**3. Anisotropic AR changes related to strong EQ**

Кraev studied the calculating method of AR in a homogeneous anisotropy medium[22]. Later, Brace *et a*l.[23], Chen *et al*.[24] and Lu *et al*.[25] reported that during the loading process of most rock (soil) samples, AR changes showed the directional changes which were associated with the maximum loading direction. In recent years, people try to explore relatedearthquake anisotropic AR changes, which would have an important significance to understand the stress status in/nearby the EQ focal region, to explain the reason of relatedearthquake AR changes and to forecast an EQ. However, it is very difficult to detect the anisotropic changes from actual EQ cases. Such researches were reported only in China because China has long made a lot of fixed-site AR observations. Qian *et al*.[26] and Du *et al*.[9, 11] reported that the anisotropic AR changes that were associated with the maximum compressional stress (P-axis) azimuths of EQ focal mechanism solutions, and Du *et al*.[2, 27] try to explain the anisotropic AR changes in theory.

#### **3.1 Analysis of EQ cases on anisotropic AR changes**

The studied EQ cases are picked out according to the following three principles: ①strong EQs with magnitude of Ms 5.5, ②EQs nearby AR stations, and ③AR changes in the later stages of EQ preparation. From the formula to estimate the focal body radius *L*[29], *Ms=3.3+2.1 Log L*, for Ms5.5 EQ *L* is no more than 15 km, for Ms 6~7 EQ *L* is no more than 60 km and for Ms7.8 EQ *L* is about 140 km. According to Du *et al*.[7, 10], AR anomalies within tens km for Ms 6~6.9 EQs and within 150 km for Ms 7.0 EQs are mostly characterized by drop-type changes in the medium-term stages of EQ preparation. The underground medium commonly contains rich water, so the concentrative range of the drop-type AR changes is well coincident with the focal body radius *L*. This indicates how we pick out the EQs nearby stations.

It is very important in study of anisotropic AR changes to distinguish the precursory AR anomaly related to strong EQs from observational AR data. Therefore, NVRM is usually used to process data. Du *et al*.[11] have studied anisotropic AR changes, using NVRM, recorded at 41 stations before 27 Ms 5.5 EQs that occurred in the Chinese mainland. The results show that for over 95% of the stations, the anisotropic AR changes appeared during the later stages of EQ preparation, which were obviously related to the P-axis azimuth of EQ focal mechanism solution. The behaviors of these anisotropic changes are that the AR change recorded through the channel perpendicular (or almost perpendicular) to the azimuth is a maximum in amplitude, whereas that recorded through the channel along (or close to) the azimuth is a minimum.

After the Ms6.1 and 5.8 Shandan-Minle EQs, Du *et al* again processed the AR data observed at SHD station (43 km) from the two epicentral areas 1997 to 2004 using NVRM, as a result, it can be seen from figure 12 that the medium-term drop-type to short-term rise-type AR changes are similar to the AR changes in the focal area as foretold by the DD model (Dilatancy-Diffusion Model)[13-14] in appearance, a pattern consisting of an initial medium-

People may ask why the May 12, 2008, Ms8.0 EQ was not forecasted in the medium-term period before the great EQ, which just occurred around/nearby 6 AR stations in this area? In fact, authors had no time to process and analyze the AR data observed at the 6 AR stations in those days, and the AR changes of the stations were analyzed and studied only

Кraev studied the calculating method of AR in a homogeneous anisotropy medium[22]. Later, Brace *et a*l.[23], Chen *et al*.[24] and Lu *et al*.[25] reported that during the loading process of most rock (soil) samples, AR changes showed the directional changes which were associated with the maximum loading direction. In recent years, people try to explore relatedearthquake anisotropic AR changes, which would have an important significance to understand the stress status in/nearby the EQ focal region, to explain the reason of relatedearthquake AR changes and to forecast an EQ. However, it is very difficult to detect the anisotropic changes from actual EQ cases. Such researches were reported only in China because China has long made a lot of fixed-site AR observations. Qian *et al*.[26] and Du *et al*.[9, 11] reported that the anisotropic AR changes that were associated with the maximum compressional stress (P-axis) azimuths of EQ focal mechanism solutions, and Du *et al*.[2, 27]

The studied EQ cases are picked out according to the following three principles: ①strong EQs with magnitude of Ms 5.5, ②EQs nearby AR stations, and ③AR changes in the later stages of EQ preparation. From the formula to estimate the focal body radius *L*[29], *Ms=3.3+2.1 Log L*, for Ms5.5 EQ *L* is no more than 15 km, for Ms 6~7 EQ *L* is no more than 60 km and for Ms7.8 EQ *L* is about 140 km. According to Du *et al*.[7, 10], AR anomalies within tens km for Ms 6~6.9 EQs and within 150 km for Ms 7.0 EQs are mostly characterized by drop-type changes in the medium-term stages of EQ preparation. The underground medium commonly contains rich water, so the concentrative range of the drop-type AR changes is well coincident with the focal body radius *L*. This indicates how we pick out the

It is very important in study of anisotropic AR changes to distinguish the precursory AR anomaly related to strong EQs from observational AR data. Therefore, NVRM is usually used to process data. Du *et al*.[11] have studied anisotropic AR changes, using NVRM, recorded at 41 stations before 27 Ms 5.5 EQs that occurred in the Chinese mainland. The results show that for over 95% of the stations, the anisotropic AR changes appeared during the later stages of EQ preparation, which were obviously related to the P-axis azimuth of EQ focal mechanism solution. The behaviors of these anisotropic changes are that the AR change recorded through the channel perpendicular (or almost perpendicular) to the azimuth is a maximum in amplitude, whereas that recorded through the channel along (or

term fall followed by a short-term rise.

**3. Anisotropic AR changes related to strong EQ** 

try to explain the anisotropic AR changes in theory.

**3.1 Analysis of EQ cases on anisotropic AR changes** 

after the great EQ[7].

EQs nearby stations.

close to) the azimuth is a minimum.

For example, the two observation channels, N20°E and N70°W channels, are installed at station PGU that had epicentral distances of 111 and 140 km for the 1976 Ms7.8 Tangshan EQ and Ms7.1 Luanxian aftershock; the P-axis azimuths of the two events were 75° and 297°, respectively, roughly in the EW direction. As a result, the medium-term drop-type and short-term rise-type AR changes recorded through N20°E channel (with a near NS direction) prior to the EQs were greater in amplitude than those through N70°W channel (with a near EW direction) (Fig.13). As another example, three channels, NS, EW and N45°W channels, are installed at station SHD that had an epicentral distance of 43 km for the 2003 Ms6.1 Minle- Shandan EQ; the P-axis azimuth of this EQ was 65°. As a result, the medium-term drop-type and short-term rise-type AR changes recorded through N45°W channel prior to the EQ were greater in amplitude than those through EW channel (Fig. 12).

It is obvious that the relationship between the anisotropic AR changes and the P-axis azimuth from actual EQ cases agrees well with the relationship between the directional AR changes and the maximum loading direction in most experiments of water-bearing rock (or soil) samples. This proves that such AR changes are just related to the EQ preparation process.

Fig. 13. NVRM curves of AR changes of station PGU for the 1976 Ms 7.8 Tangshan EQ

#### **3.2 Theoretical analysis on anisotropic AR changes**

According to DD model, the micro cracks inside the underground medium fast and nonlinearly develop immediately before the main rupture within an EQ focal area, their strikes align predominately in a certain direction and underground water fast come in them. Barsukov[29] interpreted a larger amplitude change in resistivity on the assumption that the micro crocks are tortuously linked each other, and underground water comes in them, as a result, the conductive aisles inside the medium are formed. Mei *et al*.[30] deduced that in the later preparation stages of strong EQs a number of micro-cracks inside the medium of an EQ focal region is increased sharply. The fact that in the medium-term statges before moderate, strong EQs of the Chinese mainland, for larger-magnitude EQs the AR anomaly amplitude increases fast, whereas the anomaly duration increases more slowly[10] supports Mei's deduction. According to Crampin *et at*.[31], the maximum compressional stress inside the

Changes in Apparent Resistivity in the Late Preparation Stages of Strong Earthquakes 213

From formulas (1) ~ (3), we can get that the TR changes along the two principal axes satisfy

medium change from homogeneous ( sx s <sup>y</sup> ) into anisotropic ( sx s <sup>y</sup> ), we can obtain the inequality of sx < sy from inequality (3), in which sx is the AR variation rate of channel X and sy is that of channel Y. From the inequality and formulae (1) and (2) as well as the calculating formula for s in the anisotropic medium, the following inequality is

> 2 1 2 1

Where <sup>1</sup> and <sup>2</sup> are TR variation rates along two electrical principle axes, and a true

 <sup>2</sup> < <sup>1</sup> . (7) If the AR changes along the loading direction and perpendicular to the direction are all increased the sigh ">"will replace "<" in inequalities (5) and (7), from inequality (4). According to inequalities (5) and (7) and their derivation conditions, we can have the following understandings: anisotropic TR changes in which the change along the loading direction is more prominent than that perpendicular to the direction cause anisotropic AR changes in which the change perpendicular to the direction is more prominent than that in the direction. It is obviously that there are a difference of 90 between the directions of both the most prominent AR change (perpendicular to the loading direction) and the most prominent TR change (along the loading direction). This result distinctly explained the relationship between the most loading direction and the anisotropic AR changes when approaching the main rupture of most rock (or soil) samples and theoretically supported the

From the TR relationship among three principal axes in the anisotropic medium, <sup>1</sup> > <sup>2</sup> = <sup>3</sup> , we assume the shape of a single micro crack as a schistose ellipsoid that takes 1 axis as its rotation axis, and whose radius is a in 2 x direction, b in 3 x direction and c in 1 x direction and a=b>c (an erect crack). And then, we assume that the resistivity in saturated-water cracks (water is rich within the underground medium) is <sup>f</sup> , that of framework is and the crack ratio is . Using Кraev's result[22] we have the

2 

< <sup>1</sup> 1 

(t is a time interval). When the underground

. (6)

(0 1 ). In the case of 0.5 1.0 (viz., 1 2 1 4 ),

. (5)

the following inequality:

obtained[11]:

2

<sup>2</sup>

1

Let the AR variation rate s <sup>s</sup> <sup>t</sup>

anisotropic coefficient 2

we get the following inequality:

research results from actual EQ cases.

**3.3 A Reason for anisotropic AR changes** 

approximate formulae of versus :

near-surface crust is commonly horizontal, and because of hydrostatic pressure of rock the horizontal cracks are closed and the erect cracks are developed, with the normal of the erect cracks being usually mostly horizontal and the strikes of the cracks being predominantly along in the direction of the maximum compressional stress axis. As a result, this forms an EDA medium with conductive fluid. According to the above-mentioned discussions, we presume that in the later preparation stages of strong EQs there probably exist two physical behaviors inside the medium in and nearby the focal area: (a) the erect micro-cracks is well developed, their number is non-linearly increased, and their strikes are predominantly along the direction of the maximum compressional stress axis. (b) in above-mentioned processes, the macro-cracks are linked each other and the underground water with low resistance comes fast in them. This forms the conductive aisles in the medium. As the result of its sensitivity to water, the electrical resistivity of the medium, therefore, undergoes significant changes.

Based on the two physical behaviors, we approximately regard the medium in/nearby the EQ focal region as a homogeneous azimuthal anisotropic medium. We establish a Descartes coordinate system o xxx 123 on the ground where 1 x , 2 x and 3 x are three electrical principal axes, respectively, which 2 x is along the horizontal loading direction (this means the P*-*axis direction of EQ focal mechanism solution in study of EQ cases), 1 x is horizontal and perpendicular to the direction and 3 x is downwards vertical to the ground surface. <sup>1</sup> , 2 and 3 are true resistivity (TR) along the three axes, respectively, and <sup>1</sup> > <sup>2</sup> = <sup>3</sup> . is the angle between ground observation channel X and the axis 1 x . Another ground observation channel Y is perpendicular to channel X . Based on the calculating formula for the relative AR changes ( s s ) in the anisotropic medium by Du *et al*.[2] (after referring to paper [22]), we can get the relation of relative AR changes ( sx sx and sy sy ) of observational channels X and Y to relative TR changes ( 1 1 and 2 2 ) in two horizontal principal axes directions. When 0 (here, channel X is perpendicular to the loading direction and channel Y is along the direction) the relation is as follows: In 1 x direction (perpendicular to the maximum loading direction)

$$\frac{\Delta\mathfrak{p}\_{\rm sx}}{\mathfrak{p}\_{\rm sx}} = \frac{\Delta\mathfrak{p}\_2}{\mathfrak{p}\_2} \tag{1}$$

In 2 x direction (along the loading direction)

$$\frac{\Delta\boldsymbol{\rho}\_{\rm sy}}{\boldsymbol{\rho}\_{\rm sy}} = \frac{1}{2} (\frac{\Delta\boldsymbol{\rho}\_1}{\boldsymbol{\rho}\_1} + \frac{\Delta\boldsymbol{\rho}\_2}{\boldsymbol{\rho}\_2}) \cdot \tag{2}$$

According to most loading experiments of rock (soil) samples, following two inequalities are generally true:

$$
\text{When } \begin{array}{c}
\underline{\Delta\mathfrak{p}\_{s}} \ll 0 \\
\mathfrak{p}\_{s}
\end{array} .
\qquad
\qquad
\begin{array}{c}
\underline{\Delta\mathfrak{p}\_{\infty}} \ll \frac{\Delta\mathfrak{p}\_{\text{sy}}}{\mathfrak{p}\_{\text{sy}}} ;
\end{array} .
\tag{3}
$$

$$\text{When } \begin{array}{c} \underline{\Lambda p}\_{s} \gg 0 \end{array} \qquad \qquad \begin{array}{c} \underline{\Lambda p}\_{\text{sc}} \gg \frac{\Delta p}{\rho\_{\text{sy}}} . \end{array} \tag{4}$$

near-surface crust is commonly horizontal, and because of hydrostatic pressure of rock the horizontal cracks are closed and the erect cracks are developed, with the normal of the erect cracks being usually mostly horizontal and the strikes of the cracks being predominantly along in the direction of the maximum compressional stress axis. As a result, this forms an EDA medium with conductive fluid. According to the above-mentioned discussions, we presume that in the later preparation stages of strong EQs there probably exist two physical behaviors inside the medium in and nearby the focal area: (a) the erect micro-cracks is well developed, their number is non-linearly increased, and their strikes are predominantly along the direction of the maximum compressional stress axis. (b) in above-mentioned processes, the macro-cracks are linked each other and the underground water with low resistance comes fast in them. This forms the conductive aisles in the medium. As the result of its sensitivity to water, the electrical resistivity of the medium, therefore, undergoes

Based on the two physical behaviors, we approximately regard the medium in/nearby the EQ focal region as a homogeneous azimuthal anisotropic medium. We establish a Descartes coordinate system o xxx 123 on the ground where 1 x , 2 x and 3 x are three electrical principal axes, respectively, which 2 x is along the horizontal loading direction (this means the P*-*axis direction of EQ focal mechanism solution in study of EQ cases), 1 x is horizontal and perpendicular to the direction and 3 x is downwards vertical to the ground surface. <sup>1</sup> , 2 and 3 are true resistivity (TR) along the three axes, respectively, and <sup>1</sup> > <sup>2</sup> = <sup>3</sup> . is the angle between ground observation channel X and the axis 1 x . Another ground observation channel Y is perpendicular to channel X . Based on the calculating formula for the relative AR changes ( s s ) in the anisotropic medium by Du *et al*.[2] (after referring to paper [22]), we can get the relation of relative AR changes ( sx sx and sy sy ) of observational channels X and Y to relative TR changes ( 1 1 and 2 2 ) in two horizontal principal axes directions. When 0 (here, channel X is perpendicular to the

loading direction and channel Y is along the direction) the relation is as follows:

sx 2 sx 2 

sy 1 2 sy 1 2

According to most loading experiments of rock (soil) samples, following two inequalities are

2 

> s

> > s

<sup>1</sup> ( )

<0, sx

>0 sx

sx 

sx 

. (2)

< sy sy

> sy sy

 

. (1)

; (3)

. (4)

In 1 x direction (perpendicular to the maximum loading direction)

When s

In 2 x direction (along the loading direction)

When s

significant changes.

generally true:

From formulas (1) ~ (3), we can get that the TR changes along the two principal axes satisfy the following inequality:

$$
\frac{\Delta\rho\_2}{\rho\_2} \prec \frac{\Delta\rho\_1}{\rho\_1}.\tag{5}
$$

Let the AR variation rate s <sup>s</sup> <sup>t</sup> (t is a time interval). When the underground medium change from homogeneous ( sx s <sup>y</sup> ) into anisotropic ( sx s <sup>y</sup> ), we can obtain the inequality of sx < sy from inequality (3), in which sx is the AR variation rate of channel X and sy is that of channel Y. From the inequality and formulae (1) and (2) as well as the calculating formula for s in the anisotropic medium, the following inequality is obtained[11]:

$$
\dot{\rho}\_2 < \frac{\lambda^2}{2\lambda - 1} \dot{\rho}\_1. \tag{6}
$$

Where <sup>1</sup> and <sup>2</sup> are TR variation rates along two electrical principle axes, and a true anisotropic coefficient 2 1 (0 1 ). In the case of 0.5 1.0 (viz., 1 2 1 4 ), we get the following inequality:

$$
\dot{\rho}\_2 \le \dot{\rho}\_1 \,. \tag{7}
$$

If the AR changes along the loading direction and perpendicular to the direction are all increased the sigh ">"will replace "<" in inequalities (5) and (7), from inequality (4). According to inequalities (5) and (7) and their derivation conditions, we can have the following understandings: anisotropic TR changes in which the change along the loading direction is more prominent than that perpendicular to the direction cause anisotropic AR changes in which the change perpendicular to the direction is more prominent than that in the direction. It is obviously that there are a difference of 90 between the directions of both the most prominent AR change (perpendicular to the loading direction) and the most prominent TR change (along the loading direction). This result distinctly explained the relationship between the most loading direction and the anisotropic AR changes when approaching the main rupture of most rock (or soil) samples and theoretically supported the research results from actual EQ cases.

#### **3.3 A Reason for anisotropic AR changes**

From the TR relationship among three principal axes in the anisotropic medium, <sup>1</sup> > <sup>2</sup> = <sup>3</sup> , we assume the shape of a single micro crack as a schistose ellipsoid that takes 1 axis as its rotation axis, and whose radius is a in 2 x direction, b in 3 x direction and c in 1 x direction and a=b>c (an erect crack). And then, we assume that the resistivity in saturated-water cracks (water is rich within the underground medium) is <sup>f</sup> , that of framework is and the crack ratio is . Using Кraev's result[22] we have the approximate formulae of versus :

$$\begin{aligned} \frac{\Delta \mathbf{p}\_1}{\rho\_1} &\approx \frac{\rho\_\mathbf{f} - \rho\_\circ}{\rho\_\circ / \mathbf{v} + \rho\_\mathbf{f}} \cdot \frac{\Delta \mathbf{v}}{\mathbf{v}}\\ \frac{\Delta \mathbf{p}\_2}{\rho\_2} &\approx \frac{\rho\_\mathbf{f} - \rho\_\circ}{\rho\_\mathbf{f} / \mathbf{v} + \rho\_\circ} \cdot \frac{\Delta \mathbf{v}}{\mathbf{v}} \end{aligned} \tag{8}$$

Changes in Apparent Resistivity in the Late Preparation Stages of Strong Earthquakes 215

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[2] Du X B, Li N, Ye Q, et al. A possible reason for the anisotropic changes in apparent

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[4] Du X B, Liu Y W, Ni M K. On the spatial characteristic of the short-term and imminent

[5] Qian F Y, Zhao Y L, Yu M M. Anomalous changes in geoelectric resistivity before

[6] Qian J D, Chen Y F, Jin A Z. The Application of Geoelectrical Resistivity Method in

[7] Du X B. Two types of changes in apparent resistivity in earthquake prediction. Science in China-Series D, 2011, 54(1): 145~156 / doi: 10.1007/s11430-010-4031-y [8] Du X B, Ren G J, Xue S Z. Study on many kinds of precursory anomalies and trial

[9] Du X B, Ruan A G, Fan S H, et al. Anisotropy of the apparent resistivity variation rate

[10] Du X B, Xue S Z, Hao Z, et al. On the relation of moderate-short term anomaly of earth resistivity to earthquake. Acta Seismologic Sinica, 2000, 13: 393~403 [11] Du X B, Ma Z H, Ye Q, et al. Anisotropic changes in earth resistivity associated with

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earth resistivity to the active fault and generating-earthquake stress field. Acta

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**5. References** 

underground water comes fast in. The physical processes induce the TR changes which drop-type pattern occurs in a medium dilatancy stage and rise-type pattern does in a closure stage of micro cracks, and also induce the anisotropic TR changes in which the most prominent change appears along the maximum compressional stress direction. 4. In a homogeneous anisotropic medium, the AR change is in agreement with the TR change in drop-type or rise-type pattern, hence, a drop-type pattern of AR change appears in a medium dilatancy stage and a rise-type pattern appears in a closure stage of micro cracks. Because of the directional discrepancy with 90 angle between the most prominent TR change and the most prominent AR change, the anisotropic AR changes, in which the most prominent change appears perpendicular or nearly

In generally, <sup>f</sup> . From formulae (8), 1 1 <0 and 2 2 <0 when 0 , and they will decrease with going bigger, which could be why most AR anomalies in/nearby the epicenter region in the late preparation stages of strong EQs are commonly a drop-type pattern; And 1 1 >0 and 2 2 >0 when 0 , and they increase with decreasing. This is coincident with the physical analysis. Because 1 , in formulae

$$\text{(8)} \ \left| \begin{array}{c} \rho\_{\text{f}} - \rho\_{\text{o}} \\ \hline \rho\_{\text{o}}/\text{v} + \rho\_{\text{f}} \\ \hline \end{array} \right| < \left| \begin{array}{c} \rho\_{\text{f}} - \rho\_{\text{o}} \\ \hline \rho\_{\text{f}}/\text{v} + \rho\_{\text{o}} \\ \hline \end{array} \right| , \text{ so for } \ \Delta \mathbf{v}/\mathbf{v} > 0 \text{ and } \ \Delta \mathbf{v}/\mathbf{v} < 0 \text{ cases } \\ \begin{array}{c} \rho\_{2} \\ \hline \rho\_{2} \\ \hline \end{array} \Big/ \begin{array}{c} \Delta \mathbf{p}\_{1} \\ \hline \Delta \mathbf{p}\_{1} \\ \hline \end{array} \Big| $$

when the AR changes of channels X and Y, sx sx and sy sy , are all increased or decreased. This is coincident with the physical meaning of inequality (5). Let i i t

$$\langle \text{i} = 1, 2 \rangle, \text{the equation, } \frac{\dot{\rho}\_2}{\dot{\rho}\_1} \approx \frac{\rho\_\circ \rho\_\circ}{\left(\rho\_\circ \text{v} + \rho\_\circ\right)^2}, \text{ can be deduced. Thus we get that } \dot{\rho}\_2/\dot{\rho}\_1 \gtrsim 1 \text{ all the}$$

time. This is coincident with the physical meaning of inequality (7).

In general, it can be seen that anisotropic TR changes is obviously associated with <sup>f</sup> , and , which is clear in theory, and anisotropic AR changes arise from anisotropic TR changes. Therefore, the reason for AR changes and their anisotropic changes as well as their pattern (drop-type or rise-type) are clear in theory also.

#### **4. Conclusions**


underground water comes fast in. The physical processes induce the TR changes which drop-type pattern occurs in a medium dilatancy stage and rise-type pattern does in a closure stage of micro cracks, and also induce the anisotropic TR changes in which the most prominent change appears along the maximum compressional stress direction.

4. In a homogeneous anisotropic medium, the AR change is in agreement with the TR change in drop-type or rise-type pattern, hence, a drop-type pattern of AR change appears in a medium dilatancy stage and a rise-type pattern appears in a closure stage of micro cracks. Because of the directional discrepancy with 90 angle between the most prominent TR change and the most prominent AR change, the anisotropic AR changes, in which the most prominent change appears perpendicular or nearly perpendicular to the maximum loading direction, just appear.
