In the observations of the earth tide,we often find out some anomalous microseisms in the tidal signals^[1]. Compare with earth tide,the anomalous microseism is a high-frequency signal,with periods from a few seconds to a day. It has durations up to several hours or even days,longer than seismic waves. These microseisms can be attributed to slow earthquakes,slow slip,non-volcanic tremors,episodic tremors,low-frequency earthquakes and the tropic cyclone^{[2, 3, 4, 5, 6, 7, 8, 9, 10, 11]}. Because some major earthquakes are accompanied by anomalous microseisms,they are regarded as the "precursor wave","silent earthquake","long period events" and "related microseisms"^{[12, 13, 14]}. The cause of these "microseisms" is complex,and their mechanism remains unclear. And these signals are weak; of which the envelopes mostly look like a spindle or tail^[1]. Currently,they have different definitions and name. They can be viewed as a kind of noise or anomalies relative to tidal and seismic observations,so we called it anomalous tremor waves^{[15, 16]}.

Earthquake precursors refer to anomalies appear before an earthquake,which should be physically related with the occurrence of the earthquake. It means the anomaly,the physics and the time the anomaly appearance are objective criteria for determination of the earthquake precursors; they are indispensable. Among them physics is the most important,and also the most difficult to know.

In a seismic monitoring network,gravimeters,tiltmeters and extensometers are similar to seismometers in observations with the same physical essence as well as overlapped frequency bands of signals. With these instruments,we can observe all information of ground motion from seismic waves to the earth tides in theory. If anomalous tremor waves indeed exist,which should be recorded by all the instruments in a same station; and the observations would support and repeat each other. To this end,since 2004,the Seismic and Tidal Station of Huazhong Unversity of Science and Technology (HUST) recorded the signals of frequency bands from seismic waves to tidal ones with the DZW gravimeter,VS-1 tiltmeter,and JCZ-1 broadband seismometer,providing data for experiments and studies.

The most typical and intuitive examples for the anomalous tremor waves before strong earthquake are as follows. Kizawa (1972) reported "precursor waves" before the M_s8.4 earthquake in Alaska of the US on March 28 in 1964 and the M_s7.5 earthquake in Niigata of Japan on June 16 in 1964 recorded by the GS-12 gravimeter in Meteorological Research Institute in Tokyo^[17]. Yang et al at the Xinjiang Seismological Network reported the slow earthquake events before M_s8.1 earthquake on November 14,2001 in the western Kunlun Mountains of China^[18]. After the Wenchuan M_s8.0 earthquake on May 12 in 2008,some researchers reported immediately that they had found the "gravity disturbance" occurred 2 days before the earthquake in Wenchuan,and speculated that it was a kind of short-term anomalies^{[19, 20]}. People discussed and paid much attention to anomalous tremor waves again^{[21, 22, 23]}. It is worth to notice that the "gravity disturbance" is a common observation recorded by broadband seismometers in China,but they are not found in other tidal stations of China. Why such a difference exists? What has been observed by HUST? Are anomalous tremor waves "incidental phenomena" or "frequent phenomena"? Can it be observed at other times besides the M_s8.0 earthquake in Wenchuan? What are the characteristics of the anomalous tremor waves caused by different reasons? What are the relation and difference between anomalous tremor waves and earthquake precursors? How can we use tidal station networks and broadband digital seismic networks to serve earthquake monitoring and prediction? To answer these questions is of importance to reveal the complexity,and for fundamental research,prediction,and precursor monitoring of earthquakes. It is likely even a very important and effective way to make the breakthrough of the earthquake prediction. In this paper we describe the anomalous tremor waves recorded b the DZW-1 gravimeter and VS-1 tiltmeter at the HUST station in recent years,and compare them with the records of the broadband digital seismometers and make analysis. We clarify the difference and cause of the "gravity disturbance" observed by the tidal station two days before the Wenchuan earthquake from several aspects of observation techniques and signal processing. Our purpose is to evaluate the anomalous tremor waves objectively and correctly; and to sum up and rethink the long-term observational data relevant to the Wenchuan earthquake and to explore the effective approach for precursor monitoring.

The HUST station is in a cave of the campus,equipped with a DZWgravimeter,a VS-1 tiltmeter (operated since July 2004) and a JCZ-1 broadband seismometer (worked since January 2006) on a 2 m×4 m bedrock platform. Besides,there are a SSY-II horizontal quartz extensometer,GK water tube clinometer and FP-1 folded pendulum tiltmeter in the cave. The general situation of the tidal observation is shown in Fig.1. We used the data acquisition card produced by National Instruments (NI) to record the signals; developed a 16-channels system for data acquisition,display and storage on the LabVIEW software platform^[24]. Each channel has a sampling rate up to 5 Hz (in practice we recorded the data in minute in order to compare with the tidal observation in the seismic monitoring station of China). We used the CMG-DM24 G¨uralp acquisition system produced by the G¨uralp Company of UK to collect data,and used the SCREAM 4.1 software to observe,monitor and save the data,with sampling rates 200 Hz and 50 Hz.

(Fig.1)

Fig.1 Flowchart of tidal observation at HUST station

In codes of earthquake monitoring,the gravimeter and tiltmeter are employed observe tidal signals and as the criteria to evaluate the quality of the seismic observation station. Therefore,in the instrument,2 secondorder low-pass filters are used to deal with signals at the output of the instrument. In order to get more seismic information,we expanded the output port of the DZW gravimeter and VS-1 tiltmeter with the help of the instrument developer. At the same time we got 2 groups of the output signals,one of them is the signal after the first low-pass filter (LP1) whose cut-off frequency is higher,which contains tidal signals and much “high frequency” information; and the other signal passed 2 low-pass filters (LP2) with a lower cut-off frequency,which outputs the same signals as those recorded by same types of observation instruments,clear,smooth and steady tidal signals almost without "high frequency" information. The tidal curves observed in August in 2005 with the DZW gravimeter and VS-1 tiltmeter at the HUST station are shown in Fig.2.

(Fig.2)

Fig.2 Tidal observation curves by DZW gravimeter and VS-1 tiltmeter at HUST station (Aug. 1-31,2005) (a) DZW(LP1); (b) VS-1 EW(LP1); (c) VS-1 NS(LP1); (d) DZW(LP2); (e) VS-1 EW(LP2); (f) VS-1 NS(LP2).

Figure2 shows that the output signals from channel LP2 of DZW gravimeter and VS-1 tiltmeter are mainly tidal signals (Fig.2(d-f)),because the high frequency signal has been filtered; which is the same as other instruments of the same type. Both tidal signals and anomalous tremor waves are present in the channel LP1 (Fig.2(a-c)). The high frequency signals including anomalous tremor waves observed by DZW gravimeter and VS-1 tiltmeter are all from channel LP1. In addition,the response the 2 channel to the tide are largely consistent,while that to seismic waves are obviously different.

In fact,since the observation at the station began,DZW gravimeter and VS-1 tiltmeter have recorded some "spindle-like" anomalous tremor waves of consistent form by the output from channel LP1,which is common and frequent^[1]. They have the same duration and morphology with the observation of broadband seismometer and can verify each other. Without any mathematical treatment,we could find anomalous tremor waves in the curve of tidal observation. Most of the signal is very weak,with duration about 1 to 3 days,much longer than the duration of seismic waves. The study shows that some of the anomalous tremor waves were caused by tropical cyclones^[11],while the rest of them were often followed by major earthquakes. Fig.3 shows the observation records by the channel LP1 of DZW gravimeter and VS-1 tiltmeter of HUST station,after a high-pass filter,before the M_s8.9 earthquake in northwest coast of Sumatra in Indonesia on December 26,2004,M_s7.2 earthquake in the South China Sea on December 26,2006,M_s7.3 earthquake in Haiti on January 13,2010 and M_s8.8 earthquake in Chile on February 27,2010. The parameters of the digital high-pass filters are the same^[25],i.e. the same window function type Hamming-1 with length 121 minutes and cut-off period 30 minutes. The results reflect that the tidal instruments have response to the high-frequency anomalous tremor waves and seismic waves. Clearly,not only the tropical cyclones can cause anomalous tremor waves,but also the tremor waves can be found before strong earthquakes. It is a usual phenomenon observed by channel LP1,but rarely found from channel LP2 or from tidal instrument of the other seismic stations.

(Fig.3)

Fig.3 Anomalous tremor waves recorded by DZW gravimeter and VS-1 tiltmeter before strong earthquakes (a),(e) and (i) are the records of DZW,VS-1 EW and VS-1 NS (Dec. 1-31,2004). (b),(f) and (j) are the records of DZW,VS-1 EW and VS-1 NS (Dec. 1-31,2006). (c),(g) and (k) are the records of DZW,VS-1 EW and VS-1 NS (Jan. 1-31,2010). (d),(h) and (l) are the records of DZW,VS-1 EW and VS-1 NS (Feb. 1-28,2010).

Figure4 shows the tidal observation after high-pass filtering (the parameter of the filter for data processing is same as in Fig.3) from the channel LP1 of DZWgravimeter and VS-1 tiltmeter at HUST station,from January 1,2008 to May 31,2008.

(Fig.4)

Fig.4 Anomalous tremor waves recorded at HUST station (Jan.1-May.31,2008) (a) DZW (LP1); (b) VS-1 EW (LP1); (c) VS-1 NS (LP1).

From January 2008 to March 2008,there were more than 10 cases of anomalous tremor waves with duration about 1~3 days observed by DZW gravimeter and VS-1 tiltmeter at the HUST station. During this period five events of M_s7.0 or greater strong occurred in the world: M_s7.3 earthquake in Mid-Atlantic Ridge on February 8,2008,M_s7.7,M_s7.6,and M_s7.0 earthquakes in Sumatra in Indonesia on February 20,February 25,February 26,2008,respectively; and M_s7.3 earthquake in Yutian,Xinjiang on March 21,2008. While there was no typhoon in the western Pacific and northern Indian Ocean,only the Western Pacific had a tropical storm (01W,January 13,2008-January 16,2008) (Note: the information related to the typhoon is from http://weather.unisys.com/usgs/ and http://www.typhoon.gov.cn/). From April 1,2008 to May 12,2008,before the Wenchuan earthquake,3 cases of obvious anomalous tremor waves were recorded roughly from April 7 to April 13,from April 17 to April 24,and from May 9 to May 12,respectively. And the magnitude of the anomalous tremor waves in April was larger than that appeared 3 days before the Wenchuan earthquake. During this period,besides the M_s8.0 earthquake in Wenchuan on May 12,2008,there were 4 strong earthquakes over M_s7.0: M_s7.3 in Loyalty Islands on April 9,2008,M_s7.1 earthquake in Macquarie Islands Region on April 12,2008,M_s7.1 earthquake in Andrea Ivanov Islands on May 2,2008 and M_s7.0 earthquake in Honshu,Japan on May 8,2008. In this period,there were 2 tyhpoons in the Western Pacific (Neoguri from April 14 to 19 in 2008,Rammasun from May 5 to 12 in 2008),which were the No.1 and No.2 typhoons in the Western Pacific in 2008. The No.1 typhoon (NARGIS ) from April 27,2008 to May 3,2008 occurred in North Indian Ocean.

TREMOR WAVES As mentioned above,anomalous tremor waves are commonly viewed from channel LP1 of the tidal observations at the HUST station,but extremely rare in the channel LP2. Fig.5 shows the original curves of the observation in April in 2008 by DZW gravimeter and VS-1 tiltmeter in HUST station. Obviously,the anomalous tremor waves respectively occurred from April 7,2008 to April 13,2008,called Tremor 1,and from April 17,2008 to April 24,2008,called Tremor 2. During the occurrence of Tremor 1 there were 2 M_s7 earthquakes; and Typhoon "Neoguri" accompanied with Tremor 2 without earthquakes. These anomalous tremor waves are very consistent by the time with the observation of JCZ-1 broadband seismometer; they verify each other,should be caused by the same physical source.

(Fig.5)

Fig.5 Tidal observation curves by DZW gravimeter and VS-1 tiltmeter at HUST station (Apr. 1-30,2008) (a) DZW(LP1); (b) VS-1 EW(LP1); (c) VS-1 NS(LP1); (d) DZW(LP2); (e) VS-1 EW(LP2); (f) VS-1 NS(LP2).

In order to compare and analyze the responses of the tidal instruments to the signals of tidal waves,anomalous tremor waves and seismic waves,we made the spectral analysis to the observations of the channel LP1 and LP2 of the DZW gravimeter and VS-1 tiltmeter. Fig.6 shows the FFT mean-square spectrum of the original minute samples in April of 2008.

(Fig.6)

Fig.6 Frequency spectra of tidal observations at HUST station (Apr.1-30,2008) (a) DZW(LP1); (b) VS-1 EW(LP1); (c) VS-1 NS(LP1); (d) DZW(LP2); (e) VS-1 EW(LP2); (f) VS-1 NS(LP2).

Obviously,the responses of the channel LP1 and LP2 of DZW gravimeter and VS-1 tiltmeter to the low frequency signals such as tidal signals are consistent,with high SNR; but to the high-frequency anomalous tremor waves and seismic waves,the responses are significantly different. The response of the signals from channel LP1 to the high frequency signals is basically flat and uniform; the response of the signals from the channel LP2 to the high frequency signals is attenuated when the frequency of the signals becomes high. This difference is because of the different processing methods for the signals and the filter circuits of the instruments. Fig.7 shows the spectrum characteristics of the background noise signal,Tremor 1 and Tremor 2 signals observed by the HUST station. It is clear that the frequency spectrum components of Tremor 1 and Tremor 2 are different from the background noise; the components of Tremor 1 are mainly 3~7 s,10~20 s and 40~60 s,but the components of Tremor 2 are only 3~7 as main frequencies. The difference of frequency spectrum characteristics may reflect the difference of anomalous tremor waves before strong earthquakes and caused by tropical cyclones,and it would be useful to determination of the tremor source and seismic studies.

(Fig.7)

Fig.7 Frequency spectra of noise signal and anomalous tremor waves (a) Spectrum of noise signal; (b) Spectrum of tremor 1; (c) Spectrum of tremor 2.

A large number of observations show that among those tidal stations,only the DZW gravimeter and VS-1 tiltmeter at the HUST station can record anomalous tremor waves. In order to reveal the cause of the difference,we studied the transfer functions and characteristics of the two instruments^[26]. In fact,the transfer function of the tidal instruments can be expressed as the product of the transfer function of the mechanical parts and circuit parts. The mechanical parts of the 2 instruments are a flexible pendulum system,so in theory they can be simplified as a second-order system. They have the same resonance period and damping,so the transfer functions of the mechanical parts are the same. While the two instruments use the same kind of circuits,so the transfer functions of the circuit parts are the same,too. Suppose the transfer functions of the mechanical parts,LP1 and LP2 of DZW gravimeter and VS-1 tiltmeter are T_LP0(ω),T_LP1(ω) and T_LP2(ω),respectively,their mathematical expressions are

where T₁₁=120; T₁₂=100; T₁=1000; T₂₁=1.2; T₂₂=0.16,T₂=0.16. T₀ = 104 V·m^-1·s² is the static sensitivity of the pendulum,and the exact value can be got by the calibration and testing to the instrument. T₀₁ = 4πζ/T₀=3.4976; T ₀² = 4π²/T ₀² =109.6623. ~ and T₀ are the damping and resonance cycle,respectively. Fig.8 shows that the amplitude-frequency and phase-frequency characteristic curves.

(Fig.8)

Fig.8 Amplitude (a) and phase (b) features of DZW gravimeter and VS-1 tiltmeter

From the expression (1),the damping and the resonance cycle of the mechanical parts are 0.167 and 0.6 s,respectively; and the damping is weak. Therefore,the tidal instrument can also observe tidal signals and anomalous tremor waves whose frequency is high. And from the expression (2) and (3),the channels LP1 and LP2 of the DZW gravimeter and VS-1 tiltmeter are 2 low-pass filters,of which the cut-off periods are 7.5 s and 42.0 s,respectively; so they have different output characteristics. Thus,the high-frequency signals such as anomalous tremor waves are filtered out in LP2,and only output in LP1. This is why the high-frequency signals can be observed by channel LP1 of the two instruments,but there are only tidal signals found in LP2.

It should be specifically mentioned that the same as most seismic stations,the data of the tidal signals are only stored per minute. Although we got lots of high-frequency signals such as anomalous tremor waves which confirm the observation of the broadband seismometer,the characteristics are conflicting with the real ground motion,significant distorted. They cannot reflect the true ground motion,so these signals are the "aliasing" or mapping to the real phenomenon of the tidal observation. To obtain the real frequency domain characteristics of the ground motion,one of the simplest methods is to increase the sampling rate of the channel LP1. However,even the channel LP1 sampling rate is enhanced,because the damping is very weak and the phase-frequency characteristics of the instruments is nonlinear,the high-frequency signals of the output are difficult to reflect the real ground motion,and the instruments is not of broad band. If we want to apply the tidal instruments such as DZW gravimeter and VS-1 tiltmeter to monitor and research broadband seismic signals,we can get the best performance characteristics while the damping ~ is about 0.6~0.8,at this time the pass-band period can be from 2.5 times of resonance frequency to zero. Therefore,to lower the resonance cycle and appropriate damping is the key of broadband tidal observation instruments.

From the seismic observation point of view,anomalous tremor waves are microseisms with complex sources; most envelopes of them are "spindle" or "tail-like",and the signals can last for 1~3 days,which can be observed by widely distributed tidal instruments and broadband digital seismic instruments. Most of the tidal stations in China cannot observe anomalous tremor waves,because the observation objectives and criteria quality of observation are tide; thus using different transfer function and output characteristics of the instruments,and filter out high frequency microseisms signals and noise,in order to ensure long period tide signals sensitive and precise,and obtain smooth and stable solid tidal curves. This paper shows that excluding the anomalous tremor waves caused by tropical cyclones (typhoons),there are many "anomalies" accompanying with strong earthquakes,which are corresponding highly. Because the signal periods of the anomalous tremor waves caused by Western Pacific tropical cyclones are mainly about 3~7 s,and the periods of the anomalous tremor waves before strong earthquakes are not only 3~7 s but also 10~60 s or even longer. These phenomena and differences may reflect the characteristics and properties of the anomalous tremor waves with different causes,which can help us to understand the processes and precursors of the earthquakes further. Therefore,it is very necessary and urgent to conduct comprehensive observations and research of the anomalous tremor waves with the broadband digital seismic instruments and tidal equipment (gravimeter,tiltmeter,etc.) in the Chinese Seismological Network.

The nature of the tidal observation and the broadband seismic observation are the same,and we can get information from the seismic waves to the earth tides; they are connected and extended in the frequency domain,and the important to seismic observations. Their crosses,penetration,complement and integration will be useful to the seismic research and observation,which will promote the study of earthquake. Therefore,we must know the transfer function of the tidal instruments. It can broaden our horizon to help us to distinguish right from wrong,kick off the false thing and save the truth,and make new discoveries.

Earthquakes and their precursors are complex,and the observation and research of the anomalous tremor waves may enlighten,amend,enhance and improve our understanding to the seismic processes,and can explore and find something "ignored" in the past,but which maybe the core to understanding earthquakes and improving the level of earthquake prediction. It is significant to the development and the improvement of the seismic science.

This work was supported by the National Nature Science Foundation of China (41274058).