With the establishment and improvement of the National Broadband Digital Network, very wideband seismometers, such as BBVS-120, CTS-1 and BBAS-2, and ultra-wideband seismometers, such as JCZ-1, strong material support has been provided for the identification of information before earthquakes, and the analysis of special information before earthquakes in the frequency domain has more advantages than that in the time domain (Yang Liming et al., 2009). Environmental factors (such as landslides, blasting, thunder and lightening, etc.) all have their inherent frequency characteristics, and in terms of seismic waves, P-wave, S-wave, surface wave and body wave, all have different dominant frequency bands. Especially low-frequency signal of seismic waves, due to its low frequency, long wavelengths, are not easily being absorbed and thus avoiding obstacles which make it travel far, the study of low-frequency components of seismic waves can therefore better reflect the changes in deep earth structure. In order to enhance the practical effect of earthquake prevention and disaster alleviation, waveform data recorded by seismometers are mined by fast Fourier transform in order to find abnormal low-frequency signals in the frequency domain before strong earthquakes. Before the Wenchuan M_{S}8.0 earthquake in 2008, there was a low-frequency fluctuation of ground microtremor, which was reproducible and applicable to the later moderate-strong earthquakes in the region. To test whether the abnormal signals were universal, Gansu Digital Seismic Network conducted an internal pre-earthquake forecast experiment according to the reproducibility of the specific signals, and found that low-frequency fluctuation signals appeared within 20-160 hours before the earthquake and lasted for about 60-160 hours, showing the characteristics of reproducibility, continuity and procedural nature (Yang Liming et al., 2009). In fact, as early as a few years ago, some scholars (Feng Deyi et al., 1983, 1994) believed that the frequency spectrum of short-period surface waves may show certain precursory anomalies before major earthquakes, but the records of seismic data were not optimistic at that time and the research results were not satisfactory. With the establishment of digital seismic networks, the output of seismometers with high precision and good stability has provided a solid foundation for the application of this method. The phenomenon of spectrum shift is a concern of many seismologists. Some scholars (Chen Yuntai et al., 1979; Guo Zengjian et al., 1991) argue that its physical essence is a type of pre-sliding or slow fracturing of faults, and a precursory inference in the theory of facture and nucleation proposed later (Dieterich J.H., 1992) also indicates that low-frequency waves appear before earthquakes, which show unique spectrum features, that is, the frequency band narrows and shifts to low frequency. Meanwhile, some scholars put forward that characteristics of the spectrum recorded by stations with different epicentral distances for the same general earthquake (not a foreshock) vary (Yang Liming et al., 2015).
In this paper, based on the Alxa Left Banner M_{S}5.8 earthquake that occurred in the north end of the North-South Seismic Belt and the northwestern margin of the Ordos block, Fourier transform is used for spectral analysis of seismic waveform data within 15 days before the earthquake to find prominent anomaly features before the earthquake.
1 METHODS AND PRINCIPLESIn this paper, continuous digital waveform data recorded by the Wuhai seismic station(WUH) which is 42km from the epicenter of the 2015 Alxa Left Banner M_{S}5.8 earthquake, the Shizuishan seismic station(SZS) which is 60km from the epicenter and the Dongshengmiao seismic station(DSM) which is 158km from the epicenter are used for fast Fourier transform with hourly waveform data as the research objects to track the change form of the maximum envelope amplitudes at 0Hz-0.25Hz, and to observe whether low-frequency abnormal signals have shown special morphologic changes and whether these changes are related to epicentral distances.
1.1 Data ProcessingSeismic waveform data recorded by Wuhai (WUH), Shizuishan (SZS) and Dongshengmiao (DSM) seismic stations, which is respectively 42km, 60km and 158km from the epicenter of the 2015 Alxa Left Banner M_{S}5.8 earthquake, are selected as research data in this paper, and hourly data in seed format recorded by seismometers are converted into ASCII format and only data of vertical components (BHZ) are extracted. In this study, no conversion of velocity or acceleration is made, and counts value are directly used, but it turns out that the initial data for this work is best from seismic wave velocity data.
1.2 Fast Fourier TransformSpectrum analysis can accurately extract periodic information, which is of great significance for the further processing of dynamic data, and since a sequence is made up of accidental errors, periodic fluctuation and trend terms, it is difficult to see trend change at a glance. However, trends with less periodic fluctuations has less influence on spectrum analysis. In this paper, Fourier spectrum transform is used for data analysis.
$ {x_i} = \frac{{{a_0}}}{2} + \sum\limits_{k = 1}^m {\left({{a_k}\cos \frac{{2\pi ki}}{N} + {b_k}\sin \frac{{2\pi ki}}{N}} \right)} $ | (1) |
$ {a_0} = \frac{2}{N}\sum\limits_{i = 0}^{N - 1} {{x_i}}, \;\;\;\;\;\;\;\;\;\;{a_k} = \frac{2}{N}\sum\limits_{i = 0}^{N - 1} {{x_i}\cos \frac{{2\pi ki}}{N}} $ | (2) |
$ {b_k} = \frac{2}{N}\sum\limits_{i = 0}^{N - 1} {{x_i}\sin \frac{{2\pi ki}}{N}}, \;\;\;\;\;\;k = 1, 2, 3 \cdots m $ | (3) |
Equation (1) can be further simplified as below:
$ {x_i} = \frac{{{a_0}}}{2} + \sum\limits_{k = 1}^{\frac{N}{2}} {\left({{c_k}\cos \left({\frac{{2\pi ki}}{N} + {\varphi _k}} \right)} \right)} $ | (4) |
where
$ {c_k} = \sqrt {a_k^2 + b_k^2}, \;\;\;\;\;\;{\varphi _k} = \arctan \left({ - \frac{{{b_k}}}{{{a_k}}}} \right) $ | (5) |
By drawing c_{k}, φ_{k} based on frequency, Fourier amplitude and phase spectrum can be obtained.
The maximum frequency Nquist is usually used in digital signal processing. The Nquist frequency is determined by sampling interval Δt, which is the reciprocal of twice the sampling interval (Wan Yongge, 2007), and at present, the sampling interval for the digital seismic network is basically 0.01s, so the maximum frequency (Nquist frequency) of seismic waves can be obtained, which is 50Hz. However, this paper focuses on low frequencies within the range of 0Hz-0.25Hz, and pays no attention to high-frequency components, therefore, the visible frequency range is adjusted to 0Hz-2Hz when taking the frequency spectrogram.
1.3 Amplitude EnvelopeThe amplitude envelope is also known as the spectrum envelope, that is, spectrum is a collection of different frequencies, forming a wide range of frequencies. Different frequencies may have different amplitudes, and the curve formed by connecting the peaks of the amplitudes of different frequencies is called a spectrum envelope. The maximum value of the envelope curve at 0Hz-0.25Hz is determined and the maximum amplitude value in this frequency range are continuously tracked at three seismic stations (Wuhai, Shizuishan and Dongshengmiao seismic stations) (as shown in Fig. 1 and Fig. 2).
Wuhai, Shizuishan and Dongshengmiao seismic stations are respectively 42km, 60km and 158km away from the Alxa Left Banner M_{S}5.8 earthquake. Although the three stations have different epicentral distances, they have all shown different degrees of spectrum shift before the earthquake, that is, the spectrum shifts to a lower frequency, which is shown as shifting to the left on the graph.Generally, the dominant frequency band is at 0.2Hz as manifested in spectrograms (Fig. 3), with amplitudes less than 30. When spectrum shift occurs, the dominant frequency band will shift towards a lower frequency, generally less than 0.1Hz (Fig. 4), and at the same time the amplitude will generally increase, which can sometimes reach more than 100, of course, there will be different forms of spectrum shifts (Fig. 5).
Spectrum shift is not continuous in this study, instead, it appears continuously and intermittently until the earthquake occurs, and within the same hour, the amplitude recorded at Shizuishan seismic station is larger. However, in the same hour left shift of the spectrum appears in Wuhai, Dongshengmiao and Shizuishan seismic stations, displaying different kinds of spectrum features after the left shift. The left shift of the spectrum recorded by the three seismic stations at 10:00 a.m., April 7, 2015 differs from what was recorded at 09:00 a.m., April 4 and 09:00 a.m., April 7, 2015, which may be related to the fracture mode of underground media.
2.2 Tracking Results of the Maximum Value of Amplitude Envelope LinesWe keep track of the maximum values of amplitude envelope lines for the three stations (0Hz-0.25Hz), and the final results show that the patterns of the maximum values of envelopes for the three stations are significantly different (Fig. 6), which is related to the epicenter distance, and through this phenomenon, it is possible to determine the epicenters of future earthquakes. This particular pattern can well display the abnormal form before the M_{S}5.8 earthquake.
Wuhai seismic station, in particular, has been showing relatively stable patterns since April 1 and started to show fluctuation of curve since 06:00 a.m., April 10. This fluctuation form is not completely consistent with the continuous rise of amplitude in Wenchuan (Yang Liming et al., 2009). However, it is believed that this pattern appearing at Wuhai seismic station corresponds to the theory of facture and nucleation, which may be a manifestation of the meta-stability stage. Dongshengmiao seismic station shows a relatively smooth pattern, and the smooth curve may be the expression of rupture termination zone or unreached zone. Although Shizuishan station shows obvious sudden jumps, this pattern is unfavorable for energy storage, which could be the transmission of energy.
Low-frequency signals are extracted from continuous seismic wave data, but continuous seismic data is mixed with various information, including influence factors such as blasting, small earthquakes, teleseism, typhoon and rainstorm, which are analyzed below.
2.3.1 BlastingBlasting is common around the epicenter of the Alxa Left Banner M_{S}5.8 earthquake on April 15, 2015, which usually occurs at the boundary between Ningxia and Inner Mongolia, 150km from the epicenter. Blasting takes place on the surface of the earth, all of which are high-frequency components, and in the spectrum analysis of seismic wave data from the three stations, only low-frequency components at 0Hz-0.25Hz are considered, thus the spectrum display interval is controlled within 2Hz. The following graph (Fig. 9) shows that frequency components of small earthquakes are mainly over 1Hz, which are filtered with the Butter-worth filter, of which, the passband edge frequency is 1.0Hz, stopband edge frequency 2.2Hz, passband ripple 1db, stopband attenuation 30db, and finally, no matter before or after filtering, the components of data at 0Hz-0.25Hz will not be affected. In addition, the most prominent feature of blasting is that it is not sustainable, therefore the interference of blasting to low-frequency abnormal signals can be eliminated.
According to the national unified official catalogue, in the period of 00:00, April 1—03:00 p.m., April 15, there occurred two small earthquakes near the epicenter before the Alxa Left Banner M_{S}5.8 earthquake on April 15, 2015, which are respectively the Alxa Left Banner M2.3 earthquake in Inner Mongolia at 08:00 p.m., April 4, 2015 and the Yongning M2.0 earthquake in Ningxia at 08:00 p.m., April 5, 2015. The data of the two earthquakes within the hour when they occurred shows (Fig. 10) that there is little low-frequency phenomenon. Although the Yongning M2.0 earthquake in Ningxia at 08:00 p.m., April 5, 2015 shows a slight low-frequency signals, the amplitude is low and will not affect the results, which could be excluded. Seismic stations are sparse at the boundary between Ningxia and Inner Mongolia where Alxa Left Banner lies, with poor monitoring ability, therefore, it is not clear whether earthquakes with magnitude less than 2.0 will have an impact on the results.
There were no earthquakes in the period of 00:00, April 1—02:00 p.m., April 14, 2015, and a M_{L}5.0 earthquake took place in Lintao, Gansu, at 03:08:36 p.m. on April 15, 2015. The earthquake, located in southern Gansu Province, was about a half an hour difference from the Alxa Left Banner M_{S}5.8 earthquake at 03:39:28 p.m., on April 15, 2015. As recorded by the Baiyin seismic station in Gansu (BYT), the frequency range of the spectrogram for seismic waves of the Lintao M5.0 earthquake is 0Hz-20Hz (Fig. 11), but the frequency range of the spectrogram recorded by the Wuhai seismic station in Inner Mongolia is mainly 0Hz-8Hz, and most of them are clustered within 2.5Hz (Fig. 12). In this case, the low-frequency signals of the Lintao M5.0 earthquake has been received by the Wuhai seismic station, only the amplitude has been weakened. Therefore, the Lintao M5.0 earthquake has a certain influence on seismic stress accumulation and initiation around Wuhai seismic station, and it was not a coincidence that a M_{S}5.8 earthquake struck Alxa Left Banner, Inner Mongolia about 30 minutes later, 42km from Wuhai seismic station. Lintao earthquake in Gansu has significant influence on the Alxa Left Banner M_{S}5.8 earthquake. However, the low-frequency abnormal signals studied in this paper have appeared since April 10, and the emphasis is on the persistence of abnormal signals.
In the period of 00:00, April 1—02:00 p.m., April 15, there was no heavy thunderstorm near the epicenter of the earthquake in the Alxa Left Banner, Inner Mongolia, and it's also very far from the coast, therefore, the influence of low-frequency signals generated by typhoons is excluded. The climate is dry in Alxa Left Banner in Inner Mongolia in April, and high winds may have an impact on data, but it's not sustainable and is excluded.
3 CONCLUSIONIn this paper, we tracked and analyzed frequency spectra of seismic waveforms recorded by Wuhai, Shizuishan and Dongshengmiao seismic stations near the Alxa Left Banner, Inner Mongolia M_{S}5.8 earthquake on April 15, 2015, and discussed morphological characteristics of spectrograms in the frequency range of 0Hz-0.25Hz and characteristics of persistence of abnormal maximum value of envelope amplitude in the frequency range before the earthquake. The main conclusions are drawn as follows:
(1) Before the Alxa Left Banner M_{S}5.8 earthquake on April 15, 2015, seismic waveforms recorded by Wuhai, Shizuishan and Dongshengmiao seismic stations all showed obvious spectrum shift, and spectrum features of low-frequency signals can be in many forms.
(2) The maximum values of amplitude envelope lines for the three stations show completely different forms of change with epicentral distances from far to near. Among them, Shizuishan seismic station shows continuous sudden jumps, which may reflect that underground rocks rupture first, but this fracture cannot result in stress accumulation. On the contrary, this stress will affect stress accumulation in underground rocks in the region where Wuhai seismic station lies, and it began to produce micro-cracks on April 10, 2015, therefore, the tracking results of the maximum value of envelope amplitude began to show fluctuations of curve since the April 10, but not intermittent sudden jumps as recorded at Shizuishan seismic station. However, in the north of the epicenter, Dongshengmiao seismic station, which is the furthest from the epicenter among the three stations, basically kept changing at level of background fluctuations during the study period, which may be due to the fact that there are large asperity bodies in the underground of Wuhai seismic station which has blocked and accumulated stress, showing that there is basically no abnormal change in the tracking curve of the maximum value of envelope amplitude for low-frequency signals recorded at Dongshengmiao station.
(3) The intermittent and continuous appearance of abnormal signals may be the early manifestation of seismic micro-fracture and meta-stable stage, or the process of fracture and damage of regional underground rocks and crack nucleation. Different patterns this index presented at Shizuishan, Wuhai and Dongshengmiao seismic stations may be used to judge the location of epicenter of a moderate-strong earthquake if seismic stations are dense enough (at least 50km), but the implementation and outcomes of the results are required.
In a word, low-frequency signals contain abundant abnormal information of underground medium, and analysis results of abnormal low-frequency signals being able to achieve real-time status with data acquisition will be significant for further research.
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