from the fact that earthquakes occur through a slip on faults, which are appreciably more conductive than the surrounding medium.

In this paper, a three-layer (Earth–air–ionosphere) physical model, as well as a two-layer (Earth–air) model, is employed to investigate the ionospheric effect on the wave fields for a finite length dipole current source co-located with the main fault of an earthquake when an observing location distance is up to 1000 km or even more. For a dipole source with specified parameters of the length L= 150 km, the current I= 1A, and the depth d= 19 km, the results show that all fields are free of the ionospheric effect for different frequencies in relative short ranges, e.g., ∼ 600 km for f= 0.1 Hz, which implies the ionospheric influence on electromagnetic field transmissions can be neglected within this range. However, the ionosphere can increase the field amplitude and slow the decay when an observation is out of this range and the ionospheric effect can be up to 1–2 orders of magnitude of the electrical fields.

This is applicable to the 12 May 2008 Wenchuan MS 8.0 earthquake during which a strong electromagnetic signal with an amplitude of ∼ 1.3 mV m-1 is recorded by the Gaobeidian ULF (f= 0.1–10 Hz) observing station 1440 km from the epicenter. The main fault rupture producing a current is equivalent to a finite length dipole current source, with a nucleation depth of 19 km and a length of 150 km. Considering the Earth–air–ionosphere model, the expected current for the most typical properties of Wenchuan area is of 5.0 × 107A, which is 1 magnitude smaller than the current value of 3.7 × 108A obtained with the Earth–air model free of an ionospheric effect. On the contrary, a signal produced by a seismic activity can be advantageously recorded by a remote station under the ionospheric effect as if the detectability of the system were improved effectively.

The 2-D power distributions of the electrical field components |Ex|, |Ey|, and the total |E| after making a logarithm calculation on the Earth's surface are characterized by different radiating patterns. There are strong power areas along four main axes as well as weak power areas between two main axes for the electrical field |Ex|, whereas the component |Ey| displays a complementary radiating pattern with strong areas and weak areas. Therefore, fortunately, a signal is always registered to any one direction if a system is designed to measure the total field |E| (or both |Ex| and |Ey| components) as the radiating pattern of which is symmetric to the center circle outside of the source.

The data presented in this paper are available by request through the following e-mail: limeixuxl@seis.ac.cn.