Natural Hazards and Earth System Sciences Detection of electromagnetic anomalies of three earthquakes in Mexico with an improved statistical method

A method for detecting seismomagnetic signals is presented. This work presents evidence of geomagnetic perturbations associated with three earthquakes (EQs) that occurred in Mexico within a distance of ρ = (1.8) 100.45M, where M is the magnitude of the EQ, during the year 2010. An improved statistical analysis in relation with the polarization analysis (as the ratio of vertical magnetic field component to the horizontal one) has been developed. The variation index (S4) shows important differences one day before and one day after the EQs (magnitudes considered are from 6 to 7.2).


Introduction
Evidence of electromagnetic emission at several frequencies associated with EQs has been accumulated over the years (e.g., Hayakawa and Molchanov, 2002;Molchanov and Hayakawa, 2008).The presence of strong interferences hampers the accumulation of the experimental data to test existing ideas on the mechano-electromagnetic conversion in the Earth's crust (Guglielmi et al., 2006).In addition, many authors perform the signal processing in a wide frequency ranges reporting geomagnetic perturbations related to EQs.Such anomalies have been reported for several decades (Parrot and Johnston, 1989;Johnston, 1997;Kushwah et al., 2009;Telesca and Hattori, 2007;Telesca et al., 2008).Seismogenic phenomena in the ULF (ultra low frequency) range, with frequency from 0.005 to 1 Hz (Kopytenko et al., 1993) related with EQs has been studied since Fraser-Smith et al. (1990) and a number of papers have been published on this topic after that (Smirnova et al., 2004;Serita et al., 2005; Correspondence to: O. Chavez (omar.chavez@uaq.mx)Kushwah et al., 2009).This frequency range is of practical importance in relation with EQ activity, since these waves are able to propagate easily on the Earth's surface where a ULF sensor is installed (Ida et al., 2008).
All the aforementioned methods are applied to improve both the detection of the ULF signals associated with seismogenic phenomena at different frequencies (Hayakawa et al., 2008), and the understanding of electromagnetic phenomena associated with tectonic and volcanic activity (Currenti et al., 2005a, b).In this paper, a simple polarization analysis which is the simplest analysis method has been used.But we have looked into the problem variation in order to improve the statistical method.This improved polarizations statistical method was applied to the ULF data observed in Mexico during the year 2010.We found a significant correlation in the data obtained for three EQs in Mexico near the observing station, within the earthquake radius preparation zone (ρ), as a modification of the previously stated equation proposed by Dobrovolsky et al. (1979) andDobrobolsky (1993b), where ρ = (1.8) 10 0.45M , where M is the magnitude of the EQ (Fig. 1).Finally, the results obtained in this paper would be compared with earlier results obtained with the wavelet method (Chavez et al., 2010).

ULF geomagnetic data and EQs
ULF geomagnetic data is obtained at an observatory named Juriquilla (JU2) (geographic coordinates: −100.45 • N, 20.70 • E) as in Fig. 1.At this field site we observe three geomagnetic components (H : N-S component, D: E-W component, and Z: vertical component) by means of fluxgate sensors.The sampling frequency is 1 Hz.The analysis focused on three rather big EQs (with magnitude greater than 6.0) within a distance to the station of ρ = (1.8) 10 0.45M , where M is the magnitude of the EQ.All the events occurred during the year 2010.The first EQ took place on 4 April, the second on 30 June, and the third on 10 August.The characteristics of the EQs are presented in Table 1.The distance between the EQs and the geomagnetic observatory is consistent with that considered in a previous study (Chavez et al., 2010).In such study the perturbations associated with the magnitude of the EQs could be observed.

Signal analysis
The polarization method developed by Hayakawa et al. (1996) is based on the measurement of the ratio of spectral power of the vertical magnetic field (Z) to the horizontal magnetic fields (H and D) (i.e., Z/H or Z/D).This ratio is known to provide information of related variations of the geomagnetic field of ionospheric origin (or solar-terrestrial effect) or seismic origin (Ida et al., 2008).Generally speaking, the polarization ratio becomes larger when there are seis-mogenic emissions (Ida et al., 2008), while the geomagnetic field variation are found to show smaller values (Hayakawa et al., 1996), The time series of the ULF data was processed to obtain the polarization signals Z/H and Z/D from the three geomagnetic components H , D, and Z as was previously reported by Ida et al. (2008).Furthermore, the Fast Fourier Transform (FFT) is performed to the polarization signals to obtain the power spectrum.Figure 2 shows three ratio signals corresponding to the FFT spectra of each one of the three seismic events.This was performed in order to analyze the components of the frequency previously associated to seismogenic ULF emissions (Hayakawa et al., 2007).It can be observed that FFT spectrum is not adequate to show significant differences or common patterns between the three FFT spectra.For that reason, a Discrete Wavelet Transform (DWT) analysis was used to analyze the three ratio signals.This type of analysis was selected due to its time-frequency decomposition capabilities.This methodology has been previously reported for co-seismic event detection in H , D, and Z components (Chavez et al., 2010).For this study, six DWT levels were analyzed using a wavelet mother function Daubechies 1 (DB1), but we present only the D6 for comparative reasons (see Fig. 2).Table 2 shows the frequency bands corresponding to each DWT analysis level for signals that were sampled at a frequency of 1 Hz.The first event is presented in blue, the second in red, and the third in green (see Table 1).. Some frequency activity can be inferred from highest observable amplitude during the D6 level of the DWT decomposition at  the start of the signals followed by amplitude suppression periods.The aforementioned behaviour is common to the three analyzed seismic events.There are some important peaks during the EQs in different frequency ranges, e.g., for the three EQs we have significant increases from the D2 to the D6 (0.0078125-0.25 Hz).Those results can be associated with the distance and the magnitude of the EQs.Furthermore, Fig. 2 also shows the corresponding DWT decomposition for the signals Z/D ratio, where the middle cluster during the day is the principal perturbation.However it can be observed that important amplitudes in each level are present.The values of Z/H and Z/D are computed as representing the daily data.This process implies that the distance of analysis is directly associated to the magnitude of the EQ.days before and 5 days after the EQ.The variation index is defined by,

An
where S 4 is the variation index considering a mean period of ten days and for the i ratio (i = Z/H and Z/D), x is the average of the component i over the whole period, and σ i is the standard deviation of the same component i ratio over the whole period.
Figures 3, 4 and 5 illustrate the temporal evolution of the analysis (Z/D and Z/H) during the period of 5 days before and 5 days after the EQs (see Table 1).The day of each EQs occurrence is during the 5th day, and its specific time is shown in Table 1. Figure 3 shows the corresponding analysis (on top) and the variation index obtained for the first event.Important increments on the variation index are observed 7 h before and almost 12 h after the event.Also it is observed that these variations are observed only around day 5. Figure 4 shows this same analysis, but in this case the white areas indicate the periods where data could not be recorded due to some problems of the ULF system.However, 24 h before and 24 h after the main shock an important increase in the variation index was observed.The increment variation index is mainly associated to the Z/D ratio.The Z/H ratio has similar changes as those observed in Fig. 4, where a sudden decrease on this value previous to the main shocks is shown.In the last figure, important increases in the variation index are observed almost 30 h before and 10 h after the EQ. Figure 6 shows certain enhancement in the Z/H and Z/D plots just before, during, and after the EQs and also shows significant increments in the variation index.The data was compared with the geomagnetic activity expressed by the Dst index (data obtained from http://wdc.kugi.kyoto-u.ac.jp/dstdir/)where those indices apparently had no correlation with EQs variation index (see Fig. 5).
The increase in the polarization and the variation index resulted not only from the increase in Z/H, but also from the increase and decrease of Z/D.These figures show a significant increase of the variation index occurs before, during, and after the EQs.The indices of Dst and Kp did not show important changes during this period.This indicates that the polarization and the statistical analysis are closely associated with occurrence of EQs.The three EQs analyzed exhibit significant changes.

Conclusions
There are seismo-magnetic signals related to EQs disturbing the electromagnetic field.The principal problem of the signal detection is the discrimination of the background noise.For that reason, the use of the DWT at different levels is proposed.Additionally, an improved statistical polarization analysis method has been applied to the ULF geomagnetic data at Juriquilla station in Mexico.The three geomagnetic field components recorded behave in different ways; for that reason a general variation index is used to estimate the perturbations for each polarization during the whole period.By using the variation index, it is found that the polarization ratio between the vertical and the horizontal magnetic field components (Z/H, Z/D) at different levels (see Table 2) exhibits significant clusters during the day of analysis.An increase in the variation index value, with the maximum value a few hours before and after the EQs, are observed.The application of a DWT filter using different levels in order to obtain frequency components that correspond to associated seismic anomalies shows that there are not predetermined favorable frequency ranges -apparently it depends on the direction, the distance, and the magnitude of each EQ analyzed.This kind of ULF lead time seems to be consistent with a previous work by Chavez et al. (2010).The epicentral distance of these three superficial EQs varies from 563 to 1974 km.

Table 1 .Figure 2 .
Figure 2. Geomagnetic data analyzed: The first event is presented in blue, the second in red, 2 and the third in green.The FFT analysis does not show important peaks.And Wavelet 3 Discrete Transform of the Z/H and Z/D ratio in a superposed analysis in the ULF frequency 4 range f =0.0078125 to 0.015625 Hz.The main seismic shocks are shown with arrows.5

Fig. 2 .
Fig. 2. Geomagnetic data analyzed: The first event is presented in blue, the second in red, and the third in green.The FFT analysis does not show important peaks.Included is a Discrete Wavelet Transform (DWT) of the Z/H and Z/D ratio in a superposed analysis in the ULF frequency range f = 0.0078125 to 0.015625 Hz.The main seismic shocks are shown with arrows.

Figure 3 . 5 Fig. 3 .
Figure 3. Map showing the time series of: the analysis for the first event Z/H (top right), and 3 Z/D (top left).At the bottom, the variation index for Z/H (left), and for Z/D (right).4 5

1Figure 4 .Fig. 4 .
Figure 4. Map showing the time series of: The analysis for the fi 2 top right and left, respectively.At the bottom, the variation ind 3 (right).There is no data in the white areas.4 5

17 1Figure 5 .Fig. 5 .
Figure 5. Map showing the time series of: The analysis for the third event Z/H, and Z/D top 2 right and left, respectively.At the bottom, the variation index for Z/H (left), and for Z/D 3 (right).4 5 Fig. 5. Map showing the time series of: The analysis for the third event Z/H, and Z/D top right and left, respectively.At the bottom, the variation index for Z/H (left), and for Z/D (right).

Fig. 6 .
Fig. 6.Dst Index obtained from Kyoto observatory web page corresponding with the 3 EQs analyzed.The period of time presented is 10 days.