On the Diurnal Dependence of fbEs-Variations Due to Earthquakes

In the present work, disturbances of the half-transparency frequency b s f E of the ionospheric sporadic E-layer are investigated in connection with earthquakes. The b s f E -frequency is proportional to the square root of the maximum ionisation density of the sporadic E-layer. In this work, it is shown that in 2/3 of the cases, two days before a seismic shock with magnitude M 5.5 > and on the day of the shock, an increase of the b s f E -frequency is obtained at sunset hours at distances from the epicenter ( ) R M exp < km. In contrast, before sunrise, the b s f E -value decreases. The data analysed are obtained by the three vertical ionospheric sounding stations “Kokubunji”, “Yamagawa”, and “Wakkanai” during some tens of years.


Introduction
Recently, it has been experimentally verified that at different altitudes above the Earth's surface, and accordingly in different ionospheric layers, disturbances are observed, which occur-in comparison with the so-called non-seismic background time-with large probability at a special daytime some days before earthquakes [1].Of late, in connection with the search for ionospheric precursors of earthquakes, variations of different ionospheric parameters are being discussed.There are regular parameters among them like the frequencies 2 o f F and o f E , but it also exists parameters which characterize irregular processes.To them, for instance, the half-transparency frequency b s f E of the sporadic E-layer s E belongs.Many scientific works are devoted to effects of earthquake preparation in s E -layers.It is found that earthquake preparatory anomalies of ionospheric parameters are observed most often 1 -5 days before seismic shocks with magnitudes 5 M > .Besides it is perceived that the anomalies' occurrence is connected with the magnitude of the earthquakes and with their distances to the epicentres [2]- [6].
In the work [7], a statistical analysis of pre-earthquake ionospheric anomalies is performed, which are registered by continuous GPS TEC (Global Positioning System-Total Electron Content) measurements for earthquakes with 6 M > .It is found that anomalies are obtained one-two days before seismic shocks (on the days (−2, −1)) most often.In [8], seismo-ionospheric effects in the temporary run of the frequency 2 o f F are observed 1-5 days before earthquakes with 5 M > from 12 to 18 h LT.Before very strong earthquakes with 7 M > , sometimes anomalies are observed in the s E -layer, which amplitudes are much larger than the background ones [9] [10].
Anomalous o s f E -increases seem to be a seismic precursor, as follows from the Hyogoken-Nambu earth- quake (M = 7.2 on January 17, 1995).Before the earthquake, on the whole day January 15, the geomagnetic and solar conditions were very quiet and, thus, could not cause a o s f E -increase.Nevertheless, at epicentral dis- tances of 120 km (at Shigaraki) and 500 km (at Kokubunji), o s f E -values above 8 MHz were registered on January 15 at daytime [11].The normal o s f E -values in Japanese winter are below 6 MHz.But it is very difficult to perform statistical analyses for very strong earthquakes with 7.0 M ≥ due to the fact that they are seldom.For statistical studies, earthquakes with lower magnitudes have to be used.
Daytime dependences of the occurrence of pre-earthquake anomalies are investigated in only some works.In the works by Ondoh and Hayakawa [9] and by Ondoh [11], an anomaly of the s E -layer is obtained in the daytime two days before an earthquake with 7.2 M = .In the study [12], the anomalous growth of the parameter o s f E before strong eqarthquakes with magnitudes 6 M > in Taiwan (1994)(1995)(1996)(1997)(1998)(1999) is investigated by analysing 16 seismic shocks.In doing so, an increase of o s f E at sunset and sunrise times is obtained.In the paper [3] a graphic is presented, which shows effects of increased s E -activity during the period of the Kultuk earthquakes near the Baykal Lake in August 2008.Also in this case an anomalous growth of o s f E is pre- dominantly observed during sunset and sunrise hours.In the works [2] [13] [14] seismo-ionospheric effects in the sporadic layer are found two days before earthquakes with ( )
The distance R from the epicentre, at which earthquake precursors are observed in the ionosphere, amounts, as a rule, to some hundreds of kilometres.On the average, it may be estimated by the formula In the present work, an analysis of the b s f E -frequency is performed for some tens of earthquakes with magnitudes 5.0 M > by using data of the Japanese vertical sounding stations "Kokubunji", "Yamagawa", and "Wakkanai".It is suggested that seismo-ionospheric effects may be observed in the time interval (−2, −1, 0).

Method of Data Analysis
Here, ionospheric effects of earthquakes are investigated by using data recorded by the vertical sounding stations "Kokubunji" (Tokyo) ( 35.Sporadic s E -layers, these are clouds with increased degree of ionisation, which have a pancake form and occur at altitudes of 90 -140 km.The layers have large horizontal and small vertical dimensions, and normally consist of long-living metallic ions.The phenomenon of the wind shear is believed to be the reason of the formation of sporadic layers [16].In accordance with the wind shear model, s E -layers arise at altitudes where local horizontal winds change their direction from west to east and the vertical velocity gradients are of the order of 0.05 -0.06 s −1 or larger.The charged particles move into the direction of the point where the wind velocity equals zero, and as a result, a sporadic layer forms.The diffluence of the sporadic layers is mainly caused by ambipolar diffusion and/or turbulent diffusion.
In the order of magnitude, the maximum plasma concentration of the s E -layer reaches 10 5 -10 6 cm −3 .Such layers have a horizontal dimension of 100 -200 km.The ionisation density equals 5 3 in the day-time, and it is about 2 -3 orders of magnitude lower at night.The thickness of the sporadic layers, i.e. their vertical dimensions, varies between a few hundred metres and a few kilometres.One of the main characteristic frequencies which is observed by ionograms of vertical sounding stations is the screening (or half-transparency) frequency b s f E .Recently it is taken for granted that it corre- sponds to the maximum ionisation density in the sporadic layer ( ) . Let us investigate the daytime variations of the b s f E -frequency, which are connected to earthquakes.The aim of the present work is to illustrate at which hours of local time LT and at which distances from the epicentres of seismic shocks a modification of the daytime behaviour of the characteristic b s f E -frequency occurs because of earthquakes.
The b s f E -frequency may change within a rather broad frequency interval.In Figure 1, the temporal de- pendence of the b s f E -frequency is presented for the years 1977-1979.The observations were made by the station "Kokubunji" at 00:00 LT (LT = UT + 9h).The sporadic layer, in contradiction to regular layers, does not always exist.During the years of large solar activity of the 11 years solar cycle (1978)(1979), the sporadic layer is more often observed than during the years of lower solar activity (1977).In Figure 1, the seasonal dependence of the b s f E -frequency is clearly to be seen.The b s f E -maximum occurs in the summer months.In the daytime dependence of the b s f E -frequency, a maximum is found after noon and a minimum occurs before sunrise.After the sunset (that means beginning with about 19 h LT), a weak continuous decrease of b s f E is observed.The amplitude of the diurnal b s f E -value depends on the season (see Figure 2).To obtain observable variations of the b s f E -frequency, which are connected to processes of earthquake pre- paration, it is necessary to lower the seasonal dependence of the data, when one uses the method of superposition of epoches.Therefore, for any value of b s f E (for any hour) a dimensionless frequency is found for the time interval of 15 days, which means for the interval (−7, +7).For the normalized frequency , the superposition of epoches method may be applied.
It has to be underlined that the form of the -variations are observed after sunset (18 -23 h LT) and before sunrise (2 -4 h LT) (see Figure 3).Now the influence of the processes of earthquake preparation on the daytime behaviour of the dimensionless parameter norm b s f E will be analysed.In Figure 3, results of the method of superposition of epoches for the station "Kokubunji" are presented.The days (−2, −1, 0) before earthquakes with focus depths smaller than 60 km are considered to be seismo-active in case that the distance between epicenter and vertical sounding station is smaller than Earthquakes with magnitudes 5.0 M > are taken into account.If on one and the same day more than one earthquake happened, then these seismic shocks were suggested to contribute to only one earthquake.Red lines in Figure 3 show results for seismo-active days, the dotted blue line presents the mean value for all days, seismoactive and background ones.The main growth of the     .Let us study analogous dependences of pre-earthquake effects on the daytime dependence for other vertical sounding stations.In case of the station "Yamagawa" (Figure 7) it is found, that an increase of b s f E is  .During the considered time interval in the environment of the station "Yamagawa" 58 earthquakes occurred.Observational data for the evening hours are only available for 21 earthquakes.
Studying data registered by the vertical sounding station "Wakkanai" (Figure 8), an increase of norm b s f E is found for earthquakes with magnitudes 6 M > .During the considered time interval in the environment of the station "Wakkanai" 29 earthquakes took place.Observational data for the evening hours are available for only 9 earthquakes.
To demonstrate the seasonal dependence of the variations of the normalized frequency   -behaviour during seismo-active times, and the dotted lines present the behaviour during the background time.It is to be seen, that the variations at summer time are somewhat larger than at winter time.
Next, the influence of the solar activity on the diurnal behaviour of -growth in summer is considerable larger than in winter.In summer and/or at days with higher solar activity, the ionisation density of the E-layer increases.Consequently, an electromagnetic transfer of seismic disturbances from the lithosphere to the ionosphere is possible.
Finally, the influence of geomagnetic disturbances on the diurnal norm b s f E -variations during seismo-active and background times is studied.In doing so, days with a geomagnetic index 20 are assumed to be geomagnetically disturbed ones.Also the day after a day with 20 is suggested to be geomagnetically modified, as the negative phase of a geomagnetic storm begins days-hours after the disturbance.
Using the data of the station "Kokubunji", in

Figure 1 .
Figure 1.Monthly-mean b s f E frequency observed by the station "Kokubunji" at 00:00 LT in the years 1977-1979.

Figure 2 .
Figure 2. Daytime dependence of the b s f E -frequency registered by the vertical ionospheric sounding station "Kokubunji".The red line describes the values for the summer (April, May, June, July, August, September).The values of the winter (October, November, December, January, February, March) are presented in blue.
not symmetric, this is caused by large flashes of b s f E .And this is also the reason for the positive mean values of the daytime behaviour of norm b s f E (see the dotted line in Figure 3).It should be mentioned that the maximum norm b s f E

4 .
after sunset during 19 h LT and 24 h LT.Let us study the dependence of norm b s f E on the earthquake magnitude.In doing so, for any earthquake with 5the time interval (19 -24 h LT) is calculated.Then, the average for the pre-earthquake days (−2, −1, 0) is found.During the analysed years 1977-1988, 79 earthquakes happened.But a sporadic layer was only observed in 44 cases.The result of the study is presented in Figure From the analysis follows, that an anomalous increase of b s f E occurs for more than two thirds of the earthquakes with 5.5 M > .Two earthquakes with magnitudes 5.4 M =, for which an b s f E -growth is observed in the time interval (19 -24 h LT), are conditionally included in the earthquake group the average for weaker earthquakes.

Figure 3 .
Figure 3. Result of the superposition of epoches.Normalized frequency norm b s f E as function of the local time LT.The days (−2, −1, 0) before earthquakes with magnitudes 5.0 M > are considered as seismo-active ones.Only earthquakes with distances from the station "Kokubunji" ( ) exp R M < and focus depths 60 km H < are taken into account.Full linenorm b s f E at seismic activity, Figure 4. norm b s f E averaged over the time intervals (19 -24) LT of the days (−2, −1, 0) as function of the magnitude M.Only earthquakes with magnitudes 5.0 M > , distances from the station "Kokubunji" ( ) exp R M < and focus depths 60 km H < are taken into account.The dotted line presents the mean value of norm b s f E including the background.The red lines divide the earthquakes into groups according to different magnitudes, for which mean values are found.The numbers at the top equal the mean values of the groups.

Figure 5
Figure 5. norm b s f E averaged over the time intervals (19 -24) LT of the days (−2, −1, 0) as function of the distance R from the station Kokubunji.Only earthquakes with magnitudes 5.0 M ≥ , distances from the station "Kokubunji" ( ) exp 300 R M < + km, and focus depths 60 km H < are taken into account.The dotted line presents the mean value of norm b s f E including the background.The red line divides the earthquakes into groups of shocks occurring inside and outside the earthquake preparation region.The numbers at the top equal the mean values of the groups.

Finally, the anomalous 6 .
b s f E -variations are studied in dependence on the depth of the earthquake focus.taken into account.The result is presented in Figure Too less data of earthquake observations are available to make a statistically reliable conclusion.But, it seems to be very probable, that for earthquakes with focus depths 60 km H > an increase of b s f E is not obtained in the time interval (19 -24) LT.The mean value of norm b s f E for this group of earthquakes is almost equal to the background value of norm b s f E Figure 6.norm b s f E averaged over the time intervals (19 -24) LT of the days (−2, −1, 0) as function of the focal depth H.Only earthquakes with magnitudes 5.5 M ≥ , distances from the station "Kokubunji" ( ) exp R M < and focus depths 100 km H < are taken into account.The dotted line presents the mean value of norm b s f E including the background.The red line divides the earthquakes into groups for which mean values are found.The numbers at the top equal the mean values of the groups.

Figure 7
Figure 7. norm b s f E averaged over the time intervals (19 -24) LT of the days (−2, −1, 0) as function of the magnitude M.Only earthquakes with magnitudes 5.5 M ≥ , distances from the station "Yamagawa" ( ) exp R M < and focus depths 100 km H < are taken into account.The dotted line presents the mean value of norm b s f E including the background.The red line divides the earthquakes into groups for which mean values are found.
taken into account.The results of the analysis for data of the station "Kokubunji" are presented in Figure9for summer months (April-September) and winter months (October-March) separately.
Figure 8. norm b s f E averaged over the time intervals (19 -24) LT of the days (−2, −1, 0) as function of the magnitude M.Only earthquakes with magnitudes 5.5 M ≥ , distances from the station "Wakkanai"

Figure 9 .
Figure 9. Daytime dependence of norm b s f E at different seasons.The red lines on the left side show the result for summer (April-September) and the blue lines on the right side for winter (October-March).Full lines represent norm b s f E observed by discussed.Using the data of the station "Kokubunji", in Figure 10 norm b s f E is presented for diffent solar activity.On the left side of Figure 10, results of the analysis (full line) are presented, which are obtained for Wolf numbers 80 W > .The right side of Figure 10 (full line) shows the result for the other days with 80 W < .The dotted lines demonstrate the results for the related background times.One may conclude that the increase of norm almost the same values at high and low solar activity.But considering seismo-active periods, at daytime, the increase of norm b s f E is about two times larger than at night.An analogous behaviour of norm b s f E is found in case of the seasonal dependence.During summer and winter times, the background values of norm

Figure 11 ,Figure 10 .
Figure 10.Daytime dependence of norm b s f E at different levels of solar activity.The red lines on the left side show the result for days with high solar activity, 100 W > , and the blue lines on the right side take days with 100 W < into account.Full lines represent norm b s f E observed by the station "Kokubunji" at times with shocks with magnitudes 5.5 M ≥, dotted

Figure 11 .
Figure 11.Daytime dependence of norm b s f E at different levels of geomagnetic disturbances.The red lines on the left side show the result for days with high geomagnetic activity 20 p k Σ > and the following day, and the blue lines on the right