**4. ESR spectra of fault rocks**

In general, ESR spectra obtained from natural minerals present various phases, because they reflect multiple geological events having taken place during the long geological time. Especially, faults repeatedly move, so that the fault rocks have been influenced by multiple frictional heating events and show complicated ESR spectra consisting of overlapping multiple signals. Therefore, we must separate individual signals from the whole spectrum on the basis of the physical parameters such as the g-value or peak-to-peak linewidth. In this section, I will introduce some examples of magnetized fault rocks and attempt to identify the FMR signals detected from the fault rocks by comparing their physical parameters with those obtained from known ferrimagnetic minerals.

### **4.1 Nojima fault**

The Nojima fault is one of the most famous earthquake faults in Japan, which caused the 1995 Kobe earthquake (Magnitude 7.3). After the Kobe earthquake, the black fault rock with high magnetic susceptibility was found in the Nojima fault zone (Otsuki et al., 2003; Fukuchi, 2003). This fault rock consists of multiple sheets of a few mm wide veins, each of which was produced from granitic fault gouge during ancient earthquakes (Fig. 13). Despite no obvious melting textures, it was named "Nojima pseudotachylyte" as a descriptive name that comes from its glassy dark appearance and intrusive structure. Fig. 14 shows the ESR spectra obtained from the pseudotachylyte veins (PT-1 and PT-2) and baked fault gouge (GG-1) with the original fault gouge (NG-1) that is the source rock of the pseudotachylyte veins. Besides a

Fig. 13. Nojima pseudotachylyte veins in the Nojima fault zone.

specularite (Fig. 8b). On the other hand, pyrite is a cubic mineral and shows paramagnetism.

In general, ESR spectra obtained from natural minerals present various phases, because they reflect multiple geological events having taken place during the long geological time. Especially, faults repeatedly move, so that the fault rocks have been influenced by multiple frictional heating events and show complicated ESR spectra consisting of overlapping multiple signals. Therefore, we must separate individual signals from the whole spectrum on the basis of the physical parameters such as the g-value or peak-to-peak linewidth. In this section, I will introduce some examples of magnetized fault rocks and attempt to identify the FMR signals detected from the fault rocks by comparing their physical parameters with

The Nojima fault is one of the most famous earthquake faults in Japan, which caused the 1995 Kobe earthquake (Magnitude 7.3). After the Kobe earthquake, the black fault rock with high magnetic susceptibility was found in the Nojima fault zone (Otsuki et al., 2003; Fukuchi, 2003). This fault rock consists of multiple sheets of a few mm wide veins, each of which was produced from granitic fault gouge during ancient earthquakes (Fig. 13). Despite no obvious melting textures, it was named "Nojima pseudotachylyte" as a descriptive name that comes from its glassy dark appearance and intrusive structure. Fig. 14 shows the ESR spectra obtained from the pseudotachylyte veins (PT-1 and PT-2) and baked fault gouge (GG-1) with the original fault gouge (NG-1) that is the source rock of the pseudotachylyte veins. Besides a

The synthetic pyrite shows an intermediate spectrum of specularite and troillite.

**4. ESR spectra of fault rocks** 

**4.1 Nojima fault** 

those obtained from known ferrimagnetic minerals.

Fig. 13. Nojima pseudotachylyte veins in the Nojima fault zone.

Fig. 14. ESR spectra obtained from the Nojima pseudotachylyte veins and fault gouge.

Fig. 15. Variation of the ESR spectrum obtained from the Nojima fault gouge with step-bystep heating in air.

paramagnetic Fe3+ ion signal at g=4.25 and other paramagnetic signals derived from quartz or clay minerals between 300–400 mT, no FMR signal is detected from the original fault gouge (NG-1). This means that there originally existed no ferrimagnetic mineral inside the fault gouge, because the FMR signals derived from magnetite and maghemite are thermally so stable, as shown in Figs. 5–7, that they cannot perfectly disappear by later frictional heating or the oxidation caused by the heating. The g-values and peak-to-peak linewidths of the signals detected from the black veins and baked gouge are 2.13–2.28 and 102–155 mT, respectively. Hence, these signals have almost the same physical parameters as the superparamagnetic signals detected from heated lepidocrocite rather than maghemite with high crystallinity or one produced by the oxidation of magnetite (Figs. 6, 7, 9 and 10).

Moreover, Fig. 15 shows the variation of the ESR spectrum obtained from the original fault gouge (NG-1) by step-by-step heating (5 min.) in air (Fig. 14a). The g-value and peak-topeak linewidth of the signals detected by heating are 2.17–2.23 and 102–128 mT, so that they are consistent with those detected from the Nojima fault rocks and from the superparamagnetic signals of baked lepidocrocite. This strongly suggests that the magnetic source of the Nojima pseudotachylyte and baked gouge may be superparamagnetic maghemite produced by thermal dehydration of lepidocrocite, and besides that the Nojima pseudotachylyte may have been produced in an oxidizing environment.

#### **4.2 Uchinoura shear zone**

The Uchinoura shear zone is distributed in the Middle Miocene Osumi granodiorite pluton, which is located at the southern end of the Kyushu Island in Japan about 170 km away from the Nankai Trough subduction zone, and consists of a series of ENE trending faults (Fabbri et al., 2000). Along the Uchinoura shear zone, pseudotachylyte veins are exposed with cataclastic rocks such as foliated cataclasite. Fig. 16 shows a photograph of the black pseudotachylyte vein (PT) intruded into foliated cataclasite (FC). ESR spectra obtained from the Osumi granodiorite (OG), foliated calaclasite (FC) and pseudotachylyte vein (PT) are shown in Fig. 17. The Osumi granodiorite has a paramagnetic Fe3+ ion signal at g=4.23 and another paramagnetic signal between 300–400 mT similar to the signal of goethite and/or hematite (Fig. 8). On the other hand, the foliated cataclasite and pseudotachylyte vein have an FMR signal with the g-value of 2.57–2.88 and the peak-topeak linewidth of 218–223 mT. These physical parameters obtained from the fault rocks are consistent with those from magnetite, and indeed we can detect similar FMR signals by heating biotite in the Osumi granodiorite over 800–1000°C in vacuum (Fig. 4c). For producing magnetite from biotite by heating in vacuum, high temperatures over 600– 800°C are necessary, while biotite can be easily oxidized by heating in air and changes into hematite without producing magnetite. The ESR data indicate that the pseudotachylyte veins along the Uchinoura shear zone may have been formed by frictional heating in a reducing environment at depths.

Fig. 16. Pseudotachylyte veins distributed along the Uchinoura shear zone.

Fig. 17. ESR spectra obtained from the Osumi granite, foliated cataclasite and pseudotachylyte veins distributed along the Uchinoura shear zone.

#### **4.3 Taiwan Chelungpu fault**

330 Earthquake Research and Analysis – Seismology, Seismotectonic and Earthquake Geology

peak linewidth of the signals detected by heating are 2.17–2.23 and 102–128 mT, so that they are consistent with those detected from the Nojima fault rocks and from the superparamagnetic signals of baked lepidocrocite. This strongly suggests that the magnetic source of the Nojima pseudotachylyte and baked gouge may be superparamagnetic maghemite produced by thermal dehydration of lepidocrocite, and besides that the Nojima

The Uchinoura shear zone is distributed in the Middle Miocene Osumi granodiorite pluton, which is located at the southern end of the Kyushu Island in Japan about 170 km away from the Nankai Trough subduction zone, and consists of a series of ENE trending faults (Fabbri et al., 2000). Along the Uchinoura shear zone, pseudotachylyte veins are exposed with cataclastic rocks such as foliated cataclasite. Fig. 16 shows a photograph of the black pseudotachylyte vein (PT) intruded into foliated cataclasite (FC). ESR spectra obtained from the Osumi granodiorite (OG), foliated calaclasite (FC) and pseudotachylyte vein (PT) are shown in Fig. 17. The Osumi granodiorite has a paramagnetic Fe3+ ion signal at g=4.23 and another paramagnetic signal between 300–400 mT similar to the signal of goethite and/or hematite (Fig. 8). On the other hand, the foliated cataclasite and pseudotachylyte vein have an FMR signal with the g-value of 2.57–2.88 and the peak-topeak linewidth of 218–223 mT. These physical parameters obtained from the fault rocks are consistent with those from magnetite, and indeed we can detect similar FMR signals by heating biotite in the Osumi granodiorite over 800–1000°C in vacuum (Fig. 4c). For producing magnetite from biotite by heating in vacuum, high temperatures over 600– 800°C are necessary, while biotite can be easily oxidized by heating in air and changes into hematite without producing magnetite. The ESR data indicate that the pseudotachylyte veins along the Uchinoura shear zone may have been formed by

pseudotachylyte may have been produced in an oxidizing environment.

frictional heating in a reducing environment at depths.

Fig. 16. Pseudotachylyte veins distributed along the Uchinoura shear zone.

**4.2 Uchinoura shear zone** 

The Taiwan Chelungpu fault moved in the 1999 Chi-Chi earthquake (Magnitude 7.6), which occurred in the collision zone of the Eurasian and Philippine Sea plates. After the earthquake, the Taiwan Chelungpu Fault Drilling Project (TCDP) was launched in 2002 to elucidate the rupture process caused in a subduction seismogenic zone, and continuous drill cores were collected from two main boreholes (Holes A and B) penetrating through the Chelungpu fault plane at depths (Ma et al, 2006). In the Hole B cores, there are three major fault zones at about 1136 m, 1194 m and 1243 m depths, in which a black material zone respectively exists. The black material zone is considered to have been formed by frictional heating (Hirono et al., 2006). Fig. 18 shows the black material zone in the 1194 m major fault zone. Black fault gouge exists along with the black indurated material, which may have been produced by frictional melting. Fig. 19 shows ESR spectra obtained from the black and gray gouges and black indurated material. Besides a paramagnetic Fe3+ ion signal (g=4.23) and an organic radical (g=2.004) (Fukuchi et al., 2007), a broad signal (g=2.27–2.44 and

Fig. 18. Black material zone distributed at about 1194 m depth in the TCDP Hole B cores.

Fig. 19. ESR spectra obtained from the black material zone Taiwan Chelungpu fault zone.

*ΔHpp*=150–173 mT) is detected from one black gouge and the gray gouge (BG1 and GG-1), while two types of large signal (g=8.48–9.47 and g=2.45–2.52) are detected from the black indurated material (BM-1) and another black gouge (BG-2). The broad signal at g=2.27–2.44 may be identified with the FMR signal of maghemite produced from lepidocrocite and/or hematite, while the lineshape of the large signal at g=8.48–9.47 is similar to that of the signal with g=10.8 obtained from specularite (Figs. 8 and 9). On the other hand, the signal at g=2.45–2.52 has the peak-to-peak linewidth of 114–123 mT, so that it may be derived from maghemite produced from lepidocrocite, goethite or hematite produced from goethite (Figs. 10 and 11). These results suggest that the black material zone may have been repeatedly subjected to frictional heating in an oxidizing environment.

#### **5. Basic equations for frictional heat analysis**

Coseismic frictional heat can be detected by measuring FMR signals in fault rocks. To calculate the frictional heat from FMR signals, we need the chemical kinetics for FMR signals besides the diffusion equations of frictional heat. As mentioned above, there are mainly two FMR signals derived from maghemite and magnetite among the FMR signals detected from natural fault rocks. Although the two FMR signals have different g-values, peak-to-peak linewidths and lineshapes, the growth processes of these signals are essentially based on the same mechanism, that is, the thermal decomposition and grain growth during heating, and are fundamentally expressed by the zero-order kinetic equation (Fukuchi, 2003). Actual fault rocks may have a mixed signal of the two FMR signals with other paramagnetic or antiferromagnetic signals, so that we must experimentally investigate the chemical kinetics on every fault rock. In this section, I will explain the basic equations necessary for calculating the frictional heat from FMR signals by inversion.

#### **5.1 Chemical kinetics of ESR signals**

There are a lot of studies on the chemical kinetics of ESR signals detected from paramagnetic minerals in connection with luminescence emitted from them. ESR signals derived from electrons or holes trapped at lattice defects in paramagnetic minerals commonly decay with

Fig. 19. ESR spectra obtained from the black material zone Taiwan Chelungpu fault zone.

subjected to frictional heating in an oxidizing environment.

**5. Basic equations for frictional heat analysis** 

by inversion.

**5.1 Chemical kinetics of ESR signals** 

*ΔHpp*=150–173 mT) is detected from one black gouge and the gray gouge (BG1 and GG-1), while two types of large signal (g=8.48–9.47 and g=2.45–2.52) are detected from the black indurated material (BM-1) and another black gouge (BG-2). The broad signal at g=2.27–2.44 may be identified with the FMR signal of maghemite produced from lepidocrocite and/or hematite, while the lineshape of the large signal at g=8.48–9.47 is similar to that of the signal with g=10.8 obtained from specularite (Figs. 8 and 9). On the other hand, the signal at g=2.45–2.52 has the peak-to-peak linewidth of 114–123 mT, so that it may be derived from maghemite produced from lepidocrocite, goethite or hematite produced from goethite (Figs. 10 and 11). These results suggest that the black material zone may have been repeatedly

Coseismic frictional heat can be detected by measuring FMR signals in fault rocks. To calculate the frictional heat from FMR signals, we need the chemical kinetics for FMR signals besides the diffusion equations of frictional heat. As mentioned above, there are mainly two FMR signals derived from maghemite and magnetite among the FMR signals detected from natural fault rocks. Although the two FMR signals have different g-values, peak-to-peak linewidths and lineshapes, the growth processes of these signals are essentially based on the same mechanism, that is, the thermal decomposition and grain growth during heating, and are fundamentally expressed by the zero-order kinetic equation (Fukuchi, 2003). Actual fault rocks may have a mixed signal of the two FMR signals with other paramagnetic or antiferromagnetic signals, so that we must experimentally investigate the chemical kinetics on every fault rock. In this section, I will explain the basic equations necessary for calculating the frictional heat from FMR signals

There are a lot of studies on the chemical kinetics of ESR signals detected from paramagnetic minerals in connection with luminescence emitted from them. ESR signals derived from electrons or holes trapped at lattice defects in paramagnetic minerals commonly decay with time on heating and their decay processes may be expressed by the 1st, 2nd order or other kinetic model (Fukuchi, 1989, 1992; Fukuchi & Imai, 2001; Ikeya, 1993). On the other hand, the chemical kinetics of FMR signals has been studied using the FMR signal of maghemite in the Nojima fault gouge (Fukuchi, 2003; Fukuchi et al., 2005). The FMR signal of maghemite grows with the thermal decomposition of lepidocrocite and the grain growth of maghemite during heating. As shown in Fig. 10, the signal intensity increases with time on heating and its growth process follows the zero-order reaction kinetics; *dI*/*dt*=*a*, where *I* is the FMR signal intensity, *t* is time and *a* is the velocity constant. *a* is equivalent to the slope of the growth line of the FMR signal; *I*=*at*. When the temperature *T* is constant, *a* is expressed by the Arrhenius' equation; *a*=*ν*exp[–*E*/*RT*], where *ν* is the frequency factor, *E* is apparent activation energy and *R* is the gas constant. Now we consider one-dimensional thermal conduction. When the temperature changes with distance *x* and time *t*, the velocity constant *a*(*x*,*t*) is expressed by

$$a(\mathbf{x}, t) = \nu \exp\left[-\frac{E}{RT(\mathbf{x}, t)}\right] \tag{1}$$

where *T*(*x*,*t*) is the temperature at distance *x* and time *t*. When we deal with seismic frictional heating, *T*(*x*,*t*) means the frictional heat temperature at a distance from a fault plane (*x*=0) and a passing time *t* after earthquake rupture. If we set the FMR signal intensity as *I*(*x*,*t*), *∂I*(*x*,*t*) /*∂t*=*a*(*x*,*t*). Then, *I*(*x*,*t*) is expressed by

$$I(\mathbf{x},t) = \int\_{\mathbf{0}}^{t} a(\mathbf{x},t)dt = \int\_{\mathbf{0}}^{t} \nu \exp\left[-\frac{E}{RT(\mathbf{x},t)}\right]dt\tag{2}$$

*ν* and *E* are experimentally determined from the Arrhenius plot of velocity constants measured at various temperatures (Fukuchi, 2003). In actual frictional heat analysis, we must collect the fault rock sample with a finite thickness. Therefore, when the sampling thickness is *w*0, the mean FMR signal intensity *F* (*w*0, *x*, *t*) between the distances of *x* and *x*+*w*0 from the fault plane is expressed as follows (Fukuchi et al., 2005):

$$F(w\_0, x, t) = \frac{1}{w\_0} \int\_{\mathbf{x}}^{x + w\_0} I(\mathbf{x}, t) d\mathbf{x} = \frac{1}{w\_0} \int\_{\mathbf{x}}^{x + w\_0} \int\_0^t a(\mathbf{x}, t) dt d\mathbf{x} = \frac{1}{w\_0} \int\_{\mathbf{x}}^{x + w\_0} \int\_{\mathbf{0}}^t \nu \exp\left[ -\frac{E}{RT(\mathbf{x}, t)} \right] dt d\mathbf{x} \tag{3}$$

#### **5.2 One-dimensional diffusion models of frictional heat**

As for the temperature during seismic frictional heating, some one-dimensional diffusion models of frictional heat have been proposed (e.g. McKenzie & Brune, 1972; Cardwell et al., 1978). According to McKenzie & Brune (1972), the equation for the diffusion of frictional heat is expressed by

$$
\rho \mathbf{C}\_p \frac{\partial \mathbf{T}}{\partial \mathbf{t}} = \mathbf{k}^\* \frac{\partial^2 \mathbf{T}}{\partial \mathbf{x}^2} + Q(\mathbf{x}, \mathbf{t}) \tag{4}
$$

where *ρ* is the density, *Cp* is the specific heat, *k*\* is the thermal conductivity, and *Q* is the frictional heat generation per unit volume and time. When we assume that *T*=*T*0 and *Q*=0 for *t*<0, the solution of eq.4 can be written down as follows:

$$T(\mathbf{x},t) = T\_0 + \frac{1}{2\rho C\_p \sqrt{\pi K}} \left[ \frac{t}{0} \right]\_{-\infty}^{\infty} \exp\left[ -\frac{(\mathbf{x} - \mathbf{x}\_0)^2}{4K(t - t\_0)} \right] \frac{Q(\mathbf{x}\_0, t\_0)}{\sqrt{t - t\_0}} dx\_0 dt\_0 \tag{5}$$

where *K* is the thermal diffusivity (*K*=*k*\*/*ρCp*). When we further assume that the frictional heat generation is restricted to a fault plane, *Q* is expressed by

$$\begin{aligned} Q(\mathbf{x}\_0, t\_0) &= 0 & \quad \text{( $t\_0 < 0, t\_0 > t\_1$ )}\\ &= \delta(\mathbf{x}\_0) \frac{\sigma\_f D}{t\_1} & \quad \text{( $0 \le t\_0 \le t\_1$ )} \end{aligned} \tag{6}$$

where *δ*(*x*0) is the Dirac delta function, *σf* is the frictional shear stress, *D* is the displacement, and *t*1 is the slip duration (McKenzie & Brune, 1972). Then, eq.5 is expressed as follows:

$$T(\mathbf{x},t) = T\_0 + \frac{\sigma\_f D}{\rho \mathbf{C}\_p t\_1} \left\{ \sqrt{\frac{t}{\pi K}} \exp\left[ -\frac{\mathbf{x}^2}{4Kt} \right] - \frac{\mathbf{x}}{2K} \text{erfc}\left[ -\frac{\mathbf{x}}{2\sqrt{Kt}} \right] \right\}, \qquad 0 \le t \le t\_1$$

$$= T\_0 + \frac{\sigma\_f D}{\rho \mathbf{C}\_p t\_1} \left[ \left\{ \sqrt{\frac{t}{\pi K}} \exp\left[ -\frac{\mathbf{x}^2}{4Kt} \right] - \sqrt{\frac{t-t\_1}{\pi K}} \exp\left[ -\frac{\mathbf{x}^2}{4K(t-t\_1)} \right] \right\} \tag{7}$$

$$- \frac{\mathbf{x}}{2K} \left\{ \text{erfc}\left[ -\frac{\mathbf{x}}{2\sqrt{Kt}} \right] - \text{erfc}\left[ -\frac{\mathbf{x}}{2\sqrt{K(t-t\_1)}} \right] \right\} \Big|\_{} \qquad t > t\_1$$

On the other hand, when we assume that the frictional heat is generated with a finite thickness, *Q* is expressed by

$$\begin{aligned} Q(\mathbf{x}\_0, t\_0) &= 0 & \{t\_0 < 0, t\_0 > t\_1\} \\ &= \frac{\sigma\_f D}{wt\_1} \left[ H\left(\mathbf{x}\_0 + \frac{w}{2}\right) - H\left(\mathbf{x}\_0 - \frac{w}{2}\right) \right] & \{0 \le t\_0 \le t\_1\} \end{aligned} \tag{8}$$

where *w* is the width of heat generation and *H* is the Heavyside step function (Cardwell et al., 1978). Then, eq.5 is expressed as follows:

$$\begin{split} T(\mathbf{x}, t) &= T\_0 + \frac{\sigma\_f D}{2\rho C\_p w t\_1} \int\_0^t \left| \text{erf} \left[ \frac{\mathbf{x} + (\mathbf{w} \ / 2)}{\sqrt{4K(t - t\_0)}} \right] - \text{erf} \left[ \frac{\mathbf{x} - (\mathbf{w} \ / 2)}{\sqrt{4K(t - t\_0)}} \right] \right| dt\_0, \quad 0 \le t \le t\_1 \\ &= T\_0 + \frac{\sigma\_f D}{2\rho C\_p w t\_1} \int\_0^{t\_1} \left| \text{erf} \left[ \frac{\mathbf{x} + (\mathbf{w} \ / 2)}{\sqrt{4K(t - t\_0)}} \right] - \text{erf} \left[ \frac{\mathbf{x} - (\mathbf{w} \ / 2)}{\sqrt{4K(t - t\_0)}} \right] \right| dt\_0, \quad t > t\_1 \end{split} \tag{9}$$

Since the frictional heat temperature calculated from eq.9 begins to diverge to infinity when *w*<0.5 mm (Fukuchi et al., 2005), then we should use eq.7 in place of eq.9.

The maximum temperature rise *ΔT* at *t*=*t*1 and *x*=0 obtained from eq.7 is expressed as follows (McKenzie & Brune, 1972):

$$
\Delta T = T\_m - T\_0 = \frac{\sigma\_f D}{\rho C\_p \sqrt{\pi K t\_1}} \tag{10}
$$

where *Tm* is the maximum temperature. Eq.10 is valid when *w*≈0. On the other hand, when *w*≥0.5 mm, the maximum temperature rise *ΔT* at *t*=*t*1 and *x*=0 obtained from eq.9 is expressed by

$$
\Delta T = T\_m - T\_0 = \frac{\sigma\_f D}{\rho C\_p w} \tag{11}
$$

#### **5.3 Frictional heat energy**

334 Earthquake Research and Analysis – Seismology, Seismotectonic and Earthquake Geology

where *K* is the thermal diffusivity (*K*=*k*\*/*ρCp*). When we further assume that the frictional

0 0 0 01

*D x tt*

( , ) 0 ( 0, )

*Qx t t tt*

1

*t* 

where *δ*(*x*0) is the Dirac delta function, *σf* is the frictional shear stress, *D* is the displacement, and *t*1 is the slip duration (McKenzie & Brune, 1972). Then, eq.5 is expressed as follows:

> 2 ( ,) , 0 0 1 4 2 <sup>2</sup> <sup>1</sup>

*<sup>D</sup> t t <sup>f</sup> t x <sup>x</sup> <sup>T</sup>*

*Df t xx x Txt T erfc t t C t K Kt K Kt <sup>p</sup>*

<sup>0</sup> <sup>4</sup> 4( ) 1 1

On the other hand, when we assume that the frictional heat is generated with a finite

0 0 0 01

where *w* is the width of heat generation and *H* is the Heavyside step function (Cardwell et

( ,)0 ( 0, )

*Qx t t tt*

( /2) ( /2) ( ,) , 0 <sup>2</sup> 4( ) 4( )

*<sup>D</sup> xw xw Txt T erf erf dt t t C wt Kt t Kt t*

*C t K Kt K K t t*

*exp exp*

<sup>1</sup> ( ) ( ,) ( ,) exp <sup>2</sup> <sup>0</sup> 4( ) *<sup>p</sup> x x Qx t Txt T dx dt C K Kt t t t*

*t*

<sup>2</sup> 2 2( ) <sup>1</sup>

*exp*

*xx x erfc erfc <sup>K</sup> Kt Kt t*

 

heat generation is restricted to a fault plane, *Q* is expressed by

*p*

1

1

*w*<0.5 mm (Fukuchi et al., 2005), then we should use eq.7 in place of eq.9.

0

*t*

0

*t*

*f*

*wt* 

al., 1978). Then, eq.5 is expressed as follows:

*f p*

follows (McKenzie & Brune, 1972):

*f p* thickness, *Q* is expressed by

 

0 0 0

0 0 1

( ) (0 ) *<sup>f</sup>*

2 0 00

2 2 1

 

00 0 1

*<sup>D</sup> w w Hx Hx t t*

0 0 1 1 0 0

 

0 0 1 1 0 0

( /2) ( /2) , <sup>2</sup> 4( ) 4( )

Since the frictional heat temperature calculated from eq.9 begins to diverge to infinity when

The maximum temperature rise *ΔT* at *t*=*t*1 and *x*=0 obtained from eq.7 is expressed as

0

*m*

*TT T*

*<sup>D</sup> xw xw <sup>T</sup> erf erf dt t t C wt Kt t Kt t*

(0 ) 2 2

1

(10)

*f*

*C Kt* 

 

*D*

*p*

0 0

(6)

(7)

(8)

(9)

, <sup>1</sup> *t t*

(5)

The product of the frictional shear stress and displacement, that is, *σ<sup>f</sup> D* in eqs.6−11 is equivalent to the frictional heat energy per unit area *φH*. In case of large earthquakes, frictional heat is most probably generated with a finite thickness of slip zone; *w*≫0. Then, the relationship between *φH* and *w* for a fault can be expressed by Eq.11 and *φH* is proportional to *w* (Fig.20). When we regard *Tm* as a melting point, *φH* means the frictional melting energy per unit area *φM*. Therefore eq.11 can give constraints on the relationship between *φM* and *w*. Once frictional melting occurs in a shear zone, the temperature of melt is maintained at a melting point until the materials in the shear zone are completely molten because the subsequent frictional heat should be consumed as latent heat. In addition, once frictional melting occurs, the friction coefficient immediately drops towards zero (Di Toro et al., 2004). Thus, *Tm* should not be beyond the melting point and besides *φH* should not be beyond *φM*. On the other hand, *φ<sup>H</sup>* increases with increasing the depth of the fault because *σ<sup>f</sup>* is proportional to the normal stress *σn* when the coefficient of friction is constant over the fault plane. This means that *φH* per unit depth, that is, the frictional heat energy per unit volume *ψH* is more meaningful than *φH*. When *ψH* is constant over the fault plane, the mean value *<sup>H</sup>* of *φH* for a fault is expressed using the focal depth *z*0 as follows:

0 0 <sup>0</sup> <sup>0</sup> 1 2 *<sup>z</sup> <sup>H</sup> H H <sup>z</sup> zdz z* (12)

Fukuchi et al. (2005) estimated the frictional heat energy for the Nojima fault using the FMR signal detected from the fault gouge in the Nojima fault 500m drill cores. The *φH* value of the

Fig. 20. Relationship between frictional heat energy and the width of heat generation.

Nojima fault at about 390 m in depth was calculated at 20.61 MJ/m2 with the *w* value of 14 mm by inversion using eqs.3 and 7 or 9. However, the Nojima fault has moved frequently during the Quaternary period, so that the value obtained means the total frictional heat energy since the formation of the fault gouge. According to the geological analysis of the 500 drill cores, the total uplift along the fault plane at about 390m in depth was estimated at about 230 m (Murata et al. 2001). Therefore, the *φH* value per unit faulting may be calculated at about 0.18 MJ/m2 when the displacement is 2.0 m compatible with that in the 1995 Kobe earthquake. Then, the *ψH* value may be estimated at about 460 J/m3 and the *<sup>H</sup>* value be calculated at 3.68 MJ/m2 from eq.12 when *z*0 is set as 16 km.

#### **6. Scanning ESR microscopy**

When we estimate the frictional heat by inversion using eqs.3 and 7 or 9, we need the sequential data of FMR signal along the fault plane. In addition, we must determine the width of heat generation, that is, the thickness of the slip zone on which the frictional heat strongly depends as shown by eq.9. The thickness of the slip zone is considered to be commonly an order of millimeters or less (Sibson, 2003). Therefore, we need the sequential data of FMR signal along the fault plane at a high-resolution of ≤1mm. However it is difficult to measure them using an ordinary ESR spectrometer for grain or powder samples (Fig.2). In this section, I will explain the scanning ESR microscopic technique for sequential high-resolution measurements of FMR signals.

In magnetic resonance, there are two physical quantities for spatially scanning, the external magnetic field and microwaves, however it is technically easier to locally measure ESR signals in the immediate vicinity of the surface of a sample by scanning localized microwave magnetic field leaking out of an aperture of the microwave cavity in a fixed external magnetic field. The scanning of localized microwaves can be carried out by shifting the sample using a mechanical X-Y stage with stepping motors controlled by a computer (Ikeya, 1991). Fig. 21 shows the TE111 mode cavity with a pinhole of 2.6 mm φ in diameter (Yamanaka et al., 1992). Ordinary ESR cavities have coils for 100 kHz field modulation inside, however in case of the scanning ESR microscope an external coil for 100 kHz field modulation is set above the pinhole cavity. The sample chip whose surface has been polished using 1 μm-diamond paste is put on the pinhole and the sample arm with the sample is shifted using the mechanical X-Y stage. Since the ESR spectrometer gives a first derivative line, we obtain the ESR absorption curve by integrating the first derivative curve with the magnetic field (Fig. 3). The area of the ESR absorption curve is theoretically proportional to the concentration of unpaired electrons in the sample and magnetic susceptibility. Thus, I set the value obtained by integrating the ESR absorption curve once more as the ESR absorption intensity. The FMR signal intensity is defined as the ESR absorption intensity obtained by integrating the ESR spectrum twice within the range of magnetic field where the FMR signal is detected.

The ESR absorption intensity *Ir*(*x*,*t*) detected by the ESR cavity with a pinhole of radius *r* at distance *x* and time *t* is obtained by integrating the whole absorption intensity within the hemispheric domain *V* with the volume of 2π*r*3/3; the center of the hemisphere is located at distance *x*.

$$I\_r(\mathbf{x}, t) = \iiint\_V I(\mathbf{x}, t)dV = \iiint\_V \int\_0^t \nu \exp\left[-\frac{E}{RT(\mathbf{x}, t)}\right] dt dV \tag{13}$$

Nojima fault at about 390 m in depth was calculated at 20.61 MJ/m2 with the *w* value of 14 mm by inversion using eqs.3 and 7 or 9. However, the Nojima fault has moved frequently during the Quaternary period, so that the value obtained means the total frictional heat energy since the formation of the fault gouge. According to the geological analysis of the 500 drill cores, the total uplift along the fault plane at about 390m in depth was estimated at about 230 m (Murata et al. 2001). Therefore, the *φH* value per unit faulting may be calculated at about 0.18 MJ/m2 when the displacement is 2.0 m compatible with that in the 1995 Kobe

When we estimate the frictional heat by inversion using eqs.3 and 7 or 9, we need the sequential data of FMR signal along the fault plane. In addition, we must determine the width of heat generation, that is, the thickness of the slip zone on which the frictional heat strongly depends as shown by eq.9. The thickness of the slip zone is considered to be commonly an order of millimeters or less (Sibson, 2003). Therefore, we need the sequential data of FMR signal along the fault plane at a high-resolution of ≤1mm. However it is difficult to measure them using an ordinary ESR spectrometer for grain or powder samples (Fig.2). In this section, I will explain the scanning ESR microscopic technique for sequential

In magnetic resonance, there are two physical quantities for spatially scanning, the external magnetic field and microwaves, however it is technically easier to locally measure ESR signals in the immediate vicinity of the surface of a sample by scanning localized microwave magnetic field leaking out of an aperture of the microwave cavity in a fixed external magnetic field. The scanning of localized microwaves can be carried out by shifting the sample using a mechanical X-Y stage with stepping motors controlled by a computer (Ikeya, 1991). Fig. 21 shows the TE111 mode cavity with a pinhole of 2.6 mm φ in diameter (Yamanaka et al., 1992). Ordinary ESR cavities have coils for 100 kHz field modulation inside, however in case of the scanning ESR microscope an external coil for 100 kHz field modulation is set above the pinhole cavity. The sample chip whose surface has been polished using 1 μm-diamond paste is put on the pinhole and the sample arm with the sample is shifted using the mechanical X-Y stage. Since the ESR spectrometer gives a first derivative line, we obtain the ESR absorption curve by integrating the first derivative curve with the magnetic field (Fig. 3). The area of the ESR absorption curve is theoretically proportional to the concentration of unpaired electrons in the sample and magnetic susceptibility. Thus, I set the value obtained by integrating the ESR absorption curve once more as the ESR absorption intensity. The FMR signal intensity is defined as the ESR absorption intensity obtained by integrating the ESR spectrum twice within the range of

The ESR absorption intensity *Ir*(*x*,*t*) detected by the ESR cavity with a pinhole of radius *r* at distance *x* and time *t* is obtained by integrating the whole absorption intensity within the hemispheric domain *V* with the volume of 2π*r*3/3; the center of the hemisphere is located at

(13)

<sup>0</sup> ( ,) (,) exp ( ,) *<sup>r</sup> <sup>t</sup> <sup>E</sup> I x t I x t dV dtdV <sup>V</sup> <sup>V</sup> RT x t* 

*<sup>H</sup>* value be

earthquake. Then, the *ψH* value may be estimated at about 460 J/m3 and the

calculated at 3.68 MJ/m2 from eq.12 when *z*0 is set as 16 km.

**6. Scanning ESR microscopy** 

high-resolution measurements of FMR signals.

magnetic field where the FMR signal is detected.

distance *x*.

Fig. 21. TE111 mode cavity with a pinhole of 2.6 mm φ.

Fig. 22. A 2-D ESR map obtained from the Nojima pseudotachylyte.

Fig. 22 shows a 2-Dimensional ESR map obtained from the sample chip of the Nojima pseudotachylyte. The highest intensity is obtained from the pseudotachylyte vein (PT-1) (Fig. 14). On the other hand, Fig. 23 shows a 1-Dimensional profile obtained from the sample chip along the measuring line X-X'. Measurement conditions are as follows: microwave frequency; 9.388 GHz, microwave power; 100 mW, modulation width; 100 kHz 0.32 mT, scanning speed; 10 s/sweep (2-D) or 2.0 min./sweep (1-D), scan step; 0.25 mm, accumulation; 1 time (2-D) or 3 times (1-D), measurement temperature; room temperature. As shown in Fig. 23, the FMR signals of maghemite are sequentially detected at a resolution of 0.25 mm from the Nojima pseudotachylyte. On the other hand, the detection sensitivity of the scanning ESR microscope is much lower than the ordinary ESR spectrometer. Since the resolution of the scanning ESR microscope depends on the detection sensitivity, at this stage the limit of resolution is about 0.25 mm.

Fig. 23. A 1-D profile obtained from the Nojima pseudotachylyte.
