## 2 Materials and Methods
### Digital Image Correlation Method to Observe Fault Slip  
To improve the spatial sampling rate of the fault slip measurement, a high-speed camera (Photron Fastcam SA2, Japan) was used to capture images of the upper sample surface during three stick-slip events (E1, E2, and E3 in Figure 2). The recording duration of each event was 7.127 s. The sampling rate was 1000 frames per second. The resolution of each image was 1792 \(\times\) 1792 pixels. The actual size of each pixel corresponding to the sample surface was 157.8 \(\times\) 157.8 \(\upmu\)m\({}^{2}\). Since the images needed to be exported from the camera buffer to the computer (that takes 1 h or more depending on the data transfer rate of the equipment) after each recording to ensure the next acquisition could be performed, not all of the stick-slip events could be recorded. As a result, only three stick-slip events were recorded in the experiment. Since stick-slip events of similar recurrent periods occurred repeatedly in each loading rate as shown in Figure 2, the three recorded stick-slip events were representative for the events at the same loading rate. The DIC method, which is an object recognition method based on pattern matching via a correlation algorithm in computer graphics [29; 30; 32; 33; 34], was used to process the images and calculate the displacement field of the upper sample surface. The region of interest (ROI), which is a rectangle zone covering the whole fault, was chosen to calculate the displacement field. The determination of the size of the subregion is as follows. The change of the correlation coefficient (\(CC\)) with the side length (\(R\)) of the square subregion used to calculate \(CC\) in the DIC method was tested and shown in Figure 3. \(CC\) decreased and remained unchanged before and after \(R\) reached 25 pixels, respectively. However, the standard deviations of \(CC\) decreased as \(R\) increased. Based on the principle of selecting the minimum \(R\) under the condition that the \(CC\) was sufficiently high via comprehensive consideration of the mean and standard deviation values of \(CC\)[26; 28], \(R\) = 25 pixels was used to calculate the \(CC\) in  
Figure 2: Variations of the differential stress (\(\sigma_{1}\)-\(\sigma_{2}\)) and piston displacement along the \(Y\)-axis (\(dy\)) with time (\(t\)). The inset is a magnified view of the black rectangular zone showing details of the stress drops during a loading rate of 0.5 \(\upmu\)m/s. E1, E2, and E3 are the numbers of the stick-slip events indicated by the arrows, which are also the events observed by the high-speed camera. the DIC method. The subregion was moved pixel by pixel in the calculated image when calculation was performed. All of the images were calculated with respect to the first image in each stick-slip event and, accordingly, the cumulative displacement field of the ROI was obtained. The threshold for determining whether a calculation result was reliable depended on the \(CC\). Namely, the calculated displacement on a location was reliable when the \(CC\) in the location is larger than 0.99973, which was twice the standard deviation lower than the average value of \(CC\) at \(R=25\) shown in Figure 3.  
Two bent lines on both sides of the fault (the red symmetric lines about the fault in Figure 1) were selected to calculate the fault slip. Each line was offset 5.839 mm from the fault, which made the fault not intersect the subregion with the center point located at the line and ensured the accuracy of the fault slip measurement [26; 28]. The two bent lines each contained 1700 measuring points (pixels), of which 810 were in segment \(S_{I}\) and 890 were in segment \(S_{II}\). The spacing between the measuring points was 0.214 mm. The two lines were symmetrically distributed with the fault. Each pair of symmetric measuring points from the two lines formed a fault slip gage. As a result, a total of 1700 fault slip gages with spacing of 0.214 mm were used to observe the detailed spatial distribution of the fault slip.