3.1. Selection of the Parameter That Is the Most Sensitive to Seismicity
[14] To select the best among the ULF/ELF parameters, the record was studied in the interval about 1.5 month long around the seismic swarm in the middle of March 2003. We choose this interval to study a relation between the seismicity and ULF/ELF field variations because of their remarkable behavior. The first half of the interval is seismically absolutely quiet, and the second one starts with the M_{S} = 5.9 shock on 15 March. This earthquake is the first in the EQ series with of slowly decreasing intensity. The second peak in seismic activity corresponds to M_{S} = 6 EQ registered on 19 March. Epicenters of almost all the earthquakes lie in the sea eastward from the observation point. Seismic and geomagnetic activity and ULF/ELF field parameters are summarized in Figure 2.
[15] Figure 2 shows that intervals of the enhanced P_{hh}/P_{dd} ratio start several days prior to an earthquake and last several days after it. A similar but weaker effect is seen in the power spectra of the field components. Such a behavior of spectral parameters may correspond to a source located eastward (westward) from the observation point. Coincidence of the intervals with high seismicity and steep variations of the field parameters makes the assumption plausible about a physical relation between them. Namely, we can assume that an additional local source of ULF/ELF magnetic field fluctuations appears in the epicenter zone at the last stage of the EQ preparation and after the earthquake.
[16] Characteristics of the ULF/ELF geomagnetic field in frequency bands aside of Schumann resonances are shown in Figures 3 and 4 The indexes of seismic (K_{S}) and global geomagnetic activity (Kp) are given in the first panel. Then, from top to bottom, the power spectral density of the horizontal components of the magnetic field, their spectral ratio P_{hh}/P_{dd}, ellipticity and ellipse orientation are given. Figure 3 shows the results for the frequency band 4–6 Hz, below the fundamental harmonic of Schumann resonance, and Figure 4 gives the same parameters for the frequency band 20–24 Hz, above the third harmonic of Schumann resonance.
[17] In both frequency bands the spectral power of H component and the ratio P_{hh}/P_{dd} increase 3–4 d before the first shock of the EQ swarm started on 17 March 2003. Simultaneously, the absolute value of ellipticity and the standard deviation of both ellipticity and ellipse orientation angle decreases.
[18] For the further analysis, we take the nighttime intervals of ±5 h from the local midnight and calculate the mean values and the standard deviations (RMS) of the power spectral densities, of the P_{hh}/P_{dd} spectral ratio, the ellipticity and ellipse orientation angle in the frequency band 4–6 Hz. Different combinations of spectral and polarization parameters were tested to select one the most sensitive to seismicity. Behavior of different combinations of spectral and polarization parameters is summarized in Figure 5.
[19] It is seen in Figure 5 that sensitivities of all the parameters exceed that of the P_{hh}/P_{dd} − 1 and are approximately equivalent. However, a lateral extension of a source and its explicit position influence the ellipse orientation rather than the ellipticity. Taking into account that the location and the size of a source can vary within a limited zone, we have chosen the parameter
which presents the seismic influence better than the other parameters.
[20] The results of comparison of the efficiency of two parameters ΔS and P_{hh}/P_{dd} − 1 are shown in Figure 6 for two intervals: 24 February 2003 to 6 April 2003 (Figure 6a), and 12 July 2004 to 8 August 2004 (Figure 6b). Both parameters increase with seismicity, but the time correspondence of ΔS enhancements with the groups of earthquakes is really amazing. The parameter P_{hh}/P_{dd} − 1 demonstrates several peaks at seismically quiet intervals, which correspond to low amplitudes and/or unstable polarization of the signal. The relevant peaks are suppressed in ΔS. Thus enhanced ΔS indicates the appearance of an additional signal with the polarization ellipse oriented along the magnetic meridian and the ellipticity stable at timescales of several hours.
[21] In a more general case of arbitrary direction to the source P_{hh} and P_{dd} should be changed by P_{nn} and P_{tt}, respectively, where indexes n and t correspond to the directions perpendicular and parallel to the direction from the observation point to the source, respectively. Some details of this procedure are discussed in section 2. The effect is seen in the clearest way in the frequency band 4–6 Hz.
3.2. Statistics and Reliability
[22] A detailed description of spectral and polarization parameters of natural signals at 1–40 Hz is given by Nickolaenko and Hayakawa [2002]. The average parameters of the signal measured at Karimshino agree qualitatively with their results. Diurnal and seasonal variation of spectral power density, ellipticity and ellipse orientation are similar to those described by Nickolaenko and Hayakawa [2002].
[23] The spectral density of the total horizontal power G = 〈P_{hh}〉 + 〈P_{dd}〉 for the whole period of observation is shown in Figure 7. Indices of local seismic (K_{S}) and global geomagnetic (Kp) activity are shown in Figure 7 (top), ΔS and G are given in Figures 7 (middle) and 7 (bottom), respectively. They are calculated with 2d averaging over night hours in the frequency band 4–6 Hz. The total horizontal spectral power demonstrates the typical seasonal variation with the maximum at local summer. On the other hand, the seasonal variation is not obvious in the variation of the parameter ΔS, which demonstrates an evident correlation with seismic activity. Five intervals of high seismicity are clearly seen in Figure 7 (top) and each of them corresponds to the interval of the parameter ΔS increased. It is also important that the parameter ΔS is not influenced by the geomagnetic activity.
[24] Influence of individual earthquakes on ΔS is illustrated in Figure 8. It is seen in Figure 8 that the earthquakes located to the east from the observatory at distances R < 300 km contribute mostly to the ΔS variation. Because of specific distribution of earthquakes in the observation region, these eastward earthquakes are simultaneously the closest to Karimshino.
[25] The analysis of data for individual earthquakes shows that the following earthquake parameters correspond to noticeable changes in the magnetic field polarization and, especially, in ΔS: depths H < 50 km, magnitudes M_{S} > 5.5 (E > 10^{13} J) and epicenter distances R < 300 km.
[26] Earthquakes with great magnitude are relatively rare. Thus, if only few years are included into analysis, the false correlations can occur due to random nonhomogeneity of the seasonal distribution of earthquakes. Among all the intervals with 21d duration (a central day ±10 d) two opposite groups of intervals are selected: seismic (with the EQ of M_{S} > 4.5, K_{S} > 2 and H < 70 km occurred during the central day of an interval) and seismically quiet (with no EQs of such parameters throughout the interval). The data coverage for the whole period of observations is good and the months' distribution of EQs is almost homogeneous for the total array. However, nonseismic intervals are concentrated in summer and a deficit of earthquakes exists in summer months. This may result in false interdependences between seismic activity and parameters of ULF/ELF emissions. To estimate a relation between seismic activity and ELF parameters free from seasonal effect, the following technique is used. Tree arrays of the seismic a seismically quiet intervals and general sample with the identical distribution of number of intervals over months are formed. The selection procedure is based on the condition of maximal total number of seismic intervals. Namely, we take all the months with nonzero number of both seismic and nonseismic intervals (Months 1, 3, 6, 8, 9, 12) and average the parameters for seismic intervals with unit weight, while for nonseismic intervals ELF parameters are averaged with the weight equal to ratio of seismic to nonseismic number of intervals. The resulting month distribution of seismic and nonseismic intervals and weights are given in Table 2.
Table 2. Month Distribution of Seismic and Nonseismic Intervals^{a}Month  Seismic Total  Nonseismic 

Total  Weight 


1  3  8  0.375 
3  5  5  1 
6  1  58  0.017 
8  4  14  0.286 
9  4  3  1.333 
12  5  16  0.313 
All  22   
[27] The parameters of the ELF magnetic field are calculated for seismic and nonseismic subarrays and for the general sample and compared. The results for the ellipse orientation angle θ and the parameter characterizing the degree of linear polarization l = (1 − ∣tan(β)∣)/(∣tan(β)∣ + 1) are shown in Figure 9. The latter parameter varies from zero for circular polarization to unity for linear polarization.
[28] In Figure 9 (top) the results for the angle of ellipse orientation θ are shown. In a general case, average ellipse orientation is controlled by the distribution of sources in rather a wide sector. Appearance of additional sources, concentrated near the seismic zone, results in a small variation of average ellipse orientation for seismic intervals. Actually, the polarization ellipse rotates at 5–7° toward the NS direction 3–4 d before and after an earthquake.
[29] The degree of linear polarization l for seismic, nonseismic and general samples is given in Figure 9 (bottom). For the time interval from −7 to 5 d it proves to be obviously higher for seismic intervals than for nonseismic ones and for the general sample. Two maxima of l are seen about several days before and after an earthquake.
[30] The observation point is characterized by moderate seismicity and weak earthquakes in the vicinity of Karimshino take place almost every day and nonseismic intervals are relatively rare. Thus the minimum in the beginning of a nonseismic curve can be of the same nature as one at seismic curve at 6–7 d after an EQ, because the majority of nonseismic intervals take place after shock series. Besides, the level of normal thunderstorm activity at Kamchatka is low [e.g., Watt, 1967, p. 486], and the effect of seismicity in ELF parameters is seen in the different results for both seismic and nonseismic intervals from the general sample.
[31] To estimate the reliability of the difference between seismic and nonseismic values of θ and l, the Fisher criterium for samples with different standard deviations is applied [Korn and Korn, 1968]. Figure 9 (right) shows the level of reliability of the hypothesis about the different mean values of seismic and nonseismic values of θ and l. P(θ) exceeds the 80% level at 3–4 and 1 d before an EQ and the picture for P(l) is similar. As the ∼15% of probability to adopt an invalid hypothesis is not negligible, we use an additional test to verify the hypothesis splitting of both samples in two of equal lengths. Thin dashed and dotted curves in Figure 9 (right) show the results for two subsamples. For seismic curves dispersion decreases in 3–4 d vicinity of an EQ and during this interval all seismic and nonseismic curves are clearly separated from each other. It is important, that the maximum of the precursor effect at 3–4 d before an EQ is reproduced in different techniques.
[32] The observed difference between ELF parameters for seismic and nonseismic intervals cannot be an artifact of random seasonal inhomogeneity of EQs and seasonal variation of the ELF parameters. Excluding of the seasonal variations does not eliminate a preseismic effect in θ and l. Thus the SPE analysis confirms the results seen from the individual EQ series. Probable false correlations caused by the existence of the “seasonal variation” in the EQ occurrence rate is also tested and proved to have a little influence on the found dependencies between the seismicity and the parameters of natural ULF/ELF signals. The probability to get this result by random coincidence is about 15% but additional indirect arguments such as reproducibility of results for two subsets of data are in favor of the adopted hypothesis.
[33] Finally, let us estimate the reliability of the effect by using a conventional approach, which was developed for estimation of the seismic precursor efficiency. We reproduce the definitions from Console [2001]:
[34] 1. Target volume Vt is a volume in 3D space (time and 2 coordinates of the Earth surface) determined by time of observation and geographical area of observation. Each earthquake with preconditioned magnitude threshold or target event is depicted as a point in the volume Vt.
[35] 2. Alarm volume Va is a volume in which an EQ related to that precursor is expected.
[36] 3. If an EQ occurs in the alarm volume, it is called a success (S).
[37] 4. If an EQ occurs outside of alarm volume, it is a failure of predicting.
[38] 5. An alarm that is not associated to any target EQ is called a false alarm.
[39] If NS, NA and NE are the number of success, the number of alarms and the total number of EQs in the target volume then commonly considered parameters in earthquake prediction evaluation are the following:
[40] 1. Success rate = NS/NA is the rate at which precursors are followed by target events in the alarm volume. False alarm rate = 1 − NS/NA is the rate at which precursors are not followed by target events.
[41] 2. Alarm rate NS/NE is the rate at which target events are preceded by precursors.
[42] 3. Failure rate is 1 − NS/NE.
[43] 4. Probability gain PG = [NS/(NAVa)]/[NE/Vt] is the ratio between the rate at which target events occur in the alarm volume and the average rate at which target events occur over the whole target volume.
[44] Generally, a precursor can be considered as reliable if it achieves a PG value greater than one [Console, 2001].
[45] In our case of singlesite observation, both the target volume and the alarm volume turn into the time intervals; hence the PG relation is
To estimate the timescale of the ΔS preseismic variation and its threshold level ΔS_{th}, which maximizes the probability gain, we use a conventional Superposed Epoch (SPE) analysis with the dates of main shocks with K_{S} > 1 taken as centers of time intervals. The analysis of the probability gain in dependence on the ΔS_{th} shows that noticeable changes occur in the interval ±5 d around the EQ date and the optimal threshold value of ΔS is ΔS_{th} = 10. The results of SPE analysis for 16 intervals with K_{S} > 1 central earthquakes and max(ΔS(τ)) > ΔS_{th}, where −15 < τ < 0 and τ is time in days from the EQ day, are shown in Figure 10.
[46] Figure 10 shows that the effect is almost symmetrical on the moment of the first shock and the leading time is about 5 d. We calculate the daily averaged ΔS and use the following rules:
[47] 1. An interval with ΔS exceeding the threshold level ΔS_{th} ≈ 10 is considered an alarm interval.
[48] 2. The duration of the alarm interval is 5 d after the start day (see Figure 9).
[49] 3. The anomalies occurred from the main shock until 5 d after it are considered as associated with the aftershock activity and are excluded from consideration.
[50] Application of these simple rules is evident from Figure 11. The results are summarized in the Table 3.
Table 3. Summary of ΔS Efficiency as an Earthquake Precursor for 3 aN  Observation Period Te, d  NE  NA  NS  Success Rate  Alarm Rate  PG 

1  343  9  7  6  0.85  0.66  6.47 
2  364  15  14  7  0.50  0.47  2.45 
3  264  10  13  3  0.23  0.30  1.22 
Total  971  34  34  16  0.47  0.47  2.68 