Figure 4.The graph showing the circularity of particle rotation due to the continuously given shear strain. The result of analyzing each particle starting with different φ_i values and R=3, and the rotation result of the strain ellipse in the direction of the major axis are shown together (modified from Marques and Coelho., 2003). φ: The angle of rotation; R: Particle’s aspect ratio (=a/b); S_r: The rates of pure and simple shear components.|@|~(^,^)~|@|Development history of SPO analysing method. (a) SPO of 2400 quartz measured from Takaka Hill quartzite and the orientation of c-axes given principle compressive stress for aspect ratio are shown. (b) The orientation of major axis is aligned differently according to the aspect ratio of the grain. (c), (d) The rose diagram shows the direction of the 2D-SPO in samples taken from the fault gouge. (e, f) The results of measuring 3D-SPO of samples taken from the San Andreas Fault Zone using X-CT are shown on lower-hemisphere equal area projections. (g, h) The results of measuring the 3D-SPO of a fault gouge sample from Yangsan fault for thousands of particles using synchrotron X-CT are shown in lower-hemisphere equal area projections with a result interpreted using a focal mechanism solution. (Modified from Shelley, 1995; Cladouhos, 1999; Sills, 2010; Sim et al., 2020a, 2020b).|@|~(^,^)~|@|A schematic diagram showing the process of estimating the fault motion from the major axis direction of the rigid grains included in the core sample taken from the fault gouge. (a) A schematic diagram showing the core sample taken from the fault gouge and the separation of direction vectors according to the fault motion direction. (b) The orientation of grains included in the core sample is measured on the X-CT image. (c) Direction of fault motion (V_fm) and rake values are estimated through the grain SPO and plotted on a stereo-net (Modified from Sim et al., 2020b). Vss: vector of strike-slip; V_ds: vector of dip-slip; V_fm: vector of fault motion; and V_SPO: vector of densest point of SPO.|@|~(^,^)~|@|The results of measuring the 3D-SPO of a fault gouge sample are shown in lower-hemisphere equal area projections. (a) The SPO analysis results of each representative sample with different orientation distributions of three axes are shown. The distribution of major/middle/minor axes are colored by red, blue, green, respectively. (b) the SPO analysis results according to the aspect ratio value are shown (Modified from Sim et al., 2020a, 2020b). Vc: the densest orientation vector of c axes; SDI: SPO Distribution Index.

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