Topographic Anistropy of Slickenside from Deep Borehole Sample in an Earthquake Swarm Region and Its Generation Mechanism

J. Phys. Earth, 41, 75-85, 1993

Yasuto Kuwahara,1,* Norio Oyagi,2 and Hiroshi Takahashi3

Geological Survey of Japan, Tsukuba 305, Japan1 2National Research Institute for Earth Science and Disaster Prevention , Tsukuba 305, Japan 3Satoh Kogyo Inc ., Chuou-ku, Tokyo 103, Japan

A slickenside was discovered from a boring core sample 1,880m deep in the Matsushiro earthquake swarm region in Nagano Prefecture, Japan. The slickenside has been considered to be created by earthquake faulting during the earthquake swarm period, because it accompanied fresh rock powder produced by earthquake faulting. The power spectral density of the topography of the slickenside was measured with a stylus profilometer over the wavelength range from 10-4 to 10-2m. Each profile of the surface has a "red noise" power spectrum over the wavelength range studied, with the power falling off on average between 2 and 3 orders of magnitude per decade decrease in wavelength. Meanwhile, the topography of the slickenside is found to show anisotropy in the spectral amplitude; the amplitude perpendicular to the slip direction is two to four times as large as that parallel to the slip direction. A generation mechanism for such topographic anisotropy is numerically modeled from a viewpoint of the fracture mechanics. It is supposed that the crack tip stress distribution in the plane parallel to the slip direction is represented by a model of a plane strain shear crack (Mode II crack) and that the stress distribution in the plane perpendicular to the slip direction is represented by an antiplane strain shear crack (Mode III crack). The stress field around the crack tip in the Mode III case shows a broader distribution with respect to the azimuth than that in the Mode II case. This difference of a stress field at the crack tip between the Mode II and the Mode III is a possible cause of the topographic anisotropy.

1. Introduction The topography of fault surfaces has been considered to control the mechanical and fluid transport properties of the Earth's crust. Laboratory experiments (e.g., Okubo and Dietrich, 1984; Ohnaka and Kuwahara, 1990; Kuwahara, 1989) of rock friction elucidated that the fault surface topography is the controlling factor for the sliding mode, stable and unstable slip, of a fault, and is the key parameter for size-scaling of

Received February 25, 1993; Accepted May 21, 1993 * To whom correspondence should be addressed .

75 76 Y. Kuwahara et al. shear fracture. Brown (1987, 1989) demonstrated the strong effect of topography on the fluid and electric current through a single fracture by numerical simulation. In these ways, the effect of the fault surface topography is recognized to be important in considering many aspects of crustal activities. For this reason, considerable effort has been placed on characterization of the natural fracture surface topography. Aviles et al. (1987), Brown and Scholz (1985), Okubo and Aki (1987), and Power et al. (1987) characterized the topographies of outcrops of the San Andreas fault or of other faults using the Fourier spectrum and/or the fractal analysis technique. They described the fractal property of these faults showing variations in fractal dimension Df from the short-length to the long-length band, variations in Df among fault segments, and so on. All the measurements of these studies were, however, done for the topographies of fault outcrops on the earth surface. Therefore, it is not straightforward to understand the fault topography at a large depth of seismogenic zone from their results. Brown et al. (1986) measured the surface topographies of natural joints in drill cores from depths of 2,880.4 m and of 4,420.8 m, demonstrating the fractal character of the topography and paying attention to a topographical mismatch of the two mating surfaces. The joints measured by them, however, are fractures across which there is no significant shear displacement. Thus, there is no data of the surface topography of shear fracture surface at a large depth. Since 1965, there had been earthquake swarm activity at Matsushiro, central Japan. National Research Center for Disaster Prevention of Japan drilled the 1,800m deep well nearly on the Matsushiro earthquake fault formed during the swarm activity in order to examine whether earthquakes could be induced by increase of pore water pressure by water injection into the well (Ohtake, 1974; Takahashi et al., 1970). The depth of the shallowest Matsushiro earthquakes was about 1.5 km at the boring site, and the drill-well was expected to penetrate into the layer where the earthquakes did repeatedly occur. Takahashi et al. (1970) reported that shear fracture surfaces with fresh rock powder were found in the core samples from the borehole deeper than 1,363 m. Such surfaces with linear structures in a form of striations or grooves are commonly termed slickenside (Fleuty, 1975). The surfaces of slickensides found by Takahashi et al. (1970) were considered to show scars of the Matsushiro earthquakes and a mated pair of the slickenside among those have been preserved for over twenty years. Thus, this slickenside is considered to be a rare example of fault surface created by earthquake at a large depth. In this paper, we present the result of the topography measurement of the slickenside showing topographical anisotropy and give a numerical model of the generation mechanism of the anisotropy.

2. Visible Features of the Slickenside

While the depth of the borehole was 1,800 m, the total length of the hole was as long as 1,934 m because of its considerable curving affected by geological conditions of the stratum. The borehole diameter was 190 mm at the top and 64 mm at the bottom of the well. The measured slickenside of the core sample was taken from the quartz-diorite stratum at the depth of 1,883m along the borehole, and has a diameter of 32 mm. P-wave velocity of the core sample is about 6 km/s (Takahashi et al., 1970), and grain

J. Phys. Earth Topographic Anisotropy of Slickenside 77

Fig. 1. Photograph of the slickensides of upper (hanging) and of lower (foot) block of core samples.

Fig. 2. Close-up photograph of the slickenside. Slickenlines are inclined at about 30•‹.

sizes of the sample are 2 to 5 mm. The slickenside made an angle of 38•‹ with the borehole axis which has an inclination of 39•‹. Unfortunately, a dip angle of the slickenside cannot be estimated, because the core sample was not oriented. The two mated slickensides are shown in Fig. 1. The slickenlines are clearly seen on the hanging (upper) and foot (lower) walls, respectively. A close-up photograph of the slickenside is shown in Fig. 2. The following two features are noted from these

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photographs: 1) The slickenlines are formed on a calcite vein of the thickness of the order of 0.1 mm. The calcite is considered to have grown on preexisting crack surfaces. This indicates that the faulting occurred on the preexisting open or shear crack in which the calcite grew. It is noteworthy that the calcite covers more than 80% of the crack surface. 2) Some of slickenlines are about 5 mm long, suggesting that the slip in a single event of faulting was larger than at least 5mm. The magnitude of the earthquake whose slip amount is 5mm is equal to 2.5 according to Iida (1965). Although we have not

yet been able to distinguish a mode of faulting, aseismic or seismic, for the slip on this slickenside, it suggests the possibility that not only a large earthquake but also a micro-earthquake occurs on a preexisting fault.

3. Topography Measurement

The topography was measured with a stylus profilometer (Surfcoder SE-30c made by Kosaka Laboratory Ltd.) with a stylus tip radius of 25 ƒÊm. Figure 3 shows a 3-dimensional view of the topography. The resolution of measurement in the Y-axis is 50 ƒÊm. The direction of slickenlines corresponds to the Y-direction. It can be seen that the topography profile in the Y-direction is smoother than that in X-direction. In recent studies,many researchers(e.g., Brown,1987; Brown and Scholz,1985) characterized the surface topography with a concept of fractal. They demonstrated that fracture surfaces have the fractal nature. Therefore, we make an attempt to characterize the slickenside topography as fractal. When the topography is fractal, the power spectrum of the profile is a "red noise" one, having a power-law slope as described by (1)

The fractal dimension Df is written as D f = (5-ƒ¿)/2 (Mandelbrot, 1983). Four profiles 4cm long were measured on the slickenside to represent the average

character of the surface. The length of 4cm, being as long as possible for the core

Fig. 3. Three-dimensional view of the topography of the slickenside. The slip direction is parallel to the Y-axis.

. Phys. Earth

J Topographic Anisotropy of Slickenside 79

Fig. 4. Power spectral densities for the surface topographies parallel to and perpendicular to the slip direction. sample measurement, is about 8 times larger than the slip distance. An ensemble average of these power spectra was made by averaging each spectrum computed with a fast Fourier transform algorithm. Figure 4 shows the average spectra for the profiles parallel and perpendicular to the slickenlines. The following three features are noticeable: (1) The power spectral density of the profile perpendicular to the slickenlines are 2 to 4 times larger than those parallel to the slickenlines in the whole range of wavelength studied. (2) Each spectrum is a "red noise" one. The exponent a defined in Eq. (1) is about 2.5 both for parallel and perpendicular data. In other words, the topographies parallel and perpendicular to the slickenlines have the same fractal dimension of 1.25, while the amplitudes are different by a factor of 2 to 4. (3) A careful look at Fig. 4 shows that the slope is not constant for a given direction and tends to increase at a wavelength of a few mm. The slopes observed in this study are within the range of 2 to 3, which are consistent with the slopes for the outcrop faults reported by Brown et al. (1985) and Power et al. (1987).

4. Generation Mechanism of Anisotropic Topography The anisotropic topography described above should be considered to play an important role in a history of fault activity, because the fault topography is responsible for its reaction to an external force. Consideration of the generation mechanism of anisotropic topography is, thus, basically important for modeling a fault evolution. Considering a formation process of topography, a wear effect on the surface topography apparently exists on the wavelength range smaller than the slip distance. The data of the slickenside studied, however, shows a significant degree of anisotropy even in the wavelength range larger than the slip distance of about 5 mm. Therefore, an effect other than the wear effect should be considered in modeling the generation mechanism of anisotropic topography. Such modeling of topography has been attempted for a molecular scale topography by Termonia and Meakin (1986) and for a scale of rock fracture by Kato et al. (1989). We here treat this problem as a random process based on the fracture mechanics like

Vol. 41, No. 2, 1993 80 Y. Kuwahara et al. the treatment of Kato et al. (1989). Kato et al. (1989) supposed that the topography of a fault was created by fracture propagation in the medium which has a random distribution of strength. They calculated the stress field near the tip of crack propagating irregularly and gave randomly the strengths to imaginary elements of the medium in all directions from the crack tip. They assumed that fracture was propagated by a unit length in the direction where the values of the calculated stress r divided by the given strength S was maximum. The above procedure was repeated until the total length of fracture reached a prescribed value. In their model, different topographies should result from the different stress distributions near the crack tip, if the medium strength distributions are the same. In modeling the crack propagation, the following points are important according to the results of Kato et al. (1989). 1) The calculated azimuth of the maximum stress concentration at a crack tip for the irregular crack is between the azimuth of the crack tip and the X-direction. Kato et al. (1989) showed that the stress distribution at the tip of the irregular crack is well approximated by the model of the jointed two straight cracks where one crack is the crack tip portion itself and the other one linearly approximates the other irregular portions than the crack tip portion. This means that the azimuth of maximum stress concentration is effectively controlled by the direction of the crack tip and by the average direction of the other portions of crack. 2) The probability density function of the direction of unit crack propagation should be correlated to the stress distribution function of the azimuth around the crack tip, because the probability of ƒÑ/S being maximum becomes higher according as ƒÑ is larger if the strength distribution in space is random. 3) The standard deviation of the strength distribution in the medium determines the roughness amplitude. Although the actual irregular crack propagates in 3-dimensional space, we suppose that the crack tip stress distribution in the plane parallel to the slip direction is represented by the plane strain shear crack model (Mode II crack) in which the shear stress ƒÑxy, is applied at infinity. It is similarly supposed that the stress distribution in the plane perpendicular to the slip direction is expressed by the antiplane strain shear crack model (Mode III crack) in which the shear stress ƒÑyz is applied. The coordinate system defined

Fig. 5. The cylindrical and the Cartesian coordinate systems at the crack tip. The shaded area represents the crack surface. The angle ƒÆ is measured from the X-axis. The slip directions of the Mode II and of the Mode III are the X-direction and the Z-direction, respectively.

J. Phys. Earth Topographic Anisotropy of Slickenside 81

Fig. 6. Stress distributions of ƒÑrƒÆ and ƒÑƒÆz with respect to ƒÆ at the crack tip for the

shear cracks of Mode II and Mode III, respectively. Both the stresses are

normalized by their maximum stresses.

Fig. 7. Illustration of the 2-dimensional model of crack extension used in the calculation. The solid lines show the topography of an irregular crack.

is shown in Fig. 5. The shear stress distributions in terms of the local cylindrical coordinate system at the crack tip in Fig. 5 should be effective on determining the crack propagation direction. Figure 6 shows the normalized stress distributions F with respect to the azimuth 0 around the crack tip for Mode II and Mode III crack, where Toyand ire are the shear stresses described in the cylindrical coordinate system. It is speculated that the Mode III crack propagates more irregularly than the Mode II, because the stress distribution for Mode III is broader than that for Mode II. Considering the above features, the fracture propagation process may be modeled by the following equations. The fracture topography Y(X) in the Cartesian coordinate system is sampled by a small unit length L as illustrated in Fig. 7 and described as

(2a) (2b) (2c)

where ƒÆi is the angle between the i-th segment of the fracture and the X-axis, and ni is a random number whose probability density function is assumed to be the same as the

stress distribution function F(ƒÆ). The constant A is the parameter which controls a

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Fig. 8. Examples of the simulated fracture topographies for Mode II and for Mode III. The unit length of the X- and Y-axes is L of the unit length of the simulated crack.

Fig. 9. Power spectral densities for the topographies of the simulated cracks for Mode II and for Mode III. The unit length is the same as in Fig. 8.

degree of an effect of the (i-1)-th crack direction on the i-th crack one. When the value of ƒÆi given by the Eq. (2c) becomes larger than ƒÎ/2, we change the value of ƒÆi to ƒÎ/2, because this physically seems a rare case. The Eq. (2c) illustrates that the i-th crack is directed to the direction of (i-1)-th crack with a high probability. The model described in the Eqs. of (2a-c) corresponds to the model of Brownian motions when A=0. In this case, the exponent cc in the Eq. (1) for the spectrum of the fracture topography is theoretically 2, implying a fractal dimension of 1.5. We calculated fracture topographies of Mode II and Mode III for the various values of the constant A according to the Eqs. (2). Topographies and those power spectra of Mode II and Mode III both of which are calculated for A=0.7 are shown in Figs. 8 and 9, respectively. As shown in the figure, the power spectral amplitudes for both of the modes are almost proportional to ƒÉ2.5, whereas the spectral amplitudes of the two modes are different. It is concluded that when A=0.7, the exponent cc is about 2.5 (Df =1.25) after the calculations to various values of A. cc is found to increase with the value of A and to be about 3 for A=1. The amplitude for Mode III is 2 to 10 times

J. Phys. Earth Topographic Anisotropy of Slickenside 83 as large as that for Mode II regardless of the value of A. This difference is almost the same as the difference in the actual slickenside data between parallel and perpendicular to the slip direction. In summary, this relatively simple model can produce the topographic characteristics of the actual slickenside. The model parameter A and the variance of the random numbers ni determine the spectral slope a and the spectral amplitude, respectively. Because the amplitude difference of topographies between parallel and perpendicular to the slip direction can be quantitatively explained by considering the difference in a crack tip stress field between Mode II and Mode III, the stress field around the tip of the actual 3-dimensional crack is most likely represented by Mode II in the direction parallel to the slip and by Mode III in the perpendicular case.

5. Discussion In modeling the generation mechanism of the anisotropic topography, we have not taken a wear effect into consideration. However, the wear effect seems to be dominant for the fault on which a large slip distance takes place. Power et al. (1987) reported a statistical feature of topography of an outcrop fault in the western U.S. (e.g., the Basin and Range Province), showing the topography amplitude perpendicular to the slip direction is almost 10 times as large as the parallel amplitude (100 times in power), while the slickenside studied here shows 2 to 4 times difference in power. The faults described by Power et al. (1987) have total slips of the order of 10 m and have probably been active since Miocene. They suggested that considerable smoothing and wear must take place in the slip direction. According to the present numerical model in terms of fracture mechanics, on the other hand, the amplitude power in the direction perpendicular to slip is at most 10 times as large as that in the direction parallel to slip. The difference of 100 times reported by Power et al. (1987) cannot be explained by our model. This large difference is most likely caused by the wear effect. Thus, the present model does not seem to work for a long-time active fault with a large slip distance. In addition to the wear effect on the topography, it may be necessary to evaluate a rupture speed effect on the topography in the next step. According to the result of Freund (1979), the Mode II stress field shows a broader distribution for a higher rupture speed when the rupture speed is less than the Rayleigh wave speed, and shows two peaks in distribution when the speed exceeds the Rayleigh wave speed. In these cases, branching of cracks possibly occurs. Considering this phenomenon, our present crack model should be regarded as a model to the first order approximation. There are still a few effects we should consider in modeling the topography as stated above. However, the topographic anisotropy is necessarily brought without the wear effect by the stress distribution itself at a crack tip of shear fracture, because there must be an anisotropy of the stress distribution at the crack tip in any model based on the fracture mechanics. In considering the fault evolution relating to the topographic anisotropy, it is important that the static frictional coefficient in a rougher surface is generally larger than that in a smoother one (Barton, 1976). The frictional coefficient in the slip direction is expected to be smaller than that in the slip-perpendicular direction, since the topography in the slip direction is smoother than that in perpendicular one.

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This means that the slip direction on a given fault is difficult to be changed once the fault takes place.

6. Concluding Remarks The topography of slickenside at a depth of 1,880 m in Matsushiro earthquake swami region has two noticeable characteristics: (1) The topographies parallel and perpendicular to the slickenlines can be regarded as the fractal topography in the wavelength range from 100pm to 1 cm, having the same fractal dimension of 1.25. (2) The slickenside topography is anisotropic. The power spectral density of the profile perpendicular to the slickenlines are 2 to 4 times larger than those parallel to the slickenlines. The simple crack model based on the fracture mechanics can successfully produce the above two characteristics of the slickenside topography. In this model, the fractal nature of the topography results from the fracture in the random medium. The anisotropic topography is cased by the difference of the stress field around crack tip between parallel to and perpendicular to the slip direction.

We are grateful to K. Aki and H. Sato for giving us an opportunity to make this work. We are indebted to Y. Seki whoperformed a chemicalanalysis of the mineralscovering the slickenside. We thank O. Nishizawa and P. A. Jarvis for their helpful comments on the manuscript. We acknowledgeH. Yukutake and N. Kato for their criticallyreviewing the manuscript and valuable comments. This work was partly supported by the project of special coordination funds for promoting scienceand technologyof the Scienceand TechnologyAgency of Japan entitled "Study of earthquake fractureand seismicwave propagation in the inhomogeneousstructure of the earth."

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