## 4 Results
### Microstructural Analysis
#### 4.2.2 Image Analysis  
Image analyses have been conducted for three areas in deformation bands (B6_8.2 m_Area I_DB, B6_8.2 m_Area III_DB and B6_8.2 m_Area V_DB), and two areas in host grains (B6_8.2 m_Area II_H and B6_8.2 m_Area IV_H) from borehole core sample B6 (Figure 5a). In addition, one area for each host part and deformation band in a fine- to medium-grained sandstone from the Shakubetsu Formation (KT2) was analyzed. Further, one area in host parts of a fine- to medium-sandstone sample from an outcrop of the Shitakara Formation (KT4), where no deformation bands developed, was analyzed for a reference to host parts. First, an example of data acquisition with GIMP for the image analysis was shown for one area in deformation bands (B6_8.2 m_Area V_DB, Figure 9). The outline of detrial grains was relatively well acquired based on the comparison between the microphotographs (Figure 9a) and images processed by GIMP (Figure 9b). The diagram of the area frequency versus logarithmic grain size (\(D\)) was subsequently constructed for all the areas of host parts and deformation bands in different samples (Figure 10). In addition, the diagram of cumulative logarithmic frequency versus logarithmic grain size (\(D\)) was constructed for all areas in the different samples (Figure 11). Further, the histogram of aspect ratio \(R\) (Figure 12), the orientation distribution of the long axis of detrital grains (Figure 13), and the histogram of the circularity \(C\) (Figure 14) was obtained for all areas in the different samples. Figure 8: Microphotograph of phyllosilicate bands in outcrop sample KT3. See Figure 1b for the locality. (**a**) Phyllosilicate bands (plane-polarized light). Note that chlorite and iron oxide or hydroxide (probably limonite) grains aligned parallel to the bedding plane (the short dimension of the microphotograph) (**b**) SEM-BSE microphotograph of altered chlorite grains aligned parallel to the phyllosilicate bands, including limonite grains. Measurements points for microchemical analysis with SEM-EDS and EPMA are indicated by filled red circles. The measurement points P2 and P4 are outside of the view. See Table 3 for the compositions. Chl, chlorite; Lm, limonite; Kln, kaolinite. Figure 9: An example of the grain outline data acquired with GIMP. Sample B6_8.2 m_Area V_DB. (**a**) Microphotograph of the deformation bands area (cross-polarized light). (**b**) Acquisition of grain boundaries with GIMP. The average grain sizes in the deformation bands were significantly smaller, which are 29 \(\upmu\)m, 30 \(\upmu\)m and 24 \(\upmu\)m for the deformation bands areas I, III and V, than those in the host parts, which were 47 \(\upmu\)m and 135 \(\upmu\)m for the areas II and IV of borehole core sample B6 (Figure 10). In outcrop sample KT2, while the average grain size in the host area was 148 \(\upmu\)m, that in the deformation band was 33 \(\upmu\)m. In outcrop sample KT4, the average grain size was 109 \(\upmu\)m. The logarithmic grain size distribution in outcrop sample KT4 was similar to that in the host area in outcrop sample KT2, which was also like that in one host area (B6_8.2 m_Area IV_H) from borehole core sample B6 (Figure 10). However, the average grain size in another host area (B6_8.2 m_Area II_H) was significantly smaller than that in the area B6_8.2 m_Area IV_H. Therefore, the grain sizes of undeformed sandstones were reduced to sizes less than one-half to one-fifth of the original ones by cataclasis to form deformation bands. It should also be noted that the frequency distributions of these grain sizes in the host areas generally showed a log-normal distribution, while those in the deformation band areas are negatively skewed (Figure 10). The cumulative logarithmic frequency (N) of logarithmic grain size (\(D\)) clearly indicated that the distribution follows a power law (i.e., fractal distribution) in deformation bands areas, while it is exponential in host areas (Figure 11).