Earthquake Research in China
Volume 24，Number 3，2010
Tectonic Stress Wave，Microfracture Wave，and a Modified
Elastic-Rebound Model of
Earthquakes1
Zhao Fuyuan
National Astronomical Observatories，Chinese Academy of Sciences，Beijing 100012 ，China
Based on a sample of some real earthquakes，we have suggested in previous papers that
there is a density-tectonic stress wave with ultra-low frequency which is emitted from the
epicenter region for months before earthquakes，and a micro-fracture wave 1 ～ 10 days
before earthquakes. The former has been observed by different kinds of measurements and
the latter has been observed by a few chance observations which consists of
electromagnetic，gravitational and sonic fluctuations. We show real observational results
that depict the two waves and they have very different frequencies，which are not difficult
to discriminate.
The classical elastic-rebound model is one of the most influential theories on
earthquakes，and the thermodynamic elastic-rebound model has amended the classical
framework. Considering the two waves above，we attempt to further modify the elasticrebound model， and the new framework could be called the “micro-fracture elasticrebound model”. We infer that tectonic earthquakes could have three special phases： the
accumulation of tectonic stress，micro-fracture，and main-fracture. Accordingly，there
would be three waves which come from the epicenter of a tectonic earthquake，i. e. ，the
tectonic stress wave with ultra-low frequency a few months before the earthquake，the
micro-fracture wave about 1 ～ 10 days before the earthquake and the main-fracture wave
（ common earthquake wave） .
Key words： Earthquake； Density-tectonic stress wave with ultra-low frequency； Fracture
mechanics； Rock fracture； Micro-fracture； Micro-fracture wave； Elasticrebound
INTRODUCTION
Earthquake waves occurring with the main fracture have been well formulated and studied.
1
Received on March 30，2010； and revised on May 11，2010.
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Earthquake Research in China
We have proposed that there are two special waves before the main fracture of a tectonic
earthquake； the density-tectonic stress waves with ultra-low frequency （ or tectonic stress waves，
for simplicity ） coming from the epicenter region for a few months before earthquakes and the
micro-fracture waves just less than 10 days before the earthquakes （ Zhao Fuyuan，et al. ，2007；
Zhao Fuyuan，2008； Zhao Fuyuan and Zhang Guodong，2009 ） . The basis of our proposition
until now does not have any mathematical deduction，but rather is only based on observational
results.
China suffers frequent earthquake occurrence. In the meantime， more real samples of
earthquakes，which serve as case studies， have been acquired. In recent decades， many
observations of earthquakes using different approaches have been carried out. By checking the
results from different approaches，we deem that there are above two special kinds of waves，and
based on this persuasion，we further modify the classical elastic-rebound model to the “microfracture elastic-rebound model”
1
AN ACCIDENTAL FINDING WITH ASTROMETRIC OBSERVATIONS
With the 1976 Tangshan earthquake of M S 7. 8，astronomers，in cooperation with the Beijing
Astronomical Observatory found that evident astrometric residual anomalies in universal time and
latitude were present in the data observed by a classical prismatic astrolabe，for about 1 month
prior to the earthquake. Such large anomalies had never occurred since the instrument began
operation in about 15 years. Fig. 1 shows the astrometric residual anomalies （ Li Zhisen，et al. ，
1978） .
Fig. 1
Astrometric residual anomalies in the latitude
measurement of the Beijing Astronomical Observatory before
the Tangshan earthquake，1976
A group of astronomers were interested in whether the residual anomalies had a physical
connection to the subsequent earthquake. They noticed that in the classical prismatic astrolabe in
the light path there is a mercury dish which works as a mirror to reflect starlight into the detector.
Moreover，the positions of most stars are rather stable （ the proper motion of most stars in a year is
less than 0. 1″） ，which can be regarded as stable coordinates with respect to the Earth. The
tectonic earthquake disturbances of density-tectonic stress in the stratum may cause the local
plumb line to slightly deviate relative to the normal case，and this could be exhibited as the
surface of a mercury dish being tilted. Consequently residual anomalies would be present in the
observed data. Therefore， the group preferred to conclude that the correlation between the
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residual anomalies and the subsequent earthquake can basically be identified. Fig. 2 shows the
mercury dish in the light path of a classical prismatic astrolabe.
Fig. 2
A mercury dish which works as a mirror in the
light path of a classical prismatic astrolabe
Later，with astrometric instruments of the same sort and with data acquired by the Purple
Mountain Observatory， Yunnan Observatory and Shanghai Observatory in China， residual
anomalies were also found before some earthquakes，although the confidence level is not 100%
（ the epicenters are 300km ～ 500km away from the observatories in most cases） . Fig. 3 shows a
sample of astrometric residual anomalies with the data from Yunnan Astronomical Observatory
before the two Luquan earthquakes in Yunnan Province in 1984 and 1985 （ Han Yanben，et al. ，
1986） .
Fig. 3
Astrometric residual anomalies in the data of
Yunnan Astronomical Observatory before the two Luquan earthquakes
in Yunnan Province in 1984 and 1985
It is noticeable that all the anomalies are within a period of months relative to the time when
the earthquakes occurred，and the earthquakes always take place when the observed anomalies
appeared to be weakening or fading.
2
SAMPLES FROM OTHER APPROACHES
To further verify the correlation between the astrometric residual anomalies and the
subsequent earthquakes，we check the data obtained by several different measurements in the
literature. With criteria that anomalies are believed to be related to disturbances of densitytectonic stress in the stratum，that anomalies are within a period of months，and the subsequent
earthquakes are believed to have taken place at the time when the anomalies appeared to be
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Fig. 4
Anomalies measured from different approaches. They are believed to be
related to disturbances of density-tectonic stress in the stratum over period of
months，and the subsequent earthquakes took place when the anomalies appear
to be weakening or fading
weakening or fading. We have found quite a few samples of anomalies from different measurements.
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These measurements include： the content ratios of radon，helium，mercury，fluorine ions and
carbon dioxide in ground water，the total content ratio of gas in ground water，the ratio of nitrogen
and helium in ground water，the conductivity of ground water，the content of radon in soil，the
stress and strain of an experimental bore，the ground deformation and micro-deformation，the
Earth's tide and non-Earth tide，the ground's apparent resistivity，the amplitude ratio of seismic
waves，and thermal anomalies. Fig. 4 shows data curves from different measurements which
coincide well with the above criteria （ Zhao Fuyuan，2008） .
Based on the sample above，we suggest that the density-tectonic stress wave with ultra-low
frequency could occur before earthquakes （ Zhao Fuyuan，et al. ，2007； Zhao Fuyuan，2008 ） .
The wave has the following characteristics： （ a ） single-peaked， （ b ） occurring before the
subsequent earthquakes for months，and （ c ） the subsequent earthquakes took place when the
wave peak appeared to be weakening or fading.
3
THE MICRO-FRACTURE WAVE
For the Wenchuan earthquake of May 12， 2008， some authors reported gravitational
disturbances with periods of 4 ～ 8 seconds in 48 hours before the earthquake. The instrument used
was a gravimeter （ Lacoste ET － 20） and the station was at a distance of more than 1000km from
the epicenter. Fig. 5 shows the curve. In the same letter，the authors also reported that before the
earthquake in the South of Kermadec Island，on May 25，1997，a gravimeter （ Lacoste ET － 21）
installed at Zhongshan Station，Antarctica，received similar gravitational disturbances 41 hours
before the earthquake （ Hao Xiaoguang，et al. ，2008） .
Fig. 5
Gravitational disturbances before the Wenchuan earthquake，May 12，2008
Another group of researchers reported that before the earthquakes in the Taiwan region and
Philippines in July，1990，an instrument in Guangzhou recorded non-tide gravity disturbances
about 72 hours before the earthquakes，as shown in Fig. 6 （ Feng Xiao and Ding Liqing，1993） .
We also notice that some authors have shown laboratory results of radiation，with materials
made of marble breaking. It was found that the radiation consisted of electromagnetic and
supersonic waves. Also， it has been reported that some radio signals were received by
astronomical radio telescopes and were regarded as a precursor of major earthquakes，5 days
before the earthquakes （ Nitsan，1977； Warwick，et al. ，1982； Brady and Rowell，1986； Cress，
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340
Fig. 6
Gravitational disturbances before the earthquakes in the
Taiwan region and Philippines in July，1990
et al. ，1987） . On the other hand，according to fracture mechanics，any major fracture must be
accompanied by a previous enlargement of micro-slits in the medium，i. e. ，a process of microfracture，in which the potential energies inside the materials are emitted.
Summarizing the above，we suggest that there must be micro-fracture waves taking place
before the main-fracture of a tectonic earthquake，and the observational results seem to give
evidence that the micro-fracture waves could be detected several days，i. e. ，1 ～ 10 days prior to
major earthquakes，as in the above cases （ Zhao Fuyuan and Zhang Guodong，2009） .
4
THE MODIFIED ELASTIC-REBOUNDING MODEL
H. Reid proposed the elastic-rebound model in 1911，which is one of the most influential
theories on earthquakes （ Fig. 7） . The thermodynamic elastic-rebound model modified the
classical one with a phase of time delay，which is between the peak of accumulated tectonic stress
and the advent of the subsequent earthquake. In terms of thermodynamic theory， when the
tectonic stress accumulates to its maximum，earthquakes do not occur right away but rather are
delayed for a short period， giving time for the system to pass through a potential barrier.
However，because the entropy of the system must reach maximum，the earthquake has to take
place to reach a new balance for the system （ Rundle，1988，1989 ） （ Fig. 8 ） . This case is
coincidental with the observational results which we cited above，that the earthquakes always
occur in the phase such that the anomalies have passed their peak values.
Considering both the tectonic stress wave and the micro-fracture wave we have suggested，we
made a connection between the two and the elastic-rebound model，so as to further modify the
model.
According to physics，any disturbance in a medium will cause a wave in the medium，no
matter if the disturbance is fast or slow. Using the phase“Slip ＆ Dislocation”in the models （ as
shown in Fig. 7，Fig. 8，and Fig. 9 ） ，the tectonic stress is accumulating，so that the observed
density-tectonic stress wave with ultra-low frequency could occur during this phase.
In addition to the observed micro-fracture wave，we add a micro-fracture phase before the
main-fracture phase to the thermodynamic elastic-rebound model，which forms the“micro-fracture
model”（ Fig. 9 ） . In the micro-fracture phase，radiation of electric-magnetic，gravitational and
sonic forms，i. e. ，the micro-fracture wave，could be emitted.
Fig. 7，Fig. 8，and Fig. 9 show the three elastic-rebound models： classical，thermodynamic
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Fig. 7
Classical elastic-rebound model
Fig. 8
Thermodynamic elastic-rebound model. A phase of
“slip weakened or faded”is added to the classical model
and micro-fracture respectively.
In particular in Fig. 9，we draw the further modified elastic-rebound model with the two preearthquake waves connected with the relative model phases.
5
SUMMARY
We suggest that in addition to the common earthquake wave （ the main-fracture wave） ，there
are two special waves which propagate from the epicenter before a tectonic earthquake，i. e. ，the
density-tectonic stress wave with ultra-low frequency coming into being a few months before the
earthquake，and the micro-fracture gravitation，electromagnetism and sonic waves，about 1 ～ 10
days before the earthquake. We relate the two waves with different phases to the model we further
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Fig. 9
Micro-fracture elastic-rebound model. A “micro-fracture”phase is added to the
thermodynamic elastic-rebound model. The two pre-earthquake
waves are drawn to connect with the relative phases.
modified and call it the micro-fracture elastic-rebound model. Evidently，the two waves can be
regarded as important earthquake precursors.
REFERENCES
Brady B. T. ，Rowell G. A. Laboratory investigation of the electrodynamics of rock fracture［J］. Nature，1986，
321：488 ～ 492.
Cress G. O. ，Brady B. T. ，Rowell G. A. Sources of electromagnetic radiation from fracture of rock samples in the
laboratory［J］. Geophysical Research Letters，1987，14：331 ～ 334.
Feng Xiao and Ding Liqing. Features of gravity variations before strong earthquakes［J］. Earthquake，1993，（2） ：
40 ～ 46.
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earthquakes［J ］. Recent Development in World Seismology，2007，12： 26 ～ 32 （ in Chinese with English
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About the Author
Zhao Fuyuan， born in 1949， graduated from Physics Department， Nankai University，
Tianjin， China， in 1975， and was a visiting scholar in the Landssternwarte， Heidelberg，
Germany，in 1989 ～ 1990. He is now working in the National Astronomical Observatories，
Chinese Academy of Sciences. Research interests include： Correlation between several
astronomical approaches and earthquakes. E-mail： fyzhao@ bao. ac. cn