Specific heat capacity and thermal diffusivity and their temperature dependencies in a rock sample from adjacent to the Taiwan Chelungpu fault

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1 Click Here for Full Article JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2009jb006816, 2010 Specific heat capacity and thermal diffusivity and their temperature dependencies in a rock sample from adjacent to the Taiwan Chelungpu fault Tetsuro Hirono 1 and Yohei Hamada 1 Received 23 July 2009; revised 10 December 2009; accepted 12 January 2010; published 29 May [1] Determination of the specific heat capacity and thermal diffusivity of rock samples, together with their temperature dependencies, is crucial for estimation of frictional heating during an earthquake. We measure these properties of a rock sample taken adjacent to the Taiwan Chelungpu fault, which slipped during the 1999 Chi Chi earthquake, by differential scanning calorimetry and by using a laser flash apparatus. We also evaluate the temperature dependencies of these properties up to 1000 C and 800 C, respectively, and determine their fitting equations. The specific heat capacity of the sample peaks at around 565 C, and the thermal diffusivity decreases with increasing temperature to 600 C but is almost constant in the temperature range of 600 C 800 C. These changes at around 550 C 600 C probably result from the a b phase transition of quartz, of which the sample is dominantly composed. We then perform a numerical analysis, adopting these values of specific heat capacity and thermal diffusivity along with their temperature dependencies, to reestimate dynamic shear stress and earthquake energetics during the Chi Chi earthquake. In this way, we determine the residual shear stress after the stress drop to be 9.0 MPa and the energy taken up by coseismic chemical reactions to be 10.4 MJ m 2, corresponding to 12.1% of the given work on the fault and tending to counteract the frictional heating. Citation: Hirono, T., and Y. Hamada (2010), Specific heat capacity and thermal diffusivity and their temperature dependencies in a rock sample from adjacent to the Taiwan Chelungpu fault, J. Geophys. Res., 115,, doi: /2009jb Introduction [2] Coseismic slip during an earthquake is expected to be accompanied by frictional heating on the fault, and the transiently reached high temperature can affect the slip behavior itself. Increased temperature on the fault can induce pressurization of interstitial fluid by thermal expansion and melting of minerals, and these changes, known as thermal pressurization [Sibson, 1973; Lachenbruch, 1980; Andrews, 2002] and melt lubrication [Hirose and Shimamoto, 2005; Spray, 2005], respectively, play a role in dynamic fault weakening. In fact, in the case of the Taiwan Chelungpu fault, which slipped during the 1999 Chi Chi earthquake (M w 7.6) [Ma et al., 1999], geochemical evidence indicates that high temperature fluid existed during the earthquake because marked anomalies of fluid mobile trace elements (Sr, Cs, Rb, and Li) and the Sr isotope were discovered [Ishikawa et al., 2008]. Thus, thermal pressurization potentially played a significant role during the earthquake. Tanikawa and Shimamoto [2009] and Tanikawa et al. [2009] performed a numerical analysis of the thermal pressurization 1 Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Japan. Copyright 2010 by the American Geophysical Union /10/2009JB mechanism during the earthquake by using experimentally determined values for the frictional and transport properties of samples from the Taiwan Chelungpu Fault Drilling Project (TCDP). Their results support the inference that thermal pressurization contributed to fault weakening during the earthquake. [3] On the other hand, increased temperature on the fault not only contributes to fault weakening but also affects earthquake energetics. Frictional heat constitutes the largest part of the total energy released from a fault at the time of an earthquake [e.g., Scholz, 2002]. Other forms of the partitioned total energy are energy radiated as seismic waves and fracture energy, which creates the rupture surface [e.g., Tinti et al., 2005; Kanamori and Rivera, 2006]. Determination of the energy budget is fundamental for understanding the physics of earthquakes, and recent seismological investigations and geological observations have sought to estimate these energies [e.g., Venkantaraman and Kanamori, 2004; Chester et al., 2005]. Recently, Pittarello et al. [2008] estimated the values of frictional heat and fracture energy in pseudotachylyte bearing faults within the Gole Larghe Fault Zone, Adamello, Italy, on the basis of field and microstructural analyses, and Hamada et al. [2009a, 2009b] evaluated the heat taken up by coseismic chemical reactions transiently induced by frictional heating during the Chi Chi earthquake. Especially, the amounts of fracture energy and 1of13

2 energy taken up by chemical reactions relative to the total work on the fault are crucial to the earthquake energetics because energy in these forms can reduce the energy available for the temperature rise, thus affecting frictional heating on the fault. [4] For evaluations of dynamic fault weakening and earthquake energetics related to frictional heating, the thermal properties of the rock sample are fundamental parameters, the values of which are needed for numerical analyses. The specific heat capacity (the heat energy required to increase the temperature of a unit quantity of a substance) of a fault related rock sample must be known in order to convert given work ( = shear stress slip distance) to the temperature rise on the fault. Thermal diffusivity is also important because heat diffusion from the fault always occurs, not only after the slip but also during the slip. However, in previous evaluations of frictional heat generation, these thermal properties are rarely constrained by measurement. In addition, in a multicomponent material such as a rock sample, these properties depend not only on temperature and pressure but also on the sample composition (that is, on each component and its mass fraction). In the case of the Taiwan Chelungpu fault, only Tanaka et al. [2007] measured the thermal conductivity and thermal diffusivity of a rock sample from the Chelungpu fault, but they did not consider the temperature dependencies of these properties. Hamada et al. [2009a, 2009b] calculated the specific heat capacity of a rock sample from the Chelungpu fault, taking into consideration the rock s composition and the temperature dependency of the specific heat capacity, but they did not measure the value directly on the rock sample. Although Hamada et al. [2009a, 2009b] evaluated dynamic shear stress and energetics during the Chi Chi earthquake, their reestimation using measured values of specific heat capacity and thermal diffusivity of a sample along with their temperature dependencies is needed. [5] Therefore, we first measure the specific heat capacity and thermal diffusivity of a rock sample from an area adjacent to the Taiwan Chelungpu fault under high temperature by differential scanning calorimetry (DSC) and by using a laser flash apparatus, and we then investigate the temperature dependencies of these thermal properties. Using these evaluated thermal properties, we try to obtain more accurate estimates of the dynamic shear stress and earthquake energetics during the Chi Chi earthquake, compared with those of previous studies [Hirono et al., 2007b; Hamada et al., 2009a, 2009b], by using numerical analysis. We also discuss how the amount of energy taken up by chemical reactions in relation to the total work on the fault affects the frictional heat at various depths. In addition, we propose a method for rough estimation of specific heat capacity without using DSC. 2. Methods 2.1. Sampling [6] TCDP drilled two boreholes (Hole A, m total depth; Hole B, m total depth) and one side track hole (Hole C) penetrating the Chelungpu fault and recovered rock samples from the three prominent fault zones discovered (Figure 1) [Ma et al., 2006; Hirono et al., 2006; 2007a]. The shallowest fault zone is most likely the one that slipped during the Chi Chi earthquake because a small temperature signal and a major stress orientation anomaly were observed in this zone [Kano et al., 2006; Lin et al., 2007; Wu et al., 2007]. The architecture of this fault zone in the first hole (Hole A), sampled from top to bottom, comprised a fracture zone, a breccia zone, a light gray clayey gouge (85 cm in thick), a thin black gouge (2 3 cm), a foliated gouge (10 cm), a black gouge (8 cm), a fragile black ultracataclasite in the shape of two hard disks (each 2 cm wide), a clayey gouge (13 cm), a breccia zone (17 cm), another fracture zone, and the return to wall rock [Sone et al., 2007; Yeh et al., 2007]. A 2 cm thick slip zone associated with the Chi Chi earthquake was found in the black gouge samples from the sidetrack hole (Hole C) [Ma et al., 2006]. [7] We collect a 10 cm thick half round core sample from the upper host rock at m depth, adjacent to the shallowest fault zone at 1111 m depth, in Hole A. This sample is from the Pliocene to the early Pleistocene Chinshui Formation, which is composed predominantly of siltstone with subsidiary thin layers of fine grained sandstone and mudstone and alternating layers of sandstone and siltstone [Song et al., 2007]. We cut the sample into a disk with a diameter of 25.4 mm and a thickness of 5 mm, and also use the powder and fragments of the rest of the sample Sample Description [8] The mineralogical assemblage of this sample consists of quartz, plagioclase, calcite, illite, smectite, and kaolinite (and/or chlorite) (Figure 2), determined by X ray diffraction spectroscopy (Spectris PANalytical, X Pert PRO MPD diffractometer; conditions, 45 kv/40 ma with Cuka radiation, divergence slit 1, receiving slit 0.1 mm, step width 0.01 ). The volume fraction of sand and silt sized grains ( 3.9 mm) is 0.536, as determined by grain size analysis of the polished sample surface by scanning electron microscope (JEOL, JSM 7001F) (Figure 3). The porosity is 20.6% and the wet bulk density is g cm 3, as calculated from measured values of wet volume, wet mass, and dry mass Differential Scanning Calorimetry [9] Differential scanning calorimetry (DSC) is carried out together with thermogravimetric (TG) analysis of the powdered sample, using a Netzsch STA 449 C Jupiter balance. The TG curve shows the total weight lost by a sample; this curve can be used to determine the dehydration, dehydroxylation, and decomposition of the sample during heating. The DSC curve shows the amount of heat required to increase the temperature of a sample; the specific heat capacity, C p, is determined by mc p dt dt ¼ dq dt ; where m is mass of the sample, dt/dt is heating rate, and dq/ dt is heat flow. A reference sample with a well defined specific heat capacity, sapphire in this study, is measured together with the sample. The temperature program for a DSC analysis is generally designed such that the temperature of the sample holder increases linearly as a function ð1þ 2of13

3 Figure 1. Geological map of central Taiwan [from Hirono et al., 2006] showing the site of the Taiwan Chelungpu Fault Drilling Project, an E W cross section through the site, and the three dominant fault zones discovered at the depths of 1111, 1153, and 1221 m in the Hole A core [Sone et al., 2007; Yeh et al., 2007]. of time. The heat flux and temperature difference between the sample and the reference throughout the heating and/or cooling is measured, and the specific heat capacity of the sample is determined by using equation (1). [10] Approximately 80 mg of sample is put in a covered Pt90Rh10 crucible. Because the sample includes clay minerals and calcite, which react at high temperature, the sample is heated three times: the first time, it is heated from 30 C to 850 C and then cooled to 40 C; for the second heating the sample is held at 40 C for 15 min, heated from 40 C to 1050 C, held at 1050 C for 15 min, cooled from 1050 C to 100 C, and then held at 100 C for 15 min; for the third heating, it is held at 40 C for 15 min, heated from 40 C to 1050 C, held at 1050 C for 15 min, cooled from 1050 C to 100 C, and then held at 100 C for 15 min. All heating and cooling are at the rate of 10 C min 1 under a Figure 2. X ray diffraction spectrum of the sample used for thermal property measurement. Ill, illite; Chl, chlorite; Qtz, quartz; Pl, plagioclase; Cal, calcite. 3of13

4 sample to reach half of the maximum temperature change, as follows [Parker et al., 1961]: ¼ 0:1388 d2 t 1=2 : ð2þ Values of are determined by nonlinear regression analysis using the software provided by Netzsch. Measurements are taken at 24.6 C and at temperature intervals of 100 C in the range of 100 C 800 C. At each temperature step, three data points are collected. Figure 3. (a) Scanning electron microscope image of the polished surface of the sample used for thermal property measurement. (b) A backscattered electron image of the same area, used for quantification of sand and silt sized grains ( 3.9 mm) by image analysis. flow of nitrogen (gas flow rate, 40 ml min 1 ). Released gases are detected simultaneously by a Fourier transform infrared (FT IR) spectrometer (Bruker Optics, Tensor 27) during heating Laser Flash Technique [11] A Netzsch LFA 457 Microflash laser flash apparatus is used to measure thermal diffusivity. The disk shaped sample, 25.0 mm in diameter and 5.13 mm thick, is coated with graphite and placed within a furnace chamber, and then the chamber is filled with Ar gas. Once the temperature has stabilized within the sample chamber, a short pulse of 2786 V for 0.33 ms from a neodymium yttrium/aluminum/ garnet (Nd YAG) laser warms the bottom surface of the sample. The phonon, a quantification of vibration occurring in a rigid crystal lattice, generated at the bottom surface moves to the top surface, and the infrared radiation emitted from the top surface is recorded by an indium antimonide (InSb) detector. In an adiabatic system, thermal diffusivity,, is empirically related to sample thickness, d, and halfrisetime, t 1/2, which is the time required for the top of the 3. Results 3.1. Measured Specific Heat Capacity and Its Interpretation [12] Weight losses of the sample after the first, second, and third heatings, determined by TG, are 6.33%, 0.41%, and 0.08%, respectively. Changes during the latter two heatings are shown in Figure 4. The release of water vapor and CO 2 gas during heating is detected by the FT IR spectrometer. Heat fluxes during the second and third heatings and coolings are also shown in Figure 4. During both heatings, the heat flux is higher at higher temperatures, and endothermic peaks are observed at around 575 C. During both coolings, exothermic valleys are observed at around 565 C. [13] We use the third DSC cooling curve to calculate the specific heat capacity of the sample (Figure 5). The specific heat capacity increases as the temperature increases, with a peak at around 565 C. [14] We next consider the cause of the change in the measured specific heat capacity with temperature. The marked peak at around 565 C is probably related to the a b phase transition of quartz because the mineral is abundant in the sample. This transition occurs at 573 C under atmospheric pressure, and the transition needs latent heat. Hemingway [1987] measured the specific heat capacity of quartz in the range of 67 C 727 C and showed a sharp peak at 573 C reflecting the latent heat of the a b phase transition (Figure 6). The slight temperature difference between the measured value of 565 C and Hemingway s [1987] value of 573 C may be a result of kinetic effects or of impurities in the quartz or its degree of crystallinity. [15] In addition, the overall increase in the measured specific heat capacity with temperature is related to the work required to produce the volume increase of a substance induced by high temperature because the specific heat capacity (C p ) is defined as the heat energy required to increase the temperature under constant pressure Measured Thermal Diffusivity and Its Interpretation [16] We plot the thermal diffusivity of the sample, determined by the laser flash technique, against temperature (Figure 7). At room temperature (24.6 C) the thermal diffusivity is m 2 s 1, and it decreases as temperature increases from 24.6 C to 600 C. At 600 C, the value is m 2 s 1. However, from 600 C to 800 C, thermal diffusivity remains almost constant ( m 2 s 1 ); m 2 s 1 at 700 C and m 2 s 1 at 800 C. 4of13

5 Figure 4. DSC and TG curves, showing the relationship between heat flux and the sample temperature and the total weight lost by a sample, respectively, for the second heating and cooling and the third heating and cooling in the temperature range of 40 C 1000 C. Weight losses of the sample after the second and third heating are 0.41% and 0.08%, respectively. During both heatings, the heat flux is higher at higher temperatures, and endothermic peaks are observed at around 575 C. During both coolings, exothermic valleys are observed at around 565 C. [17] Branlund and Hofmeister [2007] determined the thermal diffusivity of quartz to be 1000 C, and they showed a similar trend of the thermal diffusivity curve in relation to the a b phase transition to that of our sample. Heat transfer via a rigid crystal is strongly related to lattice vibration of the crystal, and a phonon is a quantification of the vibration occurring in a rigid crystal lattice. Thermal diffusivity is proportional to the mean velocity and mean free path length of the phonons [e.g., Berman, 1976]. Höfer and Schilling [2002] explained that the decrease in the thermal diffusivity of a quartz with elevated temperature is caused by an increase in phonon phonon interactions, resulting in turn from an increase in thermally activated phonons, whereas the high symmetry of b quartz results in a reduced probability of phonon phonon scattering and is accompanied by an approximately constant value of thermal diffusivity Curve Fitting [18] For numerical analysis of earthquake energetics, the measured values of specific heat capacity and thermal dif- Figure 5. Specific heat capacity of the sample (Measured), in the temperature range of 100 C 1000 C. The value increases with temperature and shows a marked peak at around 565 C. The fitted curve by polynomial equations (Fitted) is also shown. 5of13

6 Figure 6. Specific heat capacity curve of the wet bulk sample calculated from the measured values of the solid components and considering the mass fraction of interstitial water (Measured). Specific heat capacity curves of water, quartz, and illite [Japan Society of Mechanical Engineers, 1983; Hemingway, 1987; Skauge et al., 1983], and that for the bulk sample, calculated by using porosity measurement, grain size analysis, and X ray diffraction spectroscopy data (Calculated), are also shown. Figure 7. Thermal diffusivity of the sample (Measured) in the temperature range of 24.6 C 800 C. Thermal diffusivity decreases as the temperature increases from 24.6 C to 600 C, and then it becomes approximately constant from 600 C to 800 C. The fitted curve (Fitted) is also shown. 6of13

7 Table 1. Coefficients for the Determination of Measured Specific Heat Capacity and Thermal Diffusivity a Component a b c d e f g Specific heat (0 C 547 C) Specific heat (547 C 573 C) Specific heat (573 C 592 C) Specific heat (592 C 842 C) Specific heat (842 C 1000 C) Thermal diffusivity (27 C 573 C) Thermal diffusivity (573 C 1000 C) a The units of the specific heat capacity, thermal diffusivity, and temperature are J kg 1 K 1,m 2 s 1 and Kelvin, respectively. fusivity and their temperature dependencies should be expressed mathematically. A polynomial equation is often used to describe the temperature dependency of the specific heat capacity of minerals and rocks [e.g., Skauge et al., 1983; Waples and Waples, 2004; Hadgu et al., 2007]: C p ðtþ ¼a þ bt þ ct 2 þ dt 1 þ et 2 ; where T is temperature (K) and a, b, c, d, and e are coefficients. We apply this fitting equation to our measured specific heat capacity data. However, the specific heat capacity values change complicatedly with a peak at around 565 C, so we fit separate curves to temperature range segments: 0 C 547 C, 547 C 573 C, 573 C 592 C, 592 C 842 C, and 842 C 1000 C. The fitting parameters a, b, c, d, and e are summarized in Table 1, and the fitted line is shown in Figure 5, together with the measured values. [19] On the other hand, thermal diffusivity measured in the range of 25 C 600 C is well fitted by an inverse proportional equation: ðtþ ¼ f T þ g; where f and g are coefficients. In the range of 600 C 800 C, the thermal diffusivity is almost constant at m 2 s 1, similar to the trend reported by Branlund and Hofmeister [2007]. The fitting parameters f and g are also summarized in Table 1, and the fitted line is drawn on Figure Correcting the Specific Heat Capacity for Water Condition [20] The specific heat capacity of a multicomponent material, C p bulk, such as sediment or rock, is obtained by summing the specific heat capacity of each component, C pi, as follows: C p bulk ¼ Xn i¼1 C pi M i =M tot ; ð3þ ð4þ ð5þ where M i is the mass of each component and M tot is the total mass of the bulk material. For calculation of the specific heat capacity of the bulk sample, we have already measured the specific heat capacity of the solid components of the sample, but that of another component, interstitial water, also has to be considered. [21] The specific heat capacity values of water at high temperature (0 C 777 C) have been reported by the Japan Society of Mechanical Engineers [1983]. We apply a polynomial fitting equation (equation (3)) to the values under 17.5 MPa, corresponding to the effective vertical stress of 17.8 MPa around the shallowest fault zone [Hirono et al., 2007b], and we obtain the coefficients a, b, c, d, and e (Table 2). The specific heat capacity of water shows a marked peak at 377 C corresponding to the liquid vapor phase transition (Figure 6). We assume that the specific heat capacity of water from 777 C to 1000 C remains constant at J kg 1 K 1. [22] Because the measured porosity of this sample is 20.6%, the volume fractions of interstitial water and the solid components in the sample are and 0.794, respectively. The measured wet bulk density is g cm 3, so the masses of water and solid components per 1 cm 3 of the bulk sample are g and g, respectively. Therefore, their mass fractions in the bulk sample are calculated to be and , respectively. [23] Taking these mass fractions and specific heat capacities of water and the solid components into consideration, we adjust the specific heat capacity of the sample to take into account its water content (Figure 6). We again fit a polynomial (equation (3)) to the curve segments and obtained the coefficients a, b, c, d, and e (Table 3). 4. Reestimation of Dynamic Shear Stress and Energetics During the Chi Chi Earthquake [24] Dynamic shear stress and energetics during the 1999 Chi Chi earthquake have been previously discussed by Hamada et al. [2009a, 2009b]. However, for these quantitative determinations by numerical analysis, they (we) did not measure the specific heat capacity of the sample and Table 2. Coefficients for the Determination of Specific Heat Capacity of Water and Each Mineral a Component a b c d e Water (0 C 377 C) Water (377 C 777 C) Quartz (67 C 727 C) Illite (27 C 427 C) a The unit of specific heat capacity for illite only are J g 1 K 1. For all others, the units are J kg 1 K 1. The unit of temperature on the polynomial equations for these specific heat capacities is Kelvin. 7of13

8 Table 3. Coefficients for the Determination of the Specific Heat Capacity for the Wet Bulk Sample a Temperature a b c d e 0 C 372 C C 562 C C 592 C C 712 C C 1000 C a The unit of the specific heat capacity and temperature are J kg 1 K 1 and Kelvin, respectively. used the specific heat capacity values of the bulk sample calculated by summing the specific heat capacity of each component. The mass fraction of clay minerals, 0.14, that they used might have been underestimated in the calculation. They referred to the grain size distribution data, determined by the laser light diffraction method, of an artificially fragmentized sample of Tanikawa et al. [2007] and determined that the volume fraction of the <4 mm fraction was 0.14, corresponding to the mass fraction of the clay minerals. However, these data include uncertainty related to the artificial fragmentation because the degree of fragmentation can strongly affect the resultant grain size distribution. In addition, Tanaka et al. [2007] determined the specific heat capacity of a rock sample from Hole A and reported values ranging from 300 to 1000 J kg 1 K 1. These extremely low values, very close to those of metals, which require less energy to increase their temperature (e.g., 437 J kg 1 K 1 for Fe and 877 J kg 1 K 1 for Al), are unrealistic for fault related rocks such as fault gouge with a high water content. Compared with the findings of these previous reports, the specific heat capacity of the bulk sample determined here and its temperature dependency are likely to be much more accurate and appropriate. [25] Methods for determining temperature changes and energetics on a fault during earthquake slip have been well established by Hamada et al. [2009b]. According to the commonly used slip weakening model, the elastic strain energy released during an earthquake is partitioned among breakdown work (W b ), frictional heat (E H ), and radiated energy (E R )[Tinti et al., 2005; Kanamori and Rivera, 2006]. W b and E H are expressed as follows: Z W b ðtþþe H ðtþ ¼ ðtþdt; ð6þ where t is the dynamic shear stress during slip and n is the slip velocity (Figure 8). W b includes the fracture surface energy (G) [Tinti et al., 2005] and the energy taken up by coseismic chemical reaction (E Cdsd )[Hamada et al., 2009b], and the difference (W b G E Cdsd ) is transferred to frictional heat (Figure 8). In addition, a part of E H after stress drop is consumed by the chemical reaction (E Casd )[Hamada et al., 2009b] (Figure 8). Thus, the total frictional heat E Htot = W b G E Cdsd + E H E Casd. [26] According to this earthquake energy balance, the temperature (T) at any position x away from the center of the slip zone is expressed in terms of the balance at each 1 W b þ E H G E C ðxþ ¼ 0; 2 C p ðtþ w ð7þ where r is the wet bulk density, w is the thickness of the slip zone, and E C is the energy taken up by chemical reaction. For simplicity, we do not consider here the effects of thermal pressurization, convective heat transfer, or crack dilation. In the case of the Chi Chi earthquake, the values of stress drop, critical slip distance, total slip distance, and risetime were estimated to be approximately 4.75 MPa, 4.9 m, 8.3 m, and 6.0 s, respectively, by seismological investigations [Ma et al., 2006]. By assuming a constant slip velocity, the velocity is calculated to be 1.38 m s 1 by dividing the total displacement by the risetime. Thus, t (t) can be expressed as ðtþ ¼ 1:34t þ min þ 4:75 ðt 3:54Þ where t min is the residual shear stress (MPa) after the stress drop, and the units of t and t are seconds and MPa, respectively. In addition, the fracture energy during the earthquake has been estimated to be 0.65 MJ m 2 by grain size analysis of the slip zone [Ma et al., 2006]. By assuming a linear decrease with time of the increment rate of the accumulated fracture energy with time, dg/dt can be expressed as dg dt ¼ 0:104t þ 0:368 ðt 3:54Þ; ð9þ where the units of G(t) and t are MJ m 2 and seconds, respectively. Thus, G(t) can be expressed as Z GðtÞ ¼ ð 0:104t þ 0:368Þdt ðt 3:54Þ: ð10þ Figure 8. Energy budget for an earthquake on the basis of fault slip weakening model. t p, initial shear stress; t min, residual shear stress; d c, critical slip distance; d, total slip distance; W b, breakdown work; E H, frictional heat; E R, radiated energy; E Cdsd, energy taken up by chemical reaction during stress drop (breakdown); E Casd, energy taken up by chemical reaction after stress drop. ð8þ 8of13

9 Table 4. Parameters for Chemical Kinetics Modeling of Chemical Reactions During the 1999 Taiwan Chi Chi Earthquake a Chemical Reaction f(a) E a (kj mol 1 ) A (s 1 ) Enthalpy (kj g 1 ) Mass Fraction of Reacted Matter to Bulk Thermal decomposition of carbonate minerals Dehydration of interlayer water of smectite 1 a Dehydroxylation of smectite 1 a Dehydroxylation of kaolinite 1 a Dehydroxylation of illite (1 a)[ ln(1 a)] a Sources of kinetic functions and parameter and enthalpy values: for thermal decomposition of carbonate minerals [L vov et al., 2002; Hamada et al., 2009a], dehydration of interlayer water of smectite [Bray and Redfern, 1999; Noyan et al., 2008], dehydroxylation of smectite [Güler and Sarier, 1990; Noyan et al., 2008], and dehydroxylation of kaolinite [Saikia et al., 2002; L vov and Ugolkov, 2005]. Data on dehydroxylation of muscovite [Mazzucato et al., 1999; L vov and Ugolkov, 2005] were used as an alternative to those of dehydroxylation of illite. For 3.54 t 6.0, t (t) =t min and G(t) = For t > 6.0 (that is, after slip), t (t) = 0 and G(t) = With regard to the other parameters, the current temperature around the fault zone, which is assumed to correspond to the initial temperature before the earthquake, was measured to be 46.5 C [Kano et al., 2006]; the period between the Chi Chi earthquake and sample recovery was s; the wet bulk density of the gouge zone was measured to be 2.20 g cm 3 [Hirono et al., 2006]; and the thickness of the slip zone was determined to be 2 cm [Ma et al., 2006]. [27] On the other hand, various coseismic chemical reactions have been shown to have occurred during the Chi Chi earthquake. The black gouge zone, including the 2 cm thick slip zone associated with the earthquake, has lower inorganic carbon (mainly calcite), smectite, and kaolinite contents than the surrounding zones, and its magnetic susceptibility is relatively high [Ikehara et al., 2007; Hirono et al., 2006, 2008]. These values have been attributed to frictional heatinduced chemical reactions, including thermal decomposition of carbonate minerals, dehydration of interlayer water of smectite, dehydroxylation of smectite, dehydroxylation of kaolinite, and the production of magnetite from thermally decomposed paramagnetic minerals such as siderite [Ikehara et al., 2007; Hirono et al., 2008; Mishima et al., 2009]. Because these reactions are endothermic, the heat of reaction, E C, takes up energy released from the fault during the earthquake, reducing the values of other forms of energy. [28] The heat needed for a reaction is expressed as and parameter values and enthalpies for these reactions are summarized in Table 4, together with their sources. The average mass fraction of carbonate minerals in the surrounding rock adjacent to the black gouge zone is [Ikehara et al., 2007], and the relative average abundances of smectite, kaolinite, and illite in the surrounding rock are 6.0%, 10.1%, and 64.1%, respectively [Hirono et al., 2008]. The mass fraction of all clay minerals in the bulk sample is determined to be , as described above, so the mass fractions of smectite, kaolinite, and illite are calculated to be , , and , respectively (Table 4). We assume that these mass fractions in the surrounding rock correspond to the initial ones in the black gouge zone, including the 2 cm slip zone, before the earthquake. [29] To resolve the value of the unknown t min, the only constraint that we adopt is that the value of reacted fraction (a) for thermal decomposition of carbonate minerals in the central 1 mm thickness within the slip zone must be the same as the measured value, 0.92 [Ikehara et al., 2007; Hirono et al., 2007b]. We first calculate the values of a for thermal decomposition of carbonate minerals at various values of t min by the finite difference method, adopting the values of C p and with their temperature dependency that are determined in this study, equations (6) (8) and (10) E C ðtþ ¼ðtÞM H; ð11þ where a is the reacted fraction of a substance (0 a 1, a = 1 if the entire substance is reacted), M is the mass of the matter before the reaction, and H is the heat per unit mass of an endothermic reaction, which corresponds to its enthalpy. The relationship among the reacted fraction, temperature, and time, as expressed by the Arrhenius equation, is d dt ¼ f ð E a ÞA exp ; ð12þ RTðtÞ where f(a) is a kinetic function determined by the reaction mechanism, A is a constant (preexponential term), E a is the activation energy necessary for a reaction to occur, R is the gas constant ( J K 1 mol 1 ), and T is temperature (K). We here consider the reactions of thermal decomposition of carbonate minerals, dehydration of interlayer water of smectite, dehydroxylation of smectite, dehydroxylation of kaolinite, and dehydroxylation of illite. Kinetic functions Figure 9. Cumulative chemical energy used by all chemical reactions during the Chi Chi earthquake. The calculated total energy is 10.4 MJ m 2, corresponding to 12.1% of the given work on the fault. 9of13

10 Figure 10. (a) Relationship between the assumed dynamic shear stress on the fault during an earthquake and depth. (b) Given work on the fault. (c) Total energy taken up by coseismic chemical reactions. (d) Energy taken up by the reactions during slip. (e) Energy taken up by the reactions after slip. (f) Ratio of energy taken up by the reactions to the given work on the fault. (g) Resultant maximum temperature reached on the fault. (12), and f(a), and the enthalpies and kinetic parameters (A and E a ) of the chemical reactions (Table 4). The time increment used in the calculations is s, the grid size is 0.5 mm, and the boundary condition is T = 46.5 C at x > 1000 mm. Then we determine the value of t min consistent with the observed value of a. [30] The resultant values for t min and the maximum temperature of the fault are 9.0 MPa and 1080 C, respectively. Using this value of t min, the total E C of all chemical reactions is calculated to be 10.4 MJ m 2, corresponding to 12.1% of the given work on the fault ( = W b + E H, 86.1 MJ m 2 ). The energy taken up by the reactions during slip is 7.0 MJ m 2, corresponding to 67.0% of the total E C, and that absorbed after the slip is 3.4 MJ m 2, corresponding to 33.0% of the E C. We plot the cumulative energy against time from the beginning of slip (Figure 9). 5. Inhibition of the Temperature Rise as a Result of Energy Being Taken Up by Coseismic Chemical Reactions [31] We here discuss how the amount of energy taken up by coseismic chemical reactions relative to the total work on the fault affects the frictional heat. The energy by chemical reactions has an auto feedback effect that inhibits the temperature rise in the fault zone [Hamada et al., 2009b]. Higher temperatures accelerate the chemical reactions, but the reactions then reduce the energy available for the temperature rise. Sulem and Famin [2009] performed a numerical simulation of shear heating and thermal pressurization for carbonate rock and found a similar auto feedback effect for the endothermic reaction of calcite thermal decomposition. The efficiency of the feedback effect depends strongly on the amounts of reactive materials available [Hamada et al., 2009b]. However, equation (7) indicates that the efficiency may also depend on the given work ( = W b + E H ) on the fault. Although the given work depends on both shear stress and slip distance, shear stress can take various values over a larger range than can slip distance during an earthquake. If a constant frictional coefficient on a fault is assumed, shear stress bears some relationship to the vertical overburden. Therefore, we discuss here the relationship between the efficiency of the feedback effect and the depth of the fault. [32] Although we consider the change in shear stress during slip (i.e., the stress drop) in the abovementioned reestimation of dynamic shear stress and energetics during the Chi Chi earthquake, we assume here a constant value of shear stress during slip. If it is assumed that the stress normal to the fault is equal to that during the static state, that the horizontal stress is equal to the vertical stress, and that the frictional coefficient is 0.3 on the fault, the magnitude of the stress normal to the fault equals to that of the vertical stress, and then the shear stress on the fault can be calculated (Figure 10a). We adopt a rock density of 2.60 g cm 3 and a value of 35 for the dip of the fault plane [Hirono et al., 2007a]. Given work is the product of the shear stress and the slip distance of 8.3 m [Ma et al., 2006] (Figure 10b). We calculate the energy taken up by chemical reactions and the maximum temperature reached on the fault by the finite difference method, adopting the constant value of shear stress, the values of C p and and their temperature dependencies determined in this study, equations (6) (8) and (10) (12), and f(a) and the enthalpies and kinetic parameters (A and E a ) of the chemical reactions (Table 4). For simplicity, fracture energy or crack dilation is not considered here. The time increment used in the calculations is s, the grid size is 0.5 mm, and the boundary condition is T = 46.5 C at x > 1000 mm. [33] We plot the resultant values of E C, the ratio of E C to given work, and the maximum temperature reached on the fault against depth (Figures 10c 10g). The values of total E C 10 of 13

11 and E C during slip increase with depth, depending on the shear stress. They show steep increments at around km depth, but the increase is gradual at depths deeper than 3.0 km. E C after slip does not change markedly with depth, compared with total E C and E C during slip. The ratio of total E C to given work is relatively large: 16.4% at maximum at km depth (Figure 10f). The maximum temperature increases with depth and exceeds 1120 C, corresponding to the melting temperature of albite, at around 2.0 km depth. The temperature increment becomes relatively gradual at depths deeper than 1.5 km, probably because of the large ratio of E C to given work. Therefore, in the case of the Chelungpu fault, the effect of E C in inhibiting the temperature rise is relatively large at depths of km. We note that, in the strict sense, this modeling result includes uncertainties stemming from changes to other parameter values, such as porosity, density, magnitude of stress, and the stress state, with increasing depth. 6. Indirect Estimation of Bulk Specific Heat Capacity in a Multicomponent Material [34] Although we have already obtained the specific heat capacity of the bulk sample adjacent to the Chelungpu fault, we can also calculate the bulk specific heat capacity from the specific heat capacities of the main components of the sample. We roughly determine the volume fraction of mineral grains of sand and silt size ( 3.9 mm) to be by grain size analysis. By considering the measured porosity, we calculate the volume fraction of clay sized mineral grains (<3.9 mm) to be X ray diffraction analysis shows that quartz is the dominant mineral in the sample, and illite is dominant over other clay minerals (smectite, kaolinite, and chlorite) [Hirono et al., 2008], so we assume that all grains of sand and silt size were quartz and that all claysized grains are illite. Under this assumption, the volume fractions of interstitial water, quartz, and illite in the sample are 0.206, 0.536, and 0.258, respectively. By assuming densities of quartz and illite of 2.65 and 2.75 g cm 3, respectively, we calculate the masses of water, quartz, and illite per 1 cm 3 of the bulk sample to be 0.206, 1.420, and g, respectively. Therefore, their calculated mass fractions in the bulk sample are , , and , respectively. [35] The specific heat capacity values of quartz from 67 C to 727 C are reported by Hemingway [1987]. We fit a polynomial equation (equation (3)) to these values and obtained the coefficients of a, b, c, d, and e (Table 2). Coefficients for the specific heat capacity of illite from 27 C to 427 C are directly reported by Skauge et al. [1983] (Table 2). We assume that the polynomial fitting to the specific heat capacity of quartz is extrapolated to the temperature range of 0 C 67 C; that the specific heat capacity of quartz from 672 C to 1000 C is the same as that at 672 C, J kg 1 K 1 ; and that that of water from 777 C to 1000 C is the same as that at 777 C, J kg 1 K 1.In addition, the polynomial fitting for illite is extrapolated to the temperature range of 427 C 1000 C. [36] Using equation (5), we calculate the specific heat capacity of the bulk sample (Figure 6). The calculated values are generally higher than the measured values, and their average difference, except for values around the peak at 572 C, is 85 J kg 1 K 1. This difference may result from the several assumptions, such as that all sand or silt sized grains are quartz. Nonetheless, this approach to evaluating the specific heat capacity of the bulk sample from only grain size analysis and X ray diffraction spectroscopy data seems to be feasible. 7. Discussion and Conclusions [37] The value of t min = 9.0 MPa that we determine during the 1999 Chi Chi earthquake is higher than those of 1.3 MPa reported by Hirono et al. [2007b], 5.2 MPa reported by Hamada et al. [2009b], and 6.6 MPa reported by Hamada et al. [2009a]. However, Hirono et al. [2007b] used constant values for specific heat capacity and thermal diffusivity, and Hamada et al. [2009a, 2009b] used a calculated value for the specific heat capacity of the bulk sample based on an underestimated mass fraction of clay minerals and a constant thermal diffusivity value, as described above. In addition, Hirono et al. [2007b] considered only thermal decomposition of calcite as a coseismic chemical reaction during the Chi Chi earthquake; they did not consider the energy taken up by the reaction, and they assumed that the kinetics function and parameters of the reaction were the same as those of synthetic calcium carbonate reported in the literature. Hamada et al. [2009b] considered various chemical reactions, including dehydration and dehydroxylation of smectite, but they still assumed that the kinetics function and parameters of the reaction for thermal decomposition of calcite were the same as those of synthetic calcium carbonate. Hamada et al. [2009a] determined the kinetic function and parameters for thermal decomposition of carbonate minerals by isothermal heating experiments using a sample from adjacent to the fault zone, but they did not consider any other reactions. Moreover, even though illite was abundant in the gouge zone [Hirono et al., 2008], dehydroxylation of illite was not considered in any of these previous three papers. Therefore, we consider our value of t min = 9.0 MPa to be a great improvement. [38] We last discuss one remaining problem, their pressure dependency. The change in the specific heat capacity of rock at 10 MPa pressure has been reported to be only about times the value at atmospheric pressure, corresponding to an increase of about 0.1% per kilometer of rock column [Cermak and Rybach, 1982; Waples and Waples, 2004]. The increase in thermal diffusivity has been reported to be about times for every 10 MPa increment [Schon, 1996]. Therefore, in the case of nonporous hard rock, the pressure effects on specific heat capacity and thermal diffusivity may be negligible compared with the temperature effects. [39] Finally, we emphasize that determination of the specific heat capacity and thermal diffusivity of a rock sample, together with their temperature dependencies, is crucial for estimation of frictional heat during an earthquake. DSC and a laser flash apparatus are powerful tools for their determination, but, if these tools are not available, specific heat capacity can be roughly estimated from porosity measurements, grain size data, and X ray diffraction spectroscopy results. We also note that energy taken up by coseismic chemical reactions has the strong feedback effect of inhibiting the temperature rise on the fault. As Hamada et al. [2009b] suggested, the high energy values of 11 of 13

12 rocks with abundant reactive material, such as limestone and mudstone, probably account for the rarity of pseudotachylyte in fault zones in carbonate and clay rich rocks. This energy loss due to chemical reactions would affect the degree of dynamic fault weakening by frictional melting or thermal pressurization because melting of minerals and thermal expansion of pore fluid can occur only at high temperature. In addition, the effectiveness with which the temperature rise is inhibited by the energy loss depends not only on the amount of reactive material but also on the depth at which the fault develops. For more advanced understanding of this effect and accurate estimation of earthquake energetics, investigations of various other active faults around the world that include detailed physicochemical analyses are needed. [40] Acknowledgments. We thank Sheng Rong Song, Kuo Fong Ma, Jih Hao Hung, Chien Ying Wang, En Chao Yeh, Weiren Lin, and Wonn Soh for their support in our analyses of Hole A core samples. Yoshino Shinoda, Shigeyoshi Nakamura, and Hitoshi Koizumi (Bruker AXS, Japan) are gratefully acknowledged for supporting our thermal property measurements. We also thank Tomoyuki Ohtani, an anonymous reviewer, and an anonymous associate editor for constructive comments, and editor Robert Nowack for editing this paper. This research was supported by a Japan Ministry of Education, Science, Sports, and Culture Grant in Aid for Young Scientists (B) , References Andrews, D. J. (2002), A fault constitutive relation accounting for thermal pressurization of pore fluid, J. Geophys. Res., 107(B12), 2363, doi: /2002jb Berman, R. (1976), Thermal Conductivity in Solids, 193 pp., Clarendon Univ. Press, Oxford. Branlund, J. B., and A. M. Hofmeister (2007), Thermal diffusivity of quartz to 1,000 C: Effect of impurities and the a b phase transition, Phys. Chem. Miner., 34, , doi: /s Bray, H. J., and S. A. T. Redfern (1999), Kinetics of dehydration of Ca montmorillonite, Phys. Chem. Miner., 26, , doi: / s Cermak, V., and L. Rybach (1982), Thermal conductivity and specific heat of minerals and rocks, in Landolt Bornstein; Zahlenwerte und Funktionen aus Naturwissenschaften und Technik, editedbyg.angenheister, pp (Hrsg.) Bd. 1, Physikalische Eigenschaften der Gesteine, Teilbd. a., Springer, Berlin, Heidelberg, New York. Chester, J. S., F. M. Chester, and A. K. Kronenberg (2005), Fracture surface energy of the Punchbowl fault, San Andreas system, Nature, 437, , doi: /nature Güler, C., and N. Sarier (1990), Kinetics of the thermal dehydration of acid activated montmorillonite by the rising temperature technique, Thermochim. Acta, 159, 29 33, doi: / (90)80090-l. Hadgu, T., C. C. Lum, and J. E. Bean (2007), Determination of heat capacity of Yucca Mountain stratigraphic layers, Int. J. Rock Mech. Min. Sci., 44, , doi: /j.ijrmms Hamada, Y., T. Hirono, M. Ikehara, W. Soh, and S. R. Song (2009a), Estimated dynamic shear stress and frictional heat during the 1999 Taiwan Chi Chi earthquake: A chemical kinetics approach with isothermal heating experiments, Tectonophysics, 469, 73 84, doi: /j.tecto Hamada, Y., T. Hirono, W. Tanikawa, W. Soh, and S. R. Song (2009b), Energy taken up by co seismic chemical reactions during a large earthquake: An example from the 1999 Taiwan Chi Chi earthquake, Geophys. Res. Lett., 36, L06301, doi: /2008gl Hemingway, B. S. (1987), Quartz: Heat capacities from 340 to 1000 K and revised values for the thermodynamic properties, Am. Mineral., 72, Hirono, T., et al. (2006), High magnetic susceptibility of fault gouge within Taiwan Chelungpu fault: Nondestructive continuous measurements of physical and chemical properties in fault rocks recovered from Hole B, TCDP, Geophys. Res. Lett., 33, L15303, doi: /2006gl Hirono, T., et al. (2007a), Nondestructive continuous physical property measurements of core samples recovered from Hole B, Taiwan Chelungpu Fault Drilling Project, J. Geophys. Res., 112, B07404, doi: / 2006JB Hirono, T, T. Yokoyama, Y. Hamada, W. Tanikawa, T. Mishima, M. Ikehara, V. Famin, M. Tanimizu, W. Lin, W. Soh, and S. Song (2007b), A chemical kinetic approach to estimate dynamic shear stress during the 1999 Taiwan Chi Chi earthquake, Geophys. Res. Lett., 34, L19308, doi: /2007gl (Correction, Geophys. Res. Lett., 35, doi: /2007gl032512, 2008). Hirono, T., et al. (2008), Clay mineral reactions caused by frictional heating during an earthquake: An example from the Taiwan Chelungpu fault, Geophys. Res. Lett., 35, L16303, doi: /2008gl Hirose, T., and T. Shimamoto (2005), Growth of molten zone as a mechanism of slip weakening of simulated faults in gabbro during frictional melting, J. Geophys. Res., 110, B05202, doi: /2004jb Höfer, M., and F. R. Schilling (2002), Heat transfer in quartz, orthoclase, and sanidine at elevated temperature, Phys. Chem. Miner., 29, , doi: /s z. Ikehara, M., et al. (2007), Low total and inorganic carbon contents within the Chelungpu fault, Geochem. J., 41, Ishikawa, T., et al. (2008), Coseismic fluid rock interactions at high temperatures in the Chelungpu fault, Nat. Geosci., 1, , doi: / ngeo308. Japan Society of Mechanical Engineers (1983), JSME Data Book: Thermophysical Properties of Fluids, Maruzen, Tokyo. Kanamori, H., and L. Rivera (2006), Energy partitioning during an earthquake, in Earthquake: Radiated Energy and the Physics of Faulting, edited by R. Abercrombie, A. McGarr, H. Kanamori, and G. Di Toro, pp. 3 13, AGU, Washington, D. C. Kano, Y., J. Mori, R. Fujio, H. Ito, T. Yanagidani, S. Nakao, and K. Ma (2006), Heat signature on the Chelungpu fault associated with the 1999 Chi Chi, Taiwan earthquake, Geophys. Res. Lett., 33, L14306, doi: /2006gl L vov, B. V., and V. L. Ugolkov (2005), Kinetics and mechanism of dehydration of kaolinite, muscovite and talc analyzed thermogravimetrically by the third law method, J. Therm. Anal. Calorim., 82, 15 22, doi: /s L vov, B. V., L. K. Polzik, and V. L. Ugolkov (2002), Decomposition kinetics of calcite: A new approach to the old problem, Thermochim. Acta, 390, 5 19, doi: /s (02) Lachenbruch, A. H. (1980), Frictional heating, fluid pressure, and the resistance to fault motion, J. Geophys. Res., 85(B11), , doi: / JB085iB11p Lin, W., E. C. Yeh, H. Ito, J. H. Hung, T. Hirono, W. Soh, K. F. Ma, M. Kinoshita, C. Y. Wang, and S. R. Song (2007), Current stress state and principal stress rotations in the vicinity of the Chelungpu fault induced by the 1999 Chi Chi, Taiwan, earthquake, Geophys. Res. Lett., 34, L16307, doi: /2007gl Ma, K. F., C. T. Lee, Y. B. Tsai, T. C. Shin, and J. Mori (1999), The Chi Chi, Taiwan earthquake: Large surface displacements on inland thrust fault, Eos Trans. AGU, 80, , doi: /99eo Ma, K. F., et al. (2006), Slip zone and energetics of a large earthquake from the Taiwan Chelungpu fault Drilling Project, Nature, 444, , doi: /nature Mazzucato, E., G. Artioli, and A. Gualtieri (1999), High temperature dehydroxylation of muscovite 2M 1 : A kinetic study by in situ XRPD, Phys. Chem. Miner., 26, , doi: /s Mishima, T., T. Hirono, N. Nakamura, W. Tanikawa, W. Soh, and S. Song (2009), Changes to magnetic minerals caused by frictional heating during the 1999 Taiwan Chi Chi earthquake, Earth Planets Space, 61, Noyan, H., M. Önal, and Y. Sarikaya (2008), Thermal deformation thermodynamics of a smectite mineral, J. Therm. Anal. Calorim., 91, , doi: /s z. Parker, W. J., R. J. Jenkins, C. P. Butler, and G. L. Abbott (1961), Flash method for determining thermal diffusivity, heat capacity and thermal conductivity, J. Appl. Phys., 32, , doi: / Pittarello, L., G. Di Toro, A. Bizzari, G. Pennacchioni, J. Hadizadeh, and M. Cocco (2008), Energy partitioning during seismic slip in pseudotachylyte bearing faults (Gole Larghe Fault, Adamello, Italy), Earth Planet. Sci. Lett., 269, , doi: /j.epsl Saikia, N., P. Sengupta, P. K. Gogoi, and P. C. Borthakur (2002), Kinetics of dehydroxylation of kaolin in presence of oil field effluent treatment plant sludge, Appl. Clay Sci., 22, , doi: /s (02) Scholz, C. H. (2002), The Mechanisms of Earthquake Faulting, 496 pp., Cambridge Univ. Press, New York. Schon, J. H. (1996), Physical Properties of Rocks: Fundamentals and Principles of Petrophysics, 583 pp., Pergamon, New York. Sibson, R. H. (1973), Interaction between temperature and pore fluid pressure during earthquake faulting A mechanism for partial or total stress relief, Nature, 243, of 13