## 4 Results
### Microstructural Analysis
#### 4.2.2 Image Analysis
Here, the power law distribution is expressed as \(N=cD^{-n}\), where \(c\) is constant, and \(n\) is the fractal dimension. Comparable results have been reported in deformation bands from the ancient accretionary sediments in southwest Japan [50], where the deformation bands are a cataclastic web. The negative slope of the cumulative frequency (i.e., fractal dimension, \(n\)) varies between 2.1 to 2.7 for deformation bands in borehole core sample B6 and 1.3 for that in outcrop sample KT2. These \(n\)-values were comparable to a natural one (2.5) by [50] and those for naturally and experimentally fractured rocks (0.8 to 2.5) summarized by [51]. The reasons for the cause of the difference in \(n\)-value between the core and outcrop samples are unknown. Figure 10: A summary diagram of grain area percent versus logarithm of grain size (\(D\)) for the four deformation band areas and four host areas in the core and outcrop samples. N is the number of grains analyzed. The average aspect ratios in the deformation bands varying between 1.9 to 2.3 were nearly equal to those in the host areas varying between 2.1 to 2.3 for B6 core samples (Figure 12). Also, the shape of the histogram was not very different between the deformation bands and host areas. The aspect ratio was significantly smaller (1.9) only in the area B6_8.2 m_Area V_DB than those in the host areas, where fracturing of detrital grains was most pervasive based on the grain size distribution (Figure 10). This fact was consistent with the results by [44]. The average aspect ratio (2.1) was slightly higher in the deformation band area (1.9) than that in the host area for outcrop sample KT2. The result was not consistent with that of [44]. This could have been caused by the replacement of detrital grains with lower \(R\)-values (less than 1.6) by the fractured grains with higher \(R\)-values to form deformation bands (Figure 12). Figure 11: The cumulative frequency of logarithmic grain size (\(D\)) for (**a**) four deformation bands and (**b**) four host areas in the core and outcrop samples. The best fit straight lines with the slope and intercept are shown for (**a**), while the straight lines for the DBs are shown as reference in (**b**). Sample name is shown at the upper right corner of each diagram. See Figure 10 for the number of grains analyzed. In the host areas of both B6 core and outcrop samples, the overall distributions of grain long-axis were generally random (Figure 13, rose diagrams). The grain long-axis tended to be more parallel oriented to the deformation bands in the deformation band areas than in the host areas for both B6 core and outcrop samples, consistent with the results from [44]. This fact could indicate that the fractured grains became reoriented to be parallel to the deformation bands by compaction and shear during the formation. Figure 12: The histogram of aspect ratio for the (**a,c,e,g**) four deformation bands and (**b,d,f,h**) four host areas in the core and outcrop samples. Sample name is shown at the top of each diagram. The average value and one standard deviation (\(\sigma\)) are also shown. The average circularities (Cs) in the deformation bands varying between 0.65 to 0.69 were slightly higher than those in the host areas varying between 0.55 and 0.64 in both borehole B6 core and outcrop samples (Figure 14), consistent with [44]. Further, it is important to note that the histograms showing a normal distribution in the host areas become not only flattened, but also negatively skewed in the deformation bands areas. The tendency was most significant in the most pervasively fractured area B6_8.2 m_Area V_DB. The increase in the average circularity might be caused by the flaking of asperities of detrital grains [44]. Figure 13: The orientation distribution of the long axis of the fitted ellipse to the grain shape for the (**a**,\(c\),**e**,**g**) four deformation bands and (**b**,\(d\),\(f\),_h_) four host areas in the core and outcrop samples. Sample name is shown at the top of each diagram.