At the local time of 07:49:37.9 on 14 April 2010, a Ms 7.1 earthquake hit the city of Yushu, Qinghai province, with an epicenter at 33.2∘ N, 96.6∘ E and a 14 km depth in the northeastern Tibetan Plateau. The nearest VLF transmitter around the epicenter is in the proximity of Novosibirsk (NOV), which belongs to the Russian Alpha navigation system consisting of three transmitters. The other two transmitters named Krasnodar (KRA) and Khabarovsk (KHA) are far away from the Yushu earthquake, so only the satellite data radiated from NOV have been used for analysis in this paper. The location of the transmitters and the epicenter of the Yushu earthquake are denoted by blue squares and black stars, respectively, in Fig. 1. Each transmitter radiates three different frequency VLF radio signals (11.9, 12.6, and 14.9 kHz), with a 0.4 s duration and a 3.6 s cycle.

The DEMETER satellite was launched on 29 June 2004 as a sun-synchronous orbit at an altitude of 710 km, which then was changed to 660 km in December 2005 (Parrot et al., 2006), and the operation was ended in December 2010. The scientific objective of DEMETER is to detect and characterize the electromagnetic signals associated with natural phenomena (such as earthquakes, volcanic eruptions, and tsunamis) or anthropogenic activities. It operated in the region from invariant latitude -65 to 65∘, with descending and ascending orbits crossing the Equator at the local time of ∼10:00 and ∼22:00, respectively. DEMETER has a revisit orbit period of about 14 d, which means the satellite returns over the same orbit trajectory after 13 d. The payloads include several electromagnetic sensors with two working mode: burst and survey. At the ELF–VLF (extremely low-frequency) band, the intensive-electromagnetic-wave data over locations of particular interest were provided in the burst mode, and in the survey mode, electric and magnetic power spectral density (PSD) data every 2 s were provided with a sampling frequency of 40 kHz and spectral resolution of 19.53 Hz.

According to the formula of Dobrovolsky et al. (1979) the preparation zone of the earthquake can reach ρ=100.43M, where M is the magnitude of the earthquake and ρ is measured in kilometers. Considering the limited extension of the Ms 7.1 Yushu earthquake, the preparation zone ρ can reach to 1130 km; we mainly focused on the region within the region of the epicenter ±10∘ (black square in Fig. 1). In this study, the nighttime PSD data of the electric field from the DEMETER's survey mode observations were extracted study the perturbations of the VLF signal before and after the Yushu earthquake. As the VLF radio signals at daytime are too small to cause obvious SNR variation compared with those at nighttime, we did not use the daytime data in this study.

According to the method of Molchanov et al. (2006), the SNR of the electric field was calculated as follows: 1SNR=2Af0Af++Af-, where A(f0) is the amplitude of the electric-field spectrum at the central frequency and A(f±) values are the spectrums at f±=f0±Δf, where Δf is the chosen frequency band. For the three Russian VLF transmitters, the f0 is set as three VLF radio waves frequency radiated from NOV transmitters at 11.9, 12.6, and 14.9 kHz and the Δf=300 Hz.

A full-wave method has been used to seek a solution of Maxwell equations for waves varying as ejωt in a horizontally stratified medium with fixed dielectric permittivity tensors ε^ and permeability μ in each layer. Considering the region of our interest is much smaller than the radius of the earth, the earth's curvature is neglected in this study. A Cartesian coordinate system is established with x, y in the horizontal plane and z as vertical upward. We seek a solution of the Maxwell equations in the form of a linear combination of plane waves ∼ej(kbot⋅rbot), where kbot is the horizontal component of the wave vector k, which is conserved by Snell's law inside each layer; we have 2k×E=ωμ0Hk×H=-ωε^E, where ω is the angular frequency, μ is the permeability of the medium (µ≡1 for nonmagnetic medium), ε^=ε0(I+χ^) is dielectric tensor, and χ^ is electric-susceptibility tensor (Yeh and Liu, 1972). χ^ is determined by the electron density and collision frequency in the ionosphere, as well as the geomagnetic field. In our simulation, the electron density is calculated by the International Reference Ionosphere (IRI) model (Bilitza et al., 2017), and the electron collision frequency (denoted by v) is modeled by the exponential-decay law with the height (denoted by h) increasing at v=1.8×1011e-0.15h. The parameters of the geomagnetic field at the location of the VLF transmitter is calculated by the International Geomagnetic Reference Field (IGRF) model (Finlay et al., 2010).

Eliminating the z components from Eq. (1), we can obtain the following elegant form of Maxwell equations. 3dVdz=jk0T^⋅V, where V=(EbotZ0Hbot), Z0 is wave impedance and T^ is a 4×4 matrix: 4T^=-kxε31k0ε33-kxε32k0ε33-kyε31k0ε33-kyε32k0ε33kxkyk02ε331-kx2k02ε33-1+ky2k02ε33-kxkyk02ε33-ε21+ε23ε31ε33-kxkyk02-ε22+ε23ε32ε33+kx2k02ε11-ε13ε31ε33-ky2k02ε12-ε13ε32ε33+kxkyk02-kyε23k0ε33kxε23k0ε33kyε13k0ε33-kxε13k0ε33. The electromagnetic field in each layer can be obtained in the k (wave vector) domain by solving Eq. (2) recursively in a direction which provides stability against numerical “swamping” (Budden, 1985; Lehtinen and Inan, 2008). The difficulty is how to deal with numerical stability when the solution of evanescent waves “swamp” the waves of interest because of the large imaginary vertical-wave number. More details of the full-wave method are described in Lehtinen and Inan (2008).

The SNR five revisit periods before and one revisit period after the earthquake in 2010 were calculated to study the evolution of SNR above the epicenter. The SNR distributions of three frequencies (11.9, 12.6, and 14.9 kHz) within the region of the epicenter ±10∘ are shown in Fig. 2, where the value of SNR is denoted with colored dots with different sizes and the black star represents the epicenter of the Yushu earthquake. The data during geomagnetic storms (here we defined Kp > 3 and Dst < -30 nT) were plotted with hollow dots, and very small gray dots mean that the transmitter is turned off on these days. It can be found that in the first revisit period (2–14 April) before the earthquake, the SNRs of the three frequencies all decrease dramatically compared with other periods no matter whether it is before or after the earthquake. In the first revisit period from 2 to 14 April in 2010, two magnetic storms occurred on 4–7 and 11–12 April, respectively.

To minimize the impact of other factors and confirm whether the SNR anomaly is caused by the earthquake and not the variation of the ionospheric background, we focus on SNR in the black square (shown in Fig. 1) of the same period in 2007–2009 as the background, when there are no large earthquakes and the data when the transmitter was turned off or affected by geomagnetic storms are eliminated. The mean value of all the data in each period has been obtained to get the time sequence shown in Fig. 3. In Fig. 3, the black dashed line represents the occurrence date of the earthquake. The black and red solid lines represent the average values in the five periods before the earthquake and one period after the earthquake within the region of the epicenter ±10∘ in 2010 and background time, respectively. The change trends of SNR in the background time and 2010 are the same except in the first period before the earthquake. In the first period before the earthquake SNR decreased significantly in 2010, while it increased in background time at all transmitting frequencies. It means that the decrease in SNR in the first period in 2010 might be caused by Yushu earthquake.

The above results use the average value within the region of the epicenter ±10∘ in one revisit period of DEMETER to analyze the anomalies which ignore the day-to-day variability of the ionosphere. Furthermore, the daily variation of SNR in the first period before the earthquake is studied using a quartile-based process (Liu et al., 2009) to detect the anomaly of SNR. The median (M), the lower (first) quartile (denoted as LQ), and the upper (third) quartile (UQ) of every successive 11 d of SNR of the orbit data within the region of the epicenter ±10∘ have been calculated to find the deviation between the observed SNR of the 12th day and the computed median (M). Based on the assumption of the normal distribution of SNR with the mean (m) and standard deviation (σ), the expected value of M and LQ or UQ are equal to m and 1.34σ (Liu et al., 2009, and references therein). We set the lower boundary (LB in short) to LB = M + 2(M-LQ) and the upper boundary (UB) to UB = M + 2(UQ-M) to find the SNR anomalies with a stricter criterion. Thus, if an observed SNR on the 12th day is greater or smaller than its previous 11 d based on UB or LB, a positive or negative anomaly of SNR will be identified. Figure 4 shows the time series of SNR at 11.9, 12.6, and 14.9 kHz, and the red, gray, black curves denote the current SNR, associated median, and upper and lower boundary (UB and LB), respectively. Blue and green markers represent the positive and negative anomaly. As shown in Fig. 4, besides the negative anomalies which appeared on 13 April (1 d before the Yushu earthquake; the occurrence time of the Yushu earthquake is denoted by a vertical dashed line in Fig. 4) at all transmitting frequencies, another three anomalies occurred on 29 March, 8 April, and 10 April, respectively. Previous research indicates that earthquake anomalies usually occurred within 1 week before an earthquake, so the negative anomaly which occurred on 29 March at 12.6 and 14.9 kHz may be not related to the Yushu earthquake. The anomalies on 8 and 10 April only occurred on one single transmitting frequency, which may not be significant and is needed to be further researched.

The result in Fig. 4 shows the anomalies of SNR during the successive 20 d before the Yushu earthquake. However, the 20 d orbital data may be carried into the ionospheric background noise of different space. To avoid this kind of ionospheric background noise, we select the three revisit orbits to analyze the anomalies of SNR before the Yushu earthquake further (the revisit orbit on 9 April overhead the epicenter, the revisit orbit on 13 April which is 550 km away from epicenter, and the revisit orbit on 10 April which is 750 km away from the epicenter are selected). The quartile-based process is also performed for every revisit's orbital data, but the 6 d sliding-mean value (including 3 d before the current day and 2 d after the current day) have been analyzed. The green and blue bar represent negative and positive anomalies in one orbit, respectively, in Fig. 5. As we can see in the top and middle panel, on 9 and 10 April, the negative and positive anomalies both occurred like other days in the same two revisit orbits. These anomalies could be induced by the daily variation. In the bottom panel, there are no obvious anomalies in other days with the same revisit orbit of 13 April, but the SNR values have obvious negative anomalies for all orbits on 13 April. These results further confirm that the anomalies of SNR occurred on 13 April.

We speculate that the anomalies of SNR may be related to the anomalies of electron density. To confirm our conjecture, we used GPS–TEC map data distributed by CODE (Center for Orbit Determination in Europe) to check out whether the total electron content (TEC) showed similar anomalies. The resolution of TEC data from CODE is 5∘×2.5∘. We use 11 d sliding-mean values of every grid as a background, and then we can get a spatial distribution of the background. The background ±2× stand deviation is set as the threshold (upper bound and lower bound) to determine whether there are anomalies; if the intraday value exceeds the threshold, there are anomalies. We have reviewed the TEC anomalies of every day from 2 to 14 April (which means the duration of the sliding background is from 22 March to 13 April). The TEC anomalies only occurred on 13 April. The anomalies that are the most intensive were at 06:00 UT, which means only the SNR anomaly on 13 April is a possible earthquake precursor. The other two anomalies on 8 and 10 April in Fig. 4 may be caused by other factors. Figure 6a–b shows the TEC at 06:00 UT on 13 April and the sliding mean of the background (2–12 April); Fig. 6c–d shows the abnormal region where the TEC value exceeded the threshold (background ±2× standard deviation). As we can see, TEC had an abnormal enhancement on 13 April at the southwestern region of the epicenter. In addition, we collect the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) data in the abnormal region of TEC (southwestern region of the Yushu epicenter) to check whether there is abnormal variation in the D–E region electron density. As shown in Fig. 7, the result shows there indeed exists a disturbance in the E region on 13 April. Similar to the abnormal region of electron density, the SNR of orbit no. 030939-1 on 13 April also decreased in the southwestern direction in Fig. 2. This phenomenon may illustrate the decrease in SNR caused by TEC enhancement. Furthermore, this TEC enhancement was probably caused by an earthquake because it shows very intensive conjugate response. However, TEC anomalies caused by geomagnetic storms do not exhibit this kind of phenomenon generally (Zhao et al., 2008).

In Sect. 3.1, we analyzed the spatial and temporal characteristics of SNR during the five revisit periods before and one revisit period after the Yushu earthquake. It can be found that SNR decreased significantly before the earthquake over the epicenter area of the Yushu earthquake, especially in the southwestern direction. After excluding the influence of geomagnetic storms, we further explored the possible mechanism of SNR abnormal variation in this section. As mentioned in the Sect. 1, the electron density in the lower ionosphere can be disturbed through various mechanisms before earthquakes. The electron density before the Nepal earthquake was obtained from a computer ionosphere tomography method by using GPS data (Kong et al., 2018). Their results shows that the abnormal variation of electron density occurred at a height of 150 km before the Nepal earthquake and the range of variation reached about 30 %. However the electron density hardly changed at a height of 450 km. Marshall et al. (2010) have shown that 60 horizontal discharge pulses of 7 V m-1 near the ground can cause 50 % change in electron density in the lower ionosphere, and 60 horizontal discharge pulses of 10 V m-1 near the ground can even cause a 400 % change in electron density. The variation of electron density in the ionosphere caused by lightning activity and an earthquake can both be explained by one lithosphere–atmosphere–ionosphere coupling mechanism with penetration of the direct current (DC) electric field (Zhou et al., 2017; Kuo et al., 2011). These results provide us a reference for the amplitude of the perturbation of the electron density in the D–E region. Based on these results, the full-wave model was used to simulate the changes in the electric field at satellite altitude excited by ground-based VLF transmitters caused by the enhancement of or decrease in electron density in the lower ionosphere so as to further determine the change law of SNR.

As mentioned in the introduction, the major VLF wave energy almost lost in the D–E region; after that, the radio waves penetrate the topside of the ionosphere and even magnetosphere with a minor linear reduction because of the mode conversion (Lehtinen and Inan, 2009; Shao et al., 2012). The data of COSMIC also illustrate that the anomaly of electron density not only occurred in the F region (represented by the anomaly of TEC) but also occurred in the D–E region, so the full-wave method (FWM) (Lehtinen and Inan, 2009) was utilized to simulate the electric field between altitudes of 0 and 120 km induced by the NOV transmitter, which is the closest transmitter to the epicenter of the Yushu earthquake. Considering that the study area is much smaller than the radius of the earth, the earth's curvature was neglected in this study. A Cartesian coordinate system was established with x, y in the horizontal plane and z as vertical upward.

We set a Gaussian shape perturbation at 110 with 20 km standard deviation in the ionosphere. The magnitude of the perturbation was set to a maximum of 1.3 and 4 times both the increase and decrease compared to the original electron density of nighttime (the average electron density above the NOV transmitter on 2–14 April 2010 at 22:00 LT calculated from the IRI-2016 model). The perturbation patterns are shown in Fig. 8 using 4 times the increase and decrease compared to the original electron density as an example. The electron collision frequency is modeled by the exponential-decay law described in Sect. 2.3. The geomagnetic-field intensity and inclination at the location of the NOV transmitter are calculated by the IGRF model.

The electric field only from the ground surface to 120 km has been calculated by the full-wave model because the electromagnetic wave at VLF band will propagate upward as the whistler mode. The group velocities of the upward-radiated whistler mode are almost parallel, and these waves form a narrow-collimated beam, which does not have much lateral spread. The direction of group velocities is determined by the refractive-index surface. The refractive-index surface of the upgoing whistler mode at 120 km is shown in Fig. 9. A ducted propagation is adopted at this L shell (Clilverd et al., 2008), and the VLF wave power is spread in accordance with the divergence of geomagnetic field lines with a linear reduction because of the mode conversion (Lehtinen and Inan, 2009; Shao et al., 2012). The abnormal region of TEC and SNR both that occurred in the southwestern region of the Yushu epicenter could demonstrate that the VLF radio wave propagated in a ducted mode.

The simulated results of the electric field at 120 km height with a different electron density along the magnetic meridian plane within 1000 km area around the transmitter NOV with 11.9 kHz transmitting frequency are shown in Fig. 10. The simulated results are similar when the transmitting frequency is 12.6 and 14.9 kHz. It can be seen that the wave mode interference in the waveguide has been mapped into the ionosphere in the electric field (Lehtinen and Inan, 2009), and the electric field increases when the electron density decreases, and vice versa (Fig. 10a, c). Furthermore, the maximum value of the electric field varying with height is collected to study the influence of the electron disturbance. At nighttime, when i the variation of electron density is smaller, the variation of the electric field is also smaller (Fig. 10b, d). When the electron density increases by 4 times, the maximum electric field decreases about 2 dB at 120 km (see Fig. 10d). The variation is also 2 dB at DEMETER's altitude (660 km) because of the linear reductions (Lehtinen and Inan, 2009; Shao et al., 2012), which implies that the disturbed electric field decreased 20 % compared with the original electric field (Fig. 8b). In the short time interval of a few days before the earthquake, the background noise can be assumed to be stable, so the change in the electric field can reflect the change in SNR. It can be concluded that when the electron density increases by 4 times, the variation of SNR is 20 %. The simulated results illustrate that the variation of electron density in the lower ionosphere before an earthquake is one main factor of causing the abnormal variation of SNR. The more precise SNR variation needs more observation and simulation in the future.

Which coupling mechanism is effective to induce electron density anomalies in the D–E layer by earthquakes is still an open question. Molchanov et al. (2006) declared that the lower-ionospheric disturbance is caused by acoustic gravity waves triggered by earthquakes. At present, the coupling mechanism of the electric field proposed by Pulinets (2009) is widely accepted because it has been demonstrated by a series of models (Kuo et al., 2011; Namgaladze et al., 2013; Zhou et al., 2017) and observations (Gousheva et al., 2006, 2008; Li et al., 2017). As for the 2008 Wenchuan Ms 8.0 earthquake in China, Li et al. (2017) reported continuous observations about the anomalous electric field which lasted longer but weaker than the electric field induced by lightning during 1 month before the Wenchuan earthquake, which suggests that the abnormal electric field might be caused by the seismogenic activity of the Wenchuan earthquake. Xu et al. (2011) also found about 2 mV m-1 anomalous electric field in the F2 layer of the ionosphere before the Wenchuan earthquake. Gousheva et al. (2006, 2008) revealed a large number of anomalous electric fields before earthquakes using the INTERCOSMOS satellite. In addition, it is demonstrated that the anomalous electric field induced by an earthquake could change the electron density in the lower ionosphere by Kuo et al. (2011) and Zhou et al. (2017). Such as for the 2015 M 8.1 Nepal earthquake, the electron density variation was well explained by the ground electric-field coupling model established by Zhou et al. (2017).

The lightning, geomagnetic storms, and other natural sources may induce disturbance in the lower ionosphere (Marshall et al., 2010; Maurya et al., 2016; Peter et al., 2006; Zigman et al., 2007). As known, the intensive TEC change occurs during geomagnetic storms, and the change in TEC is affected intensively during the main phase of the geomagnetic storm, gradually returning to normal accompanying the recovery phase. To avoid the effect of geomagnetic storms, the data which Kp > 3 and Dst <-30 nT were excluded in this research, and the TEC anomaly detected in Fig. 6 was seen 1 d after the recovery phase of the geomagnetic storm (Fig. 11a). Furthermore, the change pattern of TEC is totally different from the one caused by an earthquake because the TEC anomalies caused by a geomagnetic storm expand from high latitudes to mid latitudes due to thermospheric neutral winds, E × B convection, and so on (Pokhotelov et al., 2008). From Fig. 11b, we can see SNR on the whole orbit are large on 5–7 and 11 April during geomagnetic storms, especially at the higher latitudes. However, the SNR pattern on 13 April is totally different; SNRs on the orbit of 13 April only decrease in the abnormal TEC region. In sum, the TEC anomaly on 13 April should be unconcerned with the geomagnetic storm. A lightning flash is very rare in our research region (only four events from February 2010 to April 2010, which can be seen from the search result of https://lightning.nsstc.nasa.gov/nlisib/nlissearch.pl?coords=?579,18, last access: 27 August 2020), so the effect of lightning could be ignored in this study.