1 INTRODUCTION

Ionospheric disturbances preceding earthquakes (IDPEs) have been studied for more than half a century, apparently since the pioneering work of Davies and Baker (1965). The authors reported on well-pronounced ionospheric disturbances recorded before the catastrophic Prince William Sound Earthquake in Alaska on March 28, 1964 (geographic coordinates of the epicenter of φe = 60.9° N and λe = 212.7° E, a shock time of 0336:16 UT, a hypocenter depth of h = 25 km, and a magnitude of M = 9.2 according to updated modern data). The records were made at the ground-based vertical ionospheric sounding station (GVISS) BOULDER located ~3700 km from the earthquake epicenter along the great circle arc. Disturbances were simultaneously observed in the E (sporadic Es layer) and F (scattering) regions of the ionosphere for about 2 h before the shock. The sequences of the planetary index Kp values on the day preceding the earthquake and the day of the shock were the following: Kp (March 27, 1964) = {1+; 00; 20; 0+; 0+; 1–; 0+; 10} and Kp(March 28, 1964) = {00; 00; 0+; 00; 00; 0+; 00; 00}, i.e., the geomagnetic conditions were very quiet.

The question of the possible existence of inhomogeneities in the ionosphere, which can be associated with the processes of earthquake preparation, at such a significant distance from the epicenter is quite natural. The common estimate of the minimal radius of the earthquake preparation zone on the solid Earth’s surface as a function of the earthquake magnitude M was proposed by Dobrovolsky et al. (1979): RD = 100.43M km. For the catastrophic Alaska earthquake, RD(M = 9.2) ≅ 9000 km, and BOULDER station was within that zone. Khegai et al. (2002) analyzed the variations in one of the most important parameters measured at GVISSs, the critical frequency of F2 layer of the ionosphere (foF2), for a few hours prior to earthquake based on data from eight GVISSs. Specific regional disturbances were detected in the ionosphere, both near the epicenter of the impending earthquake (~100 km) and at a considerable distance from it (~1000–1500 km), at least few hours prior to the earthquake against quiet heliogeophysical conditions (the daily average number of sunspots was ~15, and the average AE index was ~30 nT two days before the earthquake). Those disturbances were apparently earthquake precursors.

Thus, the question of whether IDPEs are also ionospheric precursors of an earthquake (IPEs) because they turn out to be associated with its preparation is decided for each event (earthquake) with a certain degree of probability. In most cases, this assessment is made a posteriori based on a set of various morphological features and the behavior of ionospheric parameters, which are measured with allowance for the general geophysical situation.

The commonly accepted approach consists of the following: the “background” level of time variations is determined for any measured ionospheric parameter X, and deviations from this level beyond certain limits are considered as disturbances. The median value Xmed(ti) for each time point i (i ∈ [0, n], n is the number of uniform readings per day) during a day over an ensemble of reference days (a month in a standard situation) is usually taken as the “background” level of the parameter X in ionospheric studies. The inter quartile range IQR, which is equal to the difference between the upper and lower quartiles for the selected ensemble of days, is used as a measure of the spread of the current value Xcurrent(ti) due to random deviations. Then, the band K± = Xmed(ti) ± 1.5IQR(ti) bounds the amplitude of variations in Xcurrent(ti) due to random deviations with a certain degree of probability. According to (Klotz and Johnson, 1983), in the case of normal distribution of the “error” ΔX(ti) = Xcurrent(ti) – Xmed(ti), the magnitude 1.5IQR(ti) corresponds to approximately two standard deviations, and the Xcurrent(ti) values should fluctuate due to various random factors within the band K± with a probability of 95%. Therefore, Xcurrent(ti) values which go beyond this band can be attributed to nonrandom disturbances. Thus, decisions about the presence of disturbances can be taken based on a set of parameters measured at a GVISS, the values of which can be extracted from ionograms.

It should be noted that IDPEs, which are then identified as IPEs, are usually small in amplitude as compared to ionospheric disturbances caused by magnetospheric disturbances (magnetic storms). This can significantly complicate the use of this approach to identify IPEs during their development against such a disturbed background or even make it impossible. Indeed, as shown by Khegai et al. (2007), the maximum absolute value of the ionospheric disturbance of foF2, which went beyond the scatter band and was caused by a moderate storm (Kpmax = 6.0), recorded at GVISS ROME exceeded by more than three times the maximum value of a seismoionospheric disturbance (IPE) observed at the same station about a day before an earthquake with a magnitude M = 6.0 and a epicenter distance of Re ≅ 410 km to ROME station against a quiet geomagnetic background (Kp ≤ 20). The magnetic storm began on January 10, 1962, two days after the earthquake.

In “counterbalance” or in addition to the above, we should mention the new approach to IPE identification proposed and described in an earlier work (Pulinets et al., 2021). The authors called the approach “cognitive identification” of IPE. It is based on the recognition of the “image” of a precursor created with allowance for its morphological features and, hence, does not require large deviations from unperturbed values. Therefore, the approach can be effectively used even at low signal-to-noise ratios. To increase the reliability of the identification of possible IPEs from the observed IDPEs, it is obviously necessary to involve as many simultaneously measured ionospheric parameters or their effective combinations as possible.

The purpose of this work is to consider a combination of two parameters simultaneously measured at GVISSs that can almost always be extracted from an ionogram, i.e., the critical frequency of the ionospheric F2 layer foF2 and the virtual minimum height of the F region h'F (Handbook …, 1977). Their combination in the new relative parameter δBarbier provides an additional opportunity for the analysis of ionospheric disturbances and the search for possible IPEs. The mathematical expression of δBarbier is derived from the semiempirical Barbier’s formula (Barbier, 1957, 1959; Barbier and Glaume, 1962), which was derived and tested for several GVISSs. The use of the parameter δBarbier is considered below in an analysis of ionospheric data prior to an earthquake with a magnitude of M = 6.2 that occurred on June 26, 1989, in the vicinity of GVISS MAUI (Hawaiian) as an example. Data from that station were also successfully used previously to test and verify the semiempirical formula proposed by Barbier (1957, 1959; for more details, see Barbier, 1963, 1964).

2 SEMIEMPIRICAL BARBIER’S FORMULA AND DERIVATION OF THE MATHEMATICAL EQUATION FOR δBarbier

Barbier (1957) proposed his semiempirical formula for GVISS TAMANRASSET in the Northern Hemisphere (22.8° N, 5.5° E). This formula connects the number of quantum of atmospheric emission at a wavelength of 630 nm (Q) in dark hours (from 2000 to 0400 local time) with the measured ionospheric parameters foF2 (in MHz) and h'F (in km) (Eq. (3) from Barbier and Glaume (1962)):

$$Q = K{{\left( {foF2} \right)}^{2}}{\text{exp}}\left\{ {{{ - {\kern 1pt} \left( {h{\kern 1pt} '{\kern 1pt} F - 200} \right)} \mathord{\left/ {\vphantom {{ - {\kern 1pt} \left( {h{\kern 1pt} '{\kern 1pt} F - 200} \right)} H}} \right. \kern-0em} H}} \right\} + C,$$
(1)

where Q is the glow intensity (R) estimated from ionospheric data; H is the characteristic spatial scale of altitude variations (km); K and С are certain constants. K, С, and H should be specially determined for each station; for GVISS TAMANRASSET, H = 41.3 ± 2.5 km (Barbier, 1963).

The discussion of physical processes associated with glow in different lines is beyond the scope of this work. The OI 630-nm (red line) emission in the atmosphere occurs as a result of the forbidden transition (Peterson et al., 1966) of an oxygen atom from the O(1D) to the O(3P2) state with the emission of a quantum of radiation at a wavelength of 630 nm, i.e.,

$${\text{O}}{{(}^{1}}D) \to {\text{O}}{{(}^{3}}{{P}_{2}}) + h\nu {\kern 1pt} (630\,\,{\text{nm}}).$$

An O(1D) atom is produced by the photodetachment of electrons from O– ions (Chattopadhyay and Midya, 2006)

$${{{\text{O}}}^{ - }} + h\nu \to {\text{O}}{{{\text{(}}}^{1}}D{\text{)}} + e,$$

photodissociation in the Shuman–Runge band (Solar …, 1983)

$${{{\text{O}}}_{2}} + h\nu {\kern 1pt} (\lambda < 1750\,\,{{{\AA}}}) \to {\text{O}}{{{\text{(}}}^{1}}S{\text{)}} + {\text{O}}{\kern 1pt} ^*,$$

and dissociative recombination

$${\text{O}}_{2}^{ + } + e \to {{{\text{O}}}_{2}}\left( {{\text{unstable state}}} \right) \to {\text{O}}{\kern 1pt}^ * + \,\,{\text{O}}{\kern 1pt} ^*,$$

which mainly contributes to the intensity of this emission (O* is an oxygen atom in the 1S, 1D, or 3P state).

As noted by Chattopadhyay and Midya (2006), the experimentally determined different rate constants, quenching coefficients, and transition probabilities confirm that the intensity of oxygen emission in the green and red lines is proportional only to the electron density and, thus, the variations in the OI 630-nm and OI 557.7-nm emissions are mainly determined by the altitude profile of the electron density Ne. Since the altitude profile of the electron density in the nighttime region F can be represented by the modified Chapman function (Eq. (12) in (Tinsley and Bittencourt, 1975)), where the characteristic spatial scale H'(z) (z is the altitude, km) is close to the altitude of the homogeneous atmosphere for atomic oxygen H(O) in this altitude range, one can expect that the value of H in the Barbier’s formula is also close to H(O). Equation (1) derived by Barbier was later carefully verified (Carman and Kilfoyle, 1963) for GVISS TOWNSVILLE in the Southern Hemisphere (19.25° S, 146.75° E).

Ghosh et al. (2017) defined the combined parameter F ≡ (foF2)2exp{h'F/H} based on the variable part of Barbier’s formula for the analysis of pre- and postseismic activity from ionospheric data and found a significant increase few days before several earthquakes. Note, first, that the mean of that parameter was determined over 24 h, and, second, the sign of the exponent is “+,” in contrast to Barbier’s formula. The values of this parameter are difficult to interpret on a physical basis, since Barbier’s formula was derived for dark hours, and the “–” sign of the exponent is of fundamental importance from the physical point of view.

Barbier’s formula is used below to derive the new relative parameter δBarbier with allowance for its applicability only for dark conditions (from 2000 to 0400 LT) and its clear physical interpretation.

Let us now consider the difference of parameters defined by Eq. (1):

$$\begin{gathered} \Delta Q \equiv {{Q}_{{{\text{cur}}}}} - {{Q}_{{{\text{med}}}}} \\ = [K{{\left( {foF{{2}_{{{\text{cur}}}}}} \right)}^{2}}{\text{exp}}\left\{ {{{ - {\kern 1pt} \left( {h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{cur}}}}} - 200} \right)} \mathord{\left/ {\vphantom {{ - {\kern 1pt} \left( {h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{cur}}}}} - 200} \right)} H}} \right. \kern-0em} H}} \right\} + C] \\ - \,\,[K{{\left( {foF{{2}_{{{\text{med}}}}}} \right)}^{2}}{\text{exp}}\left\{ {{{ - {\kern 1pt} \left( {h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{med}}}}} - 200} \right)} \mathord{\left/ {\vphantom {{ - {\kern 1pt} \left( {h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{med}}}}} - 200} \right)} H}} \right. \kern-0em} H}} \right\} + C] \\ = K{\text{exp}}\left( {{{200} \mathord{\left/ {\vphantom {{200} H}} \right. \kern-0em} H}} \right){{\left( {foF{{2}_{{{\text{med}}}}}} \right)}^{2}}{\text{exp}}\left( {{{h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{med}}}}}} \mathord{\left/ {\vphantom {{h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{med}}}}}} H}} \right. \kern-0em} H}} \right) \\ \times \,\,\left\{ {{{{\left[ {{{foF{{2}_{{{\text{cur}}}}}} \mathord{\left/ {\vphantom {{foF{{2}_{{{\text{cur}}}}}} {foF{{2}_{{{\text{med}}}}}}}} \right. \kern-0em} {foF{{2}_{{{\text{med}}}}}}}} \right]}}^{2}}{\text{exp}}\left[ {{{\left( {h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{med}}}}} - h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{cur}}}}}} \right)} \mathord{\left/ {\vphantom {{\left( {h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{med}}}}} - h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{cur}}}}}} \right)} H}} \right. \kern-0em} H}} \right)] - 1} \right\}, \\ \end{gathered} $$

where the subscripts “cur” and “med” indicated the current values and medians over a selected ensemble of days. The dimensionless normalized difference, or the Barbier parameter, is

$$\begin{gathered} {{\delta }_{{{\text{Barbier}}}}} \equiv {{\Delta Q} \mathord{\left/ {\vphantom {{\Delta Q} {[K{\text{exp}}\left( {{{200} \mathord{\left/ {\vphantom {{200} H}} \right. \kern-0em} H}} \right)}}} \right. \kern-0em} {[K{\text{exp}}\left( {{{200} \mathord{\left/ {\vphantom {{200} H}} \right. \kern-0em} H}} \right)}} \\ \times \,\,{{\left( {foF{{2}_{{{\text{med}}}}}} \right)}^{2}}{\text{exp(}}{{h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{med}}}}}} \mathord{\left/ {\vphantom {{h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{med}}}}}} H}} \right. \kern-0em} H}{\text{)]}}. \\ \end{gathered} $$

Then,

$$\begin{gathered} {{\delta }_{{{\text{Barbier}}}}} = {{\left[ {{{foF{{2}_{{{\text{cur}}}}}} \mathord{\left/ {\vphantom {{foF{{2}_{{{\text{cur}}}}}} {foF{{2}_{{{\text{med}}}}}}}} \right. \kern-0em} {foF{{2}_{{{\text{med}}}}}}}} \right]}^{2}} \\ \times \,\,{\text{exp}}\left[ {{{\left( {h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{med}}}}} - h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{cur}}}}}} \right)} \mathord{\left/ {\vphantom {{\left( {h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{med}}}}} - h{\kern 1pt} '{\kern 1pt} {{F}_{{{\text{cur}}}}}} \right)} H}} \right. \kern-0em} H}} \right)] - 1 \\ \end{gathered} $$
(2)

characterizes a change in the 630-nm atmospheric glow intensity, which is estimated from ionospheric data in dark hours. Indeed, if δBarbier > 0, then the glow intensity is above its median level, and, if δBarbier < 0, then the intensity is below this level. The smaller the h'Fcur value is in comparison with h'Fmed, the more likely it is that the estimated OI 630-nm glow intensity exceeds its median level, since their difference (2) is determined by an exponentially increasing factor. In this case, only H remains unknown in Eq. (2). It should be specially determined for each GVISS where observations are carried out. Let us discuss this issue in more detail.

There was very good agreement between photometric measurements of the OI 630-nm nightglow and its values calculated from measured ionospheric parameters foF2 and h'F (Barbier et al., 1962). The optical observations were carried out in the northern tropics at Haleakala station (20.71° N, 203.73° E), which is located ~25 km from GVISS MAUI (20.8° N, 203.5° E) along the great circle arc, for three nights (May 22/23 and June 3/4 and 5/6, 1961, from 2000 to 0400 LT). The observed values and the values calculated with the semiempirical Barbier’s formula (Barbier, 1957) at H = 41.3 km were compared, as they were for GVISS TAMANRASSET. The geographic latitudes of the GVISSs TAMANRASSET (22.8° N) and MAUI (20.8° N) are close.

Next, we describe the procedure to calculate the H value for any GVISS by its geographic coordinates according to the observation period (from 2000 to 0400 LT) on the day of interest, similarly to Barbier et al. (1962), with the use of the well-developed modern model of a neutral atmosphere, NRLMSISE-00 (https://ccmc.gsfc.nasa.gov/modelweb/models/ nrlmsise00.php). For this, we approximate with exponential functions the altitude profiles of the atomic oxygen concentration (O) and the density of the neutral atmosphere (ρ) derived with it (for the zero hour, LT, of the analyzed day) in an altitude range of 200–400 km, and the required H value is calculated as the average between H(O) and H(ρ), which are the characteristic scales of the exponential change in O and the ρ in these approximations. This procedure provides H = HMSIS ≡ (H(O) + H(ρ))/2. Note that the mean value is equal to the median for this definition.

Let us now verify the above H value for GVISS TAMANRASSET from 2000 to 0400 LT, June 3/4, 1961, in order to compare it with the value H = 41.3 ± 2.5 km from (Barbier, 1963). The H(ρ), H(O), and HMSIS values are given in Table 1 for GVISS TAMANRASSET and the time interval from 2000 to 0400 LT on June 3/4, 1961.

Table 1. Values of H(ρ), H(O), and HMSIS for GVISS TAMANRASSET from 2000 to 0400 LT on June 3/4, 1961
Full size table

As can be seen from Table 1, the median value HMSIS = HMED ± 1.5IQR = 41.6 ± 2.6 km found by us (with rounding) is very close to H = 41.3 ± 2.5 km (Barbier, 1963). It is also clear that the H value found by us following the procedure suggested is indeed close to H(O), as assumed above.

Thus, to calculate the combined parameter δBarbier with Eq. (2) to study the ionosphere, we need time series of foF2cur and h'Fcur observations in the studied time interval local time from 20 to 04 LT and the HMSIS value determined with the above procedure and NRLMSISE-00 model.

Below, we consider a specific example of the use of this parameter for the study of ionosphere variations before the earthquake (M = 6.2) that occurred on June 26, 1989, in the vicinity of GVISS MAUI. Based on this, the data for 1961 were used to test Barbier’s formula (1) (Barbier et al., 1962).

3 DATA ANALYSIS, RESULTS, AND DISCUSSION

An earthquake (according to the USGS catalog (https://earthquake.usgs.gov/earthquakes/eventpage/ hv311275/executive)) with geographic coordinates of the epicenter of φe = 19.36° N and λe = 204.92° E, a shock time of 0327:03 UT, a hypocenter depth of h = 8.8 km, and a magnitude of M = 6.2 occurred on June 26, 1989, at an epicenter distance of Re ≅ 220 km from GVISS MAUI along the great circle arc. The minimal radius of the earthquake preparation zone on the Earth’s surface, according to the Dobrovolsky’s estimate, is RD(M = 6.2) ≅ 460 km, and GVISS MAUI was deep inside this zone, since Re ≅ 220 км < RD(M = 6.2) ≅ 460 km (Fig. 1).

Fig. 1.
figure 1

Position of the epicenter (triangular star) of the 6.2-magnitude earthquake that occurred on June 26, 1989, near GVISS MAUI and Haleakala station (black dots), which fall within the zone of its preparation on the Earth’s surface. The arrows show the epicenter distance (Re) and the Dobrovolsky radius (RD).

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Let us analyze the seven-day time interval from June 21 to 27, 1989 (i.e., five days before and one day after the shock and the day of the earthquake). To study time variations in ionospheric parameters (foF2cur, h'Fcur, and δBarbier), we first determine the time interval for the selection of reference geomagnetically quiet days, based on which the medians foF2med and h'Fmed are then calculated for each hour of the day. That interval selected is June 26, 1989, ± 9 days, i.e., it is symmetrical around the day of the earthquake. Then, geomanetically quiet days (Kp ≤ 3– throughout the day) with no more than two values Kp = 3– per day and a time lag between them of at least 6 h were selected from this interval. Only 10 days from the above time interval satisfy these requirements: June 18, 21, 22, 23, 25, 26, 27, and 28 and July 3 and 4. The parameter H, which is required to calculate δ-Barbier (2), is found for the dark period (2000–0400 LT) for each of the reference days following the procedure described in Section 2, and the median value over these days is H = MEDHMSIS = 55.5 km.

Figure 2 shows the time variations in the planetary index Kp and the current values of δBarbier, h'F, and foF2 at GVISS MAUI during dark hours, from 1800 to 0600 LT (gray rectangles under the lowest x axis) for June 21–27, 1989. The scatter band ±1.5IQR of δBarbier values (Fig. 3b) is calculated for values in the time interval 2000–0400 LT for all the selected days. The scatter bands ±1.5IQR in Figs. 3c and 3d are calculated over the ensemble of reference days. The dashed vertical lines mark the narrow time interval on June 24, 1989, where foF2 is near its upper scatter boundary, h'F is below its lower scatter boundary for 2 h, and δBarbier is beyond its upper scatter band. For visual convenience, these areas are shown by black. The dashed region corresponds to the time interval from 2000–0400 LT on June 25, 1989, where δBarbier ≤ 0, i.e., the OI 630-nm glow intensity is continuously below its median level.

Fig. 2.
figure 2

Time variations in (a) the planetary index Kp and in the current values of (b) δBarbier, (c) h'F, (d) foF2 at GVISS MAUI during the dark hours, 1800–0600 LT (dark grey rectangles under the lowest abscissa), on June 21–27, 1989 (heavy solid lines with dots). The solid, vertical line with arrow marks the time of the earthquake; the horizontal dash-dotted lines correspond to (a) the level 2+ quiet geomagnetic conditions and (b) the δBarbier scatter band ±1.5IQR; (c) and (d) the solid lines indicate the median value of the corresponding parameter, and the dashed lines show the bands of their scatter ±1.5IQR. See the text for other explanations.

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Fig. 3.
figure 3

Time variations in (a) δBarbier, (b) the planetary index Kp, (c) the current hourly values of Bz, and (d) DST at GVISS MAUI during the dark hours on June 21–27, 1989. A short-term (0600 to 1500 UT on June 24) moderate increase in geomagnetic activity (Kp) is shown by the black rectangle under the abscissa axis; the light gray area in Fig. 3a shows a possible ionospheric precursor of the earthquake (IPE). Other designations are the same as in Fig. 2.

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Thus, two interesting features are marked as IDPE in Fig. 2. The first is a 2-h interval (from 0600 to 0700 UT on June 24, 1989) during which δBarbier goes beyond the upper boundary of its scatter band (before a small short-term moderate increase in the geomagnetic activity, judging by the behavior of the Kp index, which soon reaches 40). The second feature relates to the next day, when the estimated OI 630-nm glow intensity is always below its median level, although it does not go beyond the lower boundary of the scatter band during the dark 8 h before the earthquake against a quiet geomagnetic background (Kp ≤ 2+ from 0600 to 1400 UT on June 25, 1989). Figure 2 also shows, first, that a short-term “burst” in δBarbier (from 0600 to 0700 UT on June 24, 1989) occurs when h'F falls below the lower boundary of its scatter band and foF2 is very close to the upper limit of its scatter band. Second, a long period of negative δBarbier values (from 0600 to 1400 UT on June 25, 1989) corresponds to low foF2 values (close to the lower boundary of the scatter band) and simultaneous high h'F values (close to the upper boundary of the scatter band), which physically indicates the rise of the nighttime F2 layer and a decrease in the electron-density (Ne) maximum NmF2. We emphasize that the second IDPE is long but always within the δBarbier scatter band; however, among all of the night segments in the studied seven days, δBarbier is negative only on the night before the earthquake.

Let us consider the selected features of the behavior of δBarbier in more detail with respect to other geophysical indices DST and Bz-IMF.

Figure 3 shows the variations in δBarbier at GVISS MAUI, the planetary index Kp, and the current hourly values of Bz and DST during the dark hours of June 21–27, 1989. The absence of Bz values in Fig. 3c in different time intervals is due to a lack of data. The black box below the abscissa in Fig. 3b reflects a short-term moderate increase in geomagnetic activity from 0600 to 1500 UT on June 24, 1989. The area of light gray fill in Fig. 3a is marked with an arrow as a possible ionospheric precursor of the earthquake. The absence of Bz values in Fig. 3c at different time intervals is due to the lack of data. Other designations are the same as in Fig. 2.

Figure 3 shows an insignificant short-term increase in the geomagnetic activity on June 24, 1989, (the 2nd day, if the day of the earthquake is taken as zero). It is associated with the turn to the south of Bz-IMF, which has the form of two successive microsubstorms (see, in particular, (Akasofu, 1977; Pudovkin et al., 1977; Nishida, 1980)) from 0600 to 1500 UT (black rectangle under the abscissa in Fig. 3a). The local minima of the DST index (Fig. 3d) follow the local minima of Bz (IMF turns to the south) with a characteristic 1-h delay.

At the beginning of development of the first microsubstorm, there is a short peak in δBarbier that lasts for two hours and coincides with a simultaneous decrease in h'F and an increase in foF2 (h'F is beyond its lower boundary and foF2 is near the upper boundary of its “background” relative to the median). This peak may be due to the described onset of a short-term magnetospheric disturbance, after which (at 1500 UT) Kp ≤ 2+ for a day and a half, up to the time of the earthquake, i.e., the geomagnetic background is quiet. The long decrease in δBarbier during the dark 8 h of the day, ~13.5 h before the earthquake, may be of a seismogenic nature. This decrease in the estimated OI 630-nm glow intensity below its median level can indicate an increase in the nighttime F2 layer with a simultaneous decrease in NmF2.

Kim et al. (2017) note that the Joule heating of the nighttime ionospheric plasma of the F region inside a magnetic tube resting on the epicenter zone of an impending earthquake (which is induced by a seismogenic electric field penetrating the ionosphere) can decrease the downward plasma flux from the protonosphere. This plays an important role in maintaining the nighttime F2 layer. The decrease in the downward plasma flux decreases the main maximum of the ionospheric plasma NmF2 above the epicenter zone of the impending earthquake, while the eastern component of the zonal electric field enhanced by the seismogenic field causes an additional upward drift of the plasma, which results in the rise of the layer.

An increase by hundreds of Kelvins in the temperature in the nighttime region F of the ionosphere before the Iranian earthquake (geographical coordinates of the epicenter φe = 36.96° N and λe = 49.41° E; shock at 2100:09 UT on June 20, 1990; hypocenter depth h = 18.5 km; magnitude M = 7.4) in its source zone was previously recorded (Akmamedov, 1993) according to interferometric temperature measurements based on the OI 630-nm emission. The epicenter distance to the observatory (geographical coordinates φobs = 37.9° N and λobs = 58.4° E) was located near Ashgabat Re ≈ 800 km along the great circle arc; RD(M = 7.4) ≅ 1520 km. The measurements were carried out during the period of low magnetic and stable solar activity.

Thus, in the studied case, the first short (2 h) “burst” in δBarbier is associated with a short-term moderate increase in geomagnetic activity, and the long-term (8 h) decrease in δBarbier (below its median level against a quiet geomagnetic background) in dark time of the day, ~13.5 h before the earthquake, may be of a seismogenic nature and can be considered an ionospheric precursor (IPE). This possible IPE conceptually fits into the IPE “cognitive identification” scheme suggested in (Pulinets et al., 2021).

This study confirms that the relative Barbier parameter (δBarbier) introduced by us can be used for both the analysis of ionospheric disturbances of magnetospheric origin and the study of ionospheric anomalies of a seismogenic nature, i.e., IPEs.

4 CONCLUSIONS

1. A new relative parameter (δBarbier) was proposed for the analysis of ionospheric data. It was derived based on the semiempirical Barbier formula, which was first proposed by Barbier (1957).

2. A specific example shows the efficiency of this parameter for the interpretation of the ionospheric behavior prior to the earthquake (M = 6.2) that occurred in the vicinity of GVISS MAUI (Hawaii) on June 26, 1989. It was shown that δBarbier ≤ 0 in dark hours, from 2000 to 0400 LT, on June 25, 1989, i.e., the day before the earthquake, against a geomagnetically quiet background (Kp ≤ 2+). This behavior can be explained by a decrease in the intensity (as compared to the median level) of atomic oxygen O(1D) 630-nm emission estimated from ionospheric data, which is associated with the dissociative recombination of oxygen ions at altitudes of the F region in this period of time. This effect may be of a seismogenic nature and can serve an IPE.

3. The Barbier parameter δBarbier can be used for both the analysis of ionospheric disturbances of magnetospheric origin and the study of ionospheric anomalies of a seismogenic nature, which can serve as IPEs.