Earthquake Reaearch in China  2019, Vol. 33 Issue (1): 132-146     DOI: 10.19743/j.cnki.0891-4176.201901008
A Review of the Calculation Formula for the Four-component Borehole Strainmeter and Application to Earthquake Cases
SU Kaizhi     
Institute of Crustal Dynamics, China Earthquake Administration, Beijing 100085, China
Abstract: Based on the principle formula for the four-component strainmeters, we can directly obtain the specific plane strain, shear strain and azimuthal angle of the principal strain, and the maximum and minimum principal strains calculated afterwards are the indirect result. The problems of practicality of the sensitivity coefficients A and B of plane strain and shear strain are then discussed. Based on this idea, we analyzed the observation data of several four-component borehole strainmeters near the epicenter of the Yiliang MS5.7 earthquake in 2012 and the Ludian MS6.5 earthquake in 2014 in the Zhaotong area, Yunnan Province. The results show that the analysis based on the perspective of plane strain and shear strain has an obviously better effect than that based on the component readings, and can directly peel off the respective abnormality of the plane strain and shear strain. In addition, the correlation coefficient curves between measured data of two plane strains show significant anomalies which often occur several days before and during the earthquake.
Key words: Four-component borehole strainmeter     Ludian MS6.5 earthquake     Yiliang MS5.7 earthquake     Plane strain abnormality     Shear strain abnormality     Self-test of data     Strain anomaly    


Theoretically, there are three unknowns in plane strain measurement, which have to be solved by three independent measurements. The Institute of Crustal Dynamics, China Earthquake Administration introduced the measurement method of using a piezomagnetic borehole strainmeter from abroad in the 1960s under the guidance of Li Siguang. It was originally a three-component design (Hast N., 1958). The four-component borehole strainmeter was first proposed by the author at the National Geostress Conference of China in 1977 (Su Kaizhi, 1977). During the conference, the four-component piezomagnetic borehole strainmeter was displayed (which was manufactured by Zhang Peiyao in 1974, the archives of the Institute of Crustal Dynamics, No. 841.14). In the last 40 plus years, nearly 100 sets of four-component borehole strainmeters have been installed in the Chinese mainland (Qiu Zehua, 2017). Scholars abroad (Gladwin M.T., 1984; Ishii H. et al., 2017) also accepted the idea that four-component borehole strainmeters can perform data self-tests and adapted it into their own four-component structure, but they have not yet accepted China's most reasonable four-component equispaced pattern. There are important new earthquake cases in the four-component strainmeter research in China in recent years.

Strain observation is at a nodal point of development, so it is necessary to rethink the core issues and clarify some potentially vague ideas. For example, the component in a certain direction only reflects the strain information in this direction; the variation of the reading of the component is the linear strain of the rock in the direction; the solution for the three unknowns is limited to the measurements of three components and three equations, etc. which all have impact on the proper understanding and use of the data. This paper highlights the following two understandings.

(1) The present-day borehole strainmeter uses steel cylinders and cement downholes, adopting not the "empty hole method" but the "solid hole method" (Su Kaizhi, 1985). From the mechanical formula for the component, it can be seen that the solution given directly from the radial displacement value of the steel cylinder is the azimuth angle of the maximum principal strain and the plane strain and shear strain in the rock. Only when the four components are uniformly distributed, the solution is the most concise, and the calculation of the two strains (surface strain and shear strain) requires only one sensitivity coefficient, respectively. The source of systematic errors of the calculation results is relatively clear. Thereafter, if necessary, the maximum and minimum principal strains can be calculated by adding and subtracting, which are "reckoned regeneration results" and involve two sensitivity coefficients.

Therefore, both in the past and now, when using borehole strain relative observation data to carry out various analytical applications, such as analysis and description of various abnormal phenomena, calculation of various interference coefficients, specific means of evaluating data with strain tide records, and examination methods of coseismic strain step data, various components were mostly used as the first object for drawing and analysis, and the most appropriate way to do so is to take plane strain and shear strain as objects, as it is not appropriate to regard maximum and minimum principal strain as the primary, most direct and even the only object for analysis. This will bring new ideas and experience to our data analysis.

(2) The outstanding advantage of the four-component borehole strainmeter is that it can obtain two surface strain measurements, thus, by the self-test method, commonly known as the "1 plus 3 equals 2 plus 4 methods" (Su Kaizhi, 1977), the reliability of the data can be obtained. It is true that the correlation coefficient calculation can also be performed on the two surface strains, that is, the self-test calculation (referred to hereinafter as the "self-test factor"), and the calculation can be continuously performed in real time. The preliminary analysis of the two earthquake cases in this paper seems to imply that temporary changes of the self-test factor curve may also appear that are not from instrument failures, but may contain new information—circumstantial evidence for potential moderate-strong earthquakes in nearby areas, thus, it will initiate a new research area and bring new interest to borehole strain observation.


The structure of the four-component borehole strainmeter is shown in Fig. 1(a) is the ideal installation orientation for each component, and Fig. 1(b) is the core of the SKZ-1 borehole strainmeter — a special steel cylinder made by precise wire cutting of stainless steel rods. Inside the cylinder, there are 8 precisely positioned thin ribs, and 4 identically sized components are mounted on 2 opposite ribs to ensure accurate angles and easy assembly. Each component has a carefully selected pair of tri-electrode capacitive displacement sensors.

Fig. 1 Structural diagram of the four-component borehole strainmeter (a) Ideal mounting orientation for the four components. (b) Parts of SKZ-1 borehole strainmeter—the special steel cylinder
2 ANALYSIS OF BASIC FORMULAE 2.1 Formula for Measuring the Change of Inner Diameter of Steel Cylinder

Components embedded between the ribs in the steel cylinder can directly sense the change of the inner diameter of the steel cylinder, where

$ U = 2u \times a \times k $ (1)

In the formula, U is the change of terminal readings of ground instruments in units of mV or number; u is the radial displacement of the inner wall of the steel cylinder in micron; a is the displacement sensitivity coefficient of the sensing element itself in units of mV/microns; k is the effective amplification factor of the electronic circuit. Now the manufacturer has begun to normalize the U value into a strain unit, that is, the ratio of displacement to the relative change of diameter in the cylinder.

It can be noted that there is only one displacement sensitivity coefficient for the sensing unit. But for the real hole strainmeter, the change of rock strain is perceived by the radial displacement of the inner diameter of the steel cylinder. At this time, two sensitivity coefficients are needed (Su Kaizhi, 1984, 1985). It is necessary to analyze the mechanical relationship of steel cylinders in rock holes.

The expression for deformation of each point inside and outside the borehole with interlayers was put forward by elastic mechanics as early as the beginning of the nineteenth century (Савин Я.H., 1958). It was introduced in China in the late 1970s. When the angle between components is 45°, the change U is

$ {U_{1}} = A\left({{\varepsilon _{\rm{I}}} + {\varepsilon _{{\rm{II}}}}} \right) + B\left({{\varepsilon _{\rm{I}}} - {\varepsilon _{{\rm{II}}}}} \right){\rm{cos}}2\left(\mathit{\Psi } \right) $ (2)
$ {U_{2}} = A\left({{\varepsilon _{\rm{I}}} + {\varepsilon _{{\rm{II}}}}} \right) + B\left({{\varepsilon _{\rm{I}}} - {\varepsilon _{{\rm{II}}}}} \right){\rm{cos}}2\left({\mathit{\Psi } + {\rm{ }}45^\circ } \right) $ (3)
${U_{3}} = A\left({{\varepsilon _{\rm{I}}} + {\varepsilon _{{\rm{II}}}}} \right) + B\left({{\varepsilon _{\rm{I}}} - {\varepsilon _{{\rm{II}}}}} \right){\rm{cos}}2\left({\mathit{\Psi } + {\rm{ }}90^\circ } \right) $ (4)
$ {{U_{4}} = A\left({{\varepsilon _{\rm{I}}} + {\varepsilon _{{\rm{II}}}}} \right) + B\left({{\varepsilon _{\rm{I}}} - {\varepsilon _{{\rm{II}}}}} \right){\rm{cos}}2\left({\mathit{\Psi } + {\rm{ }}135^\circ } \right)} $ (5)

Where U is the amount of change (or increment) of the component's measured value over time, Ψ is the maximum principal strain azimuth starting from the due north direction, the positive rotation is counterclockwise, ε and ε are the maximum and minimum principal strains of the rock.

It can be seen from the above basic formula that the solution has three levels (three orders) of answers (unknown numbers), and the first level is: A(ε + ε), B(ε - ε), and principal strain azimuth. It is noted that the coefficient A is always in close contact with surface strain (ε + ε), and the coefficient B is always in close contact with shear strain (ε - ε), so Su Kaizhi (1984) referred to the coefficient A as the surface strain sensitivity, and the coefficient B as the shear strain sensitivity coefficient. The specific values of A and B can be obtained by theoretical or experimental methods, and then the surface strain (ε + ε) and the shear strain(ε - ε) values can be obtained (isolated), which are the result of the second level. It is noted that the systematic error of the surface strain value depends only on the systematic error of the A value. The systematic error of the shear strain depends only on the systematic error of the B value. These two independent calculations do not interfere with each other. This paper emphasizes this strain representation. The calculation result of the third level is the maximum and minimum principal strain, that is, adding the values of (ε + ε) and (ε - ε) and then dividing the sum by 2, or subtracting them, then dividing by 2. However, it should be noted that whether it is ε or ε, the error of the calculation result is not only related to the A and B errors, but also related to the ratio of ε and ε (Su Kaizhi, 1984). Care should be taken when using the values of ε or ε.

Existing manufacturers are trying to adjust the parameters of the four-component in the same way, so the performance differences of the four components are not taken into account in this formula, that is, the sensitivity coefficients A and B have nothing to do with the serial number of the components (Han Baoxiang et al., 2007). In fact, if the performance of components is different, especially when the ratio of B/A between components is different, it will bring about difficulty for users to make various calibration adjustments.

Through trigonometric function transformation, the working expressions of the components become very concise2.

$ {U_{1}} = A\left({{\varepsilon _{\rm{I}}} + {\varepsilon _{{\rm{II}}}}} \right) + B\left({{\varepsilon _{\rm{I}}} - {\varepsilon _{{\rm{II}}}}} \right){\rm{cos}}2\mathit{\Psi } $ (6)
$ {U_{2}} = A\left({{\varepsilon _{\rm{I}}} + {\varepsilon _{{\rm{II}}}}} \right) - B\left({{\varepsilon _{\rm{I}}} - {\varepsilon _{{\rm{II}}}}} \right){\rm{sin}}2\mathit{\Psi } $ (7)
$ {U_{3}} = A\left({{\varepsilon _{\rm{I}}} + {\varepsilon _{{\rm{II}}}}} \right) - B\left({{\varepsilon _{\rm{I}}} - {\varepsilon _{{\rm{II}}}}} \right){\rm{cos}}2\mathit{\Psi } $ (8)
${U_{4}} = A\left({{\varepsilon _{\rm{I}}} + {\varepsilon _{{\rm{II}}}}} \right) + B\left({{\varepsilon _{\rm{I}}} - {\varepsilon _{{\rm{II}}}}} \right){\rm{sin}}2\mathit{\Psi } $ (9)

2 Strictly speaking, the surface strain should be 1/2 (ε + ε), and the maximum shear strain is 1/2 (ε - ε). However, in the field of ground strain observation, for the sake of convenient description, 1/2 is often conventionally omitted.

2.2 Formula for Solving Unknown Quantity

Formula (6)-(9) are the concise formulae. From this, we can realize that the core characteristics of the data processing of four-component straimeters are: the components are divided into odd number and even number groups, the surface strain can be obtained by adding the data in the group, and the shear strain and the principal azimuth can be obtained by subtracting the data in the group. That is to say, the formula is essentially an addition/subtraction formula. For surface strain, there are:

$ {\left({{\varepsilon _{\rm{I}}} + {\varepsilon _{{\rm{II}}}}} \right)_{1}} = ({U_{1}} + {U_3})/2A $ (10)
${\left({{\varepsilon _{\rm{I}}} + {\varepsilon _{{\rm{II}}}}} \right)_{2}} = ({U_{2}} + {U_4})/2A $ (11)

It can be seen that only the sensitivity coefficient A is needed to obtain the surface strain, and the systematic error of A directly and solely determines the systematic error of the surface strain. The two surface strains given by formula (10) and formula (11) should be equal, thus, the important relationship, the "elementary formula for the four components" (Su Kaizhi, 1977)3 is obtained as:

3 It is only when the components are evenly distributed that the test formula is so simple. Gladwin (1984) changed the three-component to four-component in the end of the 20th century. He just inserted the fourth component in the original three-component pattern, perpendicular to the original one. In this case, the data self-checking formula is complex, and the weights of the four components are not uniform. The formulas for calculating shear strain and azimuth angle are also complicated and not practical enough.

$ {U_{1}} + {U_3} = {U_{2}} + {U_4} $ (12)

Formula (12) has important applications in many occasions, such as instrument quality evaluation, periodic data inspection, component displacement sensitivity fine-tuning (calibration), etc. To evaluate the consistency of the two data series, the current popular method is to calculate the correlation coefficients (Qiu Zehua, 2017). Most of the correlation coefficient curves are a straight line with a slight fluctuation, approximating to 1, and there are slightly larger fluctuations (like the law of noise) occurring occasionally, but both cases are normal. The correlation coefficient is not the only way to prove it. For example, when (U1 + U3) and (U2 + U4) curves drift slowly and diverge, the correlation coefficient will lag in response (as shown in Fig. 3 and Fig. 5), then, residual curve can be used to supplement it if necessary.

Fig. 3 Yunnan Yiliang MS5.7 earthquake (a) Yiliang seismic station; (b) Daguan seismic station; (c) Yudong seismic station

Fig. 5 The Ludian MS6.5 earthquake in Yunnan (a) Ludian seismic station; (b) Yudong seismic station; (c) Daguan seismic station; (d) Yiliang seismic station

The calculation of shear strain requires only the shear strain sensitivity coefficient B, i.e.

$ {\varepsilon _{\rm{I}}} - {\varepsilon _{{\rm{II}}}} = \frac{{\sqrt {{{({U_1} - {U_3})}^2} - {{({U_2} - {U_4})}^2}} }}{{2B}} $ (13)

The essence of formula (13) is the Pythagorean String Law. (U1 - U3) and (U2 - U4) are equivalent to the hook and the maximum shear strain is 1/2 of the chord length (when B=1).

At present, many people are willing to use "two differential strain" curves, namely (U1 - U3) and (U2 - U4) curves, instead of drawing and analyzing the maximum shear strain (ε - ε). This is a practical method. It is also possible to know whether the shear strain and azimuth angle change by visual check to the two curves.

In the calculation of the azimuth angle of the maximum principal strain, the borehole instrument without the shear strain sensitivity coefficient B has been improved to four components since the 21st century, which is called "two-group and two-component". The four components are divided into two groups, and the angle of the components in the group is 90°, so the cross-checking relationship is established. But the angle between the two groups of components deviates from 45° by 5°. When calculating the shear strain and azimuth angle, the more complex formulas than formula (13) and formula (14) have to be used4.

$ \psi = \frac{1}{2}{\rm{arctg}}(\frac{{{U_4} - {U_2}}}{{{U_1} - {U_3}}}) $ (14)

4 Since the beginning of the 21st century, Ishii Hiroshi's drillhole strain instrument has been improved from three components to four components, which is called "two-group and two-component". Four components are divided into two groups, and the angle of the components in the group is 90°. The cross-checking relationship is established. But the angle between the two groups of components deviates from 45° by 5°. When calculating the shear strain and azimuth angle, the more complex formulas that formula (13) and formula (14) have to be used.

2.3 Formula Initiated Discussions

Starting from formula (6) - formula (9), the following discussion can be initiated.

(1) Acceptance of the concept of two sensitivity coefficients is a cognitive progress. In the station, the instrument should be calibrated, that is, scale value shall be determined for the relationship between the diameter change in the steel cylinder and the output of the instrument. Some people subconsciously think that the corresponding strain value of twice the radial displacement value is the linear strain of the rock, and then think that it is enough that the "crustal strain observation only needs this displacement sensitivity coefficient".

Nowadays, the high sensitivity borehole strainmeters are all based on the solid hole method. From the change of the inner diameter of the steel cylinder, A(ε + ε) and B(ε - ε) are obtained directly. The estimation errors of A and B directly affect the errors of surface strain and shear strain. Gladwin M.T., (1984) and Zhang Lingkong et al.(2013) gave the theoretical numerical curves of A and B in formula (2) - formula (5); Zhang Lingkong et al.(2013) also substituted the parameters of several types of strainmeters in China into the theoretical formulas and obtained the following results: A=0.56-1.687, with an average of 1.121; B=1.120-1.889, with an average of 1.505. The average values of A and B deviate from the values of A and B (A=1.75, B=1.4) under the pore condition (assuming Poisson's ratio is 0.3) by a few tenths or one tenth, and the ratio A/B is also different from the average value of 0.8. For many years, some of our articles have to deal with the observation data by assuming B/A equal to 1.0, 1.5 or 2.0, because there is no clear A and B data. If no explanation is given, there will be some left-over problems.

In view of this, it is suggested that manufacturers and relevant experts work together to investigate the rock types and mechanical parameters of seismic stations and provide semi-quantitative A and B estimates. The observational stations can obtain effective macroscopic values of A and B in the environment (including topographic fluctuations and large-scale rock mechanics parameters) by calculating tidal factors. In a word, we will gradually accept and use A and B sensitivity coefficients to make the processing of observation data more reasonable.

(2) There is still room to improve the method of evaluating data quality by strain tide observations. Formula (1) - formula (4) give the rule of change of the diameter of steel cylinder with the strain state of rock, that is, U1=A(ε + ε) + B(ε - ε)cos2Ψ, as noted by Qiu Zehua et al. (2009), which is different from the rule of linear strain in a complete rock.

$ U = 1/2({\varepsilon _{\rm{I}}} + {\varepsilon _{{\rm{II}}}}){\rm{ }} + {\rm{ }}1/2({\varepsilon _{\rm{I}}} - {\varepsilon _{{\rm{II}}}}){\rm{cos}}2\mathit{\Psi } $ (15)

This involves how to use the mean square error in the tidal factor to evaluate the observed data. It is a good way to compare the theoretical curve of strain solid tide with the measured curve. The software used at present takes the amplitude of the M2 wave calculated by formula (15) as the denominator and the output value of the component as the numerator to obtain the tidal factor value, then calculating the mean square error for the non-coincidence of the two curves of each component, and averaging the four mean square errors. In essence, this calculation is to reflect the observation error of surface strain, but it is not as good as directly calculating the mean square error of surface strain, and moreover, there is currently a lack of calculation and evaluation of shear strain observation errors, so it seems unbalanced.

A more reasonable processing method is that when calculating the tidal factor and the mean square error, the theoretical value of the tidal strain amplitude no longer uses linear strain, nor evaluates the components, but judges the surface strain and shear strain, so as to minimize the systematic error and eliminate some "inexplicable" problems encountered in data analysis, such as the tidal factor differing greatly among the components and changes every month.

(3) The best way to solve the three unknowns. Under the influence of previous inherent concepts, it is customary to use three known numbers and three equations to solve the three unknowns. Since 1974, the four-component piezomagnetic stress gauge has continued the tradition of the three-component era: first, three groups are selected from the readings of four components at a time, and then the maximum and minimum principal strain values (e.g., Liu Xuyan et al., 2014) are calculated directly according to the troublesome analytic formula, to obtain four groups of solutions. Comparing the differences among the four groups of unknown solutions, it is recognized that the results are reliable if the differences are very small. Such inherent concepts and practices continued until the beginning of the 21st century in the analysis of four-component piezomagnetic stress gauge data. The author has repeatedly proved to his colleagues that as long as the self-checking formula (12) is established, the results of the four groups of calculation must be consistent, and it is unnecessary to calculate four times to get the results.

(4) Azimuth determination algorithm is recommended. Formula (14) is very simple, but for beginners, it is easy to make mistakes, and they often don't realize the main points before they run into snags. The corresponding computing software may come out, but the mental arithmetic method is still worth advocating. Being well aware of the situation can help human-computer dialogue. Here, there is a mechanical concept: "The azimuth angle of the maximum principal strain must be the closest to the azimuth of the component with the greatest change." Using visual and centric algorithms, it is easy to estimate semi-quantitative results with errors less than 25°. The steps are as follows: (1) in the four groups of differences (U1-U3), (U3-U1), (U2-U4), (U4-U2), two positive values are left behind, while the negative values are discarded; and (2) remember the two group of positive values listed in the front of the two component numbers, the angle area held by the two components is the azimuth area. Here are the two lessons we have learned from our repeated encounters with difficulties.

① Keep in mind that the working direction of the component is "both forward and backward". When we talk, write and think about the direction of components, we often simplify them. For example, the component is NE-oriented and the actual meaning should be NE-SW-oriented. When we look at the geological structure map and think about the possible focal location, we often think subconsciously to the north, but ignore and forget the south.

② In the case of compressive strain (common in practice, as shown in Fig. 3 and Fig. 5), the maximum principal strain obtained by algebraic value is the minimum principal strain in the practical sense because of the negative compression defined by some instrument output symbols. For example, one principal strain is 10 units of compression and the other is 1 unit of tension. In the calculation, the former is negative, called the minimum principal strain, and the latter is positive, which is defined as the maximum principal strain. The azimuth difference is 90°.


The establishment of a dense seismic observation network in the key monitoring areas of the earthquake (He Deqiang et al., 2014) is receiving attention. In the Zhaotong area of Yunnan Province, the Yanliang MS5.7 earthquake occurred on September 7, 2012, and the Ludian MS6.5 earthquake occurred on August 3, 2014. Three and four strain observation stations are distributed in the respective earthquake zones. The distribution of the earthquakes and stations is shown in Fig. 2. Anomalies are detected in surface strain, shear strain and self-test factor curves, which proved the practical significance of setting up dense observation networks in the seismic risk areas. Here, according to the observational concept of this paper, the strain anomalies before, during and after the earthquakes are examined in detail.

Fig. 2 Location of the observation stations and two earthquakes

For the sake of simplicity, let A=B=1, after the specific values in anomalies before, during and after the earthquake receive attention. In the end, the shear strain value is divided by B to obtain the corrected strain value.

The downward curve of strain observation means compression, and the upward means extension. The window width for calculating the correlation coefficient is 25h. Each station produces 9 curves, from top to bottom, they are: the four-component reading curves, two-group reading difference curves (commonly known as differential strain curves), two-group internal addition curves (surface strain curves) and self-test factor curve. It can be appreciated that the effect of looking over the adding and subtracting curves of the component readings is better than directly looking over the original reading curve of the component. The description and understanding of these curves are relatively superficial, and there are not many important and dramatic physical quantities, such as coseismic steps, earthquake fluctuations, high-frequency anomaly information, tidal factors and mean square errors.

3.1 The Yiliang MS5.7 Earthquake

At 11: 19 a.m. on September 7, 2012, an MS5.7 earthquake occurred at the junction of Yiliang County, Zhaotong City, Yunnan Province and Weining County, Bijie District, Guizhou Province, with a focal depth of 14km. At 12: 16 p.m., another MS5.6 earthquake occurred in Yiliang County, with a focal depth of 10km. The seismogenic structures are all NE-striking Shimen faults. Fig. 3 shows the observation results of three observation stations in the near field. The epicenter distance of the observation stations is 12km for Yiliang seismic station, 23km for Daguan seismic station and 46km for Yudong seismic station.

(1) Records from the Yiliang seismic station with the smallest epicenter distance. Fig. 3(a) shows that: ① shear strain anomalies occur earlier than surface strain anomalies; ② no obvious anomalies (quiet period, nucleation period?) were observed in the two strains a few days before the earthquake; ③10 days before the earthquake, two differential strain curves bifurcated, indicating that the main azimuth angle began to deflect (from NNE to NE, clockwise); ④ when the earthquake occurred, the jump amplitude of surface strain was much smaller than that of shear stress, which leads to the conclusion that the earthquake is of a strike-slip shear rupture. For a clearer view, the local change is shown in Fig. 4; ⑤ about 4 days after the earthquake, a rainstorm occurred in the epicentre area of the earthquake in the early morning of September 11, and compressional change occurred in surface strain. The two shear strains changed with a large jump, and the jump direction is consistent with the jump direction at the moment the earthquake hit. However, there is no abnormality in the self-checking factor on that day, and it is estimated that the change of the curves starting from September 11 is mainly influenced by the load of rainfall, but it cannot be completely ruled out that the creep of faults caused by groundwater infiltration aggravates the change of shear strain; ⑥ the largest abnormal amplitude of shear strain and surface strain is shown in Fig. 3 and Fig. 5, and the abnormality of shear strain reaches the order of 3×10-6; ⑦ the self-checking factor anomaly is the first self-checking factor curve we obtained; and (8) the reasons for bifurcation of two surface strain curves are unknown.

Fig. 4 Records of the Yiliang seismic station during the Yiliang earthquake (part of Fig. 3(a)) It is noted that the sign of change of surface strain before and during earthquake is compressive, while the sign of shear strain is upward, the trend before earthquake is downward first and upward afterward; the steep jump during earthquakes comes from near-field observations

On August 6, 2012, the rainfall in the Yiliang area was 26.1mm. The shear strain curve showed obvious disturbance, while the disturbance to surface strain was relatively small. This may be due to the expansion of obvious cracks in rocks under water pressure, resulting in the change of shear strain. On the contrary, there was little influence on surface strain. This rainfall disturbance should not be related to the Yiliang MS5.7 earthquake.

(2) Records of Daguan seismic station. There was a power cut in Daguan seismic station several days before the earthquake, and it happened that power was restored after the earthquake. It was believed that the data of this station had no use value. After sorting it out, it was found that although the abnormal curve of the self-test factor was incomplete, it still had indispensable use value. It also showed that the azimuth angle of the maximum principal strain deflected counterclockwise from NS to NW, as shown in Fig. 3(b).

(3) Records of Yudong seismic station with a large epicenter distance. The strain anomaly observed at Yudong seismic station is not obvious, and the anomaly of the self-checking factor curve deserves affirmation. The background value of the strain observation curve is more fluctuant than that of other measuring points, and the bifurcation of the two strain curves(Fig. 3(c)) shows that the reliability of the observation data is slightly worse. Unlike the following two differential strain curves before and after the Ludian MS6.5 earthquake, the bifurcation in the Yiliang MS5.7 earthquake is larger, indicating a azimuth deviation (from NW to NNW, counterclockwise).

There was a small amount of rainfall around Yudong seismic station on September 11, 2012, and strong rainfall occurred on September 26, 2012. The strain observation curve was affected by two rainfall events (rainfall on September 26 resulted in an expansion of surface strain of about 125× 10-9), but the polarity of the curve was the same. It is easy to understand the change of surface strain caused by rainfall, but there are few reports about the change of shear strain in the past. The shear strain varies under the influence of rainfall, which may be caused by the small expansion of small fissures caused by the increase of water pressure in the fissures. It is noted that the self-checking factor of Yudong seismic station did not change due to heavy rainfall, so the anomaly of the self-checking factor did not come from the surface.

It can be concluded that for the MS5.7 earthquake in Yiliang in 2012, the anomaly peaks in self-checking factor curves of strainmeter at Yiliang, Daguan and Yudong seismic stations mostly appear around the time of earthquake occurrence, and some occur several hours before the earthquake, but the anomalies gradually recover from a few days to 10 days after the earthquake (the peculiar "memory decay" characteristic of the self-checking factor).

3.2 The Ludian MS6.5 Earthquake

The Ludian MS6.5 earthquake occurred at 16: 30 p.m. on August 3, 2014. Fig. 4 shows the strain observation curves of Ludian, Yudong, Daguan and Yiliang seismic stations (the epicenter distance is 26km for Ludian, 39km for Yudong, 90km for Daguan and 91km for Yiliang) from July to August of that year. It can be seen that the strain anomaly pattern of Ludian MS6.5 earthquake and the records of Yiliang MS5.7 earthquake can corroborate with each other as the anomaly information is significant in the seismic stations with the smallest epicenter distance. Because the downhole part of the four-component instrument in the Ludian seismic station was installed on April 1, 2014, and the digital acquisition and transmission circuit was installed in early July, the observation data in early July are missing in Fig. 4.

(1) Strain records at Ludian seismic station. From Fig. 4(a). It can be seen that at first, both surface strain and shear strain have short-term and imminent earthquake anomalies lasting about 10 days and 1 day, and their variation patterns and magnitudes are different. They are shown as follows: the surface strain varies greatly before earthquakes, but the response is relatively small during earthquakes, which is similar to that in Fig. 4, and exceeds usual expectations. The shear strain has obvious changes before, during and after earthquake. The observed curves of surface strain and shear strain at Ludian seismic station almost jumped at the same time the day before the earthquake, but there were no similar records at Yudong, Daguan and Yiliang seismic stations. Whether they were slow earthquakes or pre-slip of faults still needs to be studied. Second, the MS6.5 earthquake occurred several hours after the anomaly of the self-checking factor reached its extreme value (only the curve recorded at Ludian seismic station is so "typical"); and third, anomalous change occurred in the two differential strain curves, with occasional jumps, which indicates that the principal azimuth angle has changed from NW to NNS. Fourthly, the fluctuation of the curve at the end of August is caused by rainfall disturbance, shown as the surface strain curve declining (compressional change) and the change of shear strain, which is similar to the shape of the curve of Yudong seismic station affected by rainfall in Fig. 3. Furthermore, it can be seen that the self-checking factor will not be disturbed by rainfall.

(2) The records of Yudong seismic station. The borehole of Yudong seismic station is 123m away from the tailrace channel of a reservoir power station, which is 60m wide and 1.4km away from the dam. The daily observation curve has jumped since 2013, which is estimated to be influenced by the reservoir's power generation. Visual methods can not distinguish whether the strain curve is abnormal or not, as shown in Fig. 4(b). The tidal factor curves of surface strain and shear strain show short-term anomalies 3-4 months before the earthquake, and the self-checking factor curves here have only reference significance. The maximum anomaly of the self-checking factor curve appeared before the occurrence of the earthquake, and the anomalous amplitude at the moment the earthquake occurred is less than the extreme value, and the anomalies with small amplitude lasted for several months after the earthquake. The above phenomena are different from that of Ludian, Daguan and Yiliang seismic stations, which are worth studying. At present, the origin of the self-checking factor curve jump is unknown. Whether it is related to groundwater movement of surrounding large rock mass can be further analyzed in the future.

On July 9, 2014, the strain observation at Yudong seismic station was disturbed by rainfall, but the disturbance pattern seems not typical. The surface strain changes from extension to compression. Of course, the self-examination factor did not respond.

(3) Strain records at Daguan seismic station. The strain anomaly curve at Daguan seismic station is almost the same as that recorded at Yudong seismic station (Fig. 4(c)). The visual results are not obvious and the change of tidal factors is not noticed, but the anomaly of self-checking factors is more significant. Two differential strain curves have bifurcated since July 8, 2014, indicating that the principal azimuth of the MS6.5 earthquake was reversed before the earthquake (located in NW direction, with a small counterclockwise deflection).

(4) Records from Yiliang seismic station. Fig. 4(d) shows that the surface strain and shear strain changed slowly 15 days before the MS6.5 earthquake, and the shear strain range is large, reaching an order of magnitude of 10-7. Coseismic variations need to be observed on a large scale, and the extreme value of self-checking factor curves reappeared nearly 20 days after the earthquake, accompanied by slow bifurcation of two surface strain curves. These seven self-checking curves in Fig. 3 and Fig. 4 have their particularities. What kind of post-earthquake effect will lead to a new topic.

3.3 Summary

Comparing the seven groups curves of two earthquake cases, we can see: (1) In the four-component strain observation of near-field observation points, most of the short-term and imminent changes of surface strain and shear strain can be obtained, and the two kinds of strain changes have their own distinctive characters. Their variation range, occurrence time and shape are mostly inconsistent, while before the Ludian MS6.5 earthquake, the strain anomalies of Yudong and Daguan seismic stations are not obvious; (2) shear strain changes are more active, which should be caused by strike-slip faulting; (3) the polarity of co-seismic response during an earthquake is mostly inherited from the polarity of impending earthquake anomalies, i.e. displaying the mechanical image with pre-displacement; (4) for the abnormality of self-checking factor curve, the extreme value often occurs at or shortly after the earthquake, only in the analysis of Ludian MS6.5 earthquake, the self-checking factor anomaly of Yudong seismic station is uncertain; (5) analysis of current strain data shows that the abnormality of self-checking factors does not come from surface effect, and has a self-recovery function.

The value of the near-field anomaly data given in this paper also tells us that if we can maintain and improve the seismic observation network in the earthquake-prone area, properly densify the stations of the network, and increase the construction of fast acquisition systems, we will be able to actively capture the striking information before the occurrence of moderate and strong earthquakes in the future.


This paper touches on two topics that need to be considered in depth.

(1) Precursory anomalies of the two surface strain correlation coefficients (self-checking factors) may occur up to ten or more days before the occurrence of larger earthquakes in some areas and observation stations with short epicenter distances. This coefficient can not respond to distant earthquakes, nor to small earthquakes, and cannot indicate anomalies earlier. It is a pity, but it also has its advantages: simple calculation of the correlation coefficient of surface strain, less interference and small human factors, but it is just the beginning that we touch on the topic.

After the Yiliang MS5.7 earthquake in 2012, the Zhaotong Seismic Office drew and examined the anomaly of the self-checking factor curve, which was even more puzzling after eliminating interference and instrument failure. In the Ludian MS6.5 earthquake in 2014, two of the four adjacent seismic stations observed obvious strain anomalies, and three stations found more exact anomalies of self-checking factors. At this time, we had to face up to such anomalies that we had never seen or heard before (Kong Xiangyang et al., 2015). During the same period, Chi Shunliang et al. also thought about the "inaccuracy" of the data of the four-component borehole strain meter installed in Guzan, Sichuan Province, that is, the statistical value of the correlation coefficient of surface strain gradually decreased and recovered in the time periods before, imminent, during and after the earthquake (Chi Shunliang et al., 2014).

Two types of the four-component strainmeters give statistical or curvilinear anomalies of correlation coefficients for several moderately strong earthquakes at different locations, which may have objectivity, but they are all facing the embarrassing dilemma: the original parameters used to verify reliable data are accompanied by their own anomalies when strain anomalies occur. This discovery is expected to be further confirmed, and it also needs enough examples such as the "negative earthquake" of Yudong seismic station in 2014 to help us think calmly. Moreover, what kind of mechanical mechanism makes the preconditions of elasticity formula subject to some temporary damage or disturbance?

The concomitant topic is why some pre-earthquake strain anomalies have been observed both in the past and in the present in the Chinese mainland, while few have been recorded in the United States and Japan. Today, many foreign scholars are pessimistic about earthquake prediction. Should the younger generation to look directly at this clue that may disrupt existing thinking?

The author's inaccurate answer is that the fault structures of the United States and Japan are different from those of China. There are many strike-slip faults in the Chinese mainland. The seismogenic locking point (seismogenic nucleation) must have a process of "growth-migration-earthquake occurrence-post-earthquake adjustment" dominated by mechanical process, which is liable to cause abnormal changes of horizontal strain field, especially shear strain field.

(2) A new start for the four-component strainmeters. Four uniformly distributed components are divided into two groups. The shear strain (two differential strains) curves, two surface strain curves and the maximum principal strain azimuth can be obtained by subtracting or adding the measured values. In addition to the three unknowns, there is a "redundant" value, the correlation coefficient of two surface strains. The above four can deduce colorful mechanical images.

There still has a long way to go. Now it is just the beginning. There are still many practical problems to be solved. Hardware alone includes a long lifetime of downhole instruments (such as 20 years of service), strict control of azimuth angles of installation, strict consistency of component characteristics, control of drilling quality, etc.

This paper is a memorized to Professor Li Siguang, the advocater of borehole stress-strain observation. It has been more than 40 years since the 1977 Wuhu Conference (the First National Conference on Crustal Stress of China). This paper is dedicated to the commemoration of that conference.

This meeting prompted the birth of a variety of borhole instruments and the emergence of new ideas. In the 21st century, the quality of our strain observation instruments, the breadth and depth of our horizons, and the observation data we have obtained should be better than before, all of which inspire us.


Thanks to the consistent support and trust of the staff of Zhaotong Seismic Office, Yunnan Province for the four-component strainmeter, they have made great effort to build and maintain the medium-density drilling strain network for more than ten years, which make us the opportunity and conditions to obtain such unprecedented near-field data. The author also express his thanks to Kong Xiangyang at Earthquake Prediction Research Center, Shandong Earthquake Agency, assisted in the drawing of the map.

Chi Shunliang, Zhang Jing, Chi Yi. Failure of self-consistent strain data before Wenchuan, Ludian and Kangding earthquakes and its relation with earthquake nucleation[J]. Recent Developments in World Seismology, 2014(12): 3–13, 47 (in Chinese with English abstract).
Gladwin M.T. High-precision multicomponent borehole deformation monitoring[J]. Review of Scientific Instruments, 1984, 55(12): 2011–2016. DOI:10.1063/1.1137704.
Hast N. The Measurement of Rock Pressure in Mines[M]. Stockholm: Sveriges Geologiska Under, 1958: 7-60.
He Deqiang, Li Yafang, She Ruchang, Liang Bing, Zeng Ziming, Shen Bo. Near field anomalies of Yiliang M5.7, 5.6 earthquakes on September 7, 2012[J]. Journal of Seismological Research, 2014, 37(1): 1–8 (in Chinese with English abstract).
Ishii H., Asai Y. Elastic invariants observed by borehole stress and strain meters and the reliability of the instrument[J]. Zisin, 2017, 39(2): 58–69.
Kan Baoxiang, Qiu Zehua, Tang Lei. In-situ calibration of borehole shear strainmeter at Tai'an station[J]. Journal of Geodesy and Geodynamics, 2007, 27(6): 119–123 (in Chinese with English abstract).
Kong Xiangyang, Su Kaizhi, Fujinawa Yukia. Application Prospects of SKZ-1 4-component Borehole Strain Meter[SCG15-P02] [R]. Chiba: Japan Geoscience Union Meeting, 2015.
Liu Xuyan, Wang Ziyan, Fang Hongfang, Huang Shengming, Wang Lin. Analysis of 4-component borehole strain observation based on strain invariant[J]. Chinese Journal of Geophysics, 2014, 57(10): 3332–3346 (in Chinese with English abstract).
Qiu Zehua, Kan Baoxiang, Tang Lei. Conversion and application of 4-component borehole strainmeter data[J]. Earthquake, 2009, 29(4): 83–89 (in Chinese with English abstract).
Qiu Zehua. Borehole Observation:Theory and Application[M]. Beijing: Seismological Press, 2017 (in Chinese).
Савин Г.Н. Stress Concentration near the Hole[M]. In: Lu Dinghuo, Trans. Beijing: Science Press, 1958 (in Chinese).
Su Kaizhi, He Yu. Error Problem of Relative Measurement of Ground Stress in Bore Hole Method[M]. In: Intelligence Unit of Seismological Brigade, State Seismological Bureau (Editor). Beijing: Seismological Press, 1984 (in Chinese).
Su Kaizhi. Ground Stress Measurement Method[M]. Beijing: Seismological Press, 1985 (in Chinese).
Su Kaizhi. Geostress Relative Measurement Method[M]. In: Su Kaizhi, Li Hailiang, Zhang Jun, Li Xiuhuan, Ma Xiangbo (Editors). Beijing: Seismological Press, 2003. 252-260 (in Chinese).
Su Kaizhi, Li Hailiang, Zhang Jun, Li Xiuhuan, Ma Xiangbo. New Progress in Borehole Strain Observation[M]. Beijing: Seismological Press, 2003 (in Chinese).
Tang Lei, Qiu Zehua, Song Mo. Self-test accuracy of 4-component borehole strain observation[J]. Journal of Geodesy and Geodynamics, 2010, 30(S2): 36–39 (in Chinese with English abstract).
Zhang Lingkong, Niu Anfu. Component borehole strain observations coupling coefficients calculation[J]. Chinese Journal of Geophysics, 2013, 56(9): 3029–3037 (in Chinese with English abstract).