## 3 AE Data and Methods  
In order to record ultrasonic signals radiating from microcracking and stick-slip events, and as a pulse source for performing velocity measurements, 12 piezoelectric transducers (PZT) (diameter: 5 mm, resonant frequency: 2 MHz) were mounted on the curvilinear surface of the specimen using epoxy agent (Figure 2). The specimen and two end pieces were coated with silicone sealant to prevent confining oil from leaking into the specimen. The specimens can handle a total shear displacement of approximately 2 mm, which is sufficient for up to approximately 20 stick-slip events. Our new waveform recorder has 24 A/D channels with a sampling rate of up to 100 MHz, a dynamic range of 16 bits, and 256 mega words of onboard memory for each channel. In the present study, the AE signal from each sensor is pre-amplified by 40 dB and then digitized at a sampling rate of 25 MHz and a sample length of 4096 points (approximately 160 microseconds), including 1600 points of pre-trigger data. The maximum amplitudes of AE signals from two selected sensors, which were mounted on the central surface of the specimen (indicated as k1 and k2 in Figure 2), were recorded by the peak detectors after a pre-amplifier of 20 dB. The noise level for AE signals is approximately 40 dB or less after applying the 20 dB pre-amplifiers. Thus, the threshold for the peak dete  
Figure 1: Roughness of pre-cut surface (S1) measured by laser scanner. A and B in (**b**) (rectangle region in (**a**)) indicates direction of two artificially selected profiles, which were used for the calculation of power spectral density function (PDF) of the roughness in (**c**). Figure 2: Schematic of experimental configuration and distributions of piezoelectric transducers (solid circles) and strain gases (crosses). The maximum amplitudes of AE signals from k1 and k2 were recorded by the peak detectors and used for the calculation of seismic \(b\)-value. yielding an effective dynamic range of 55 dB (=100 \(-\) 45 dB). Based on the definition of the body-wave earthquake magnitude, the magnitude (\(M\)) of an AE event is determined according to the log of the maximum amplitude (\(A_{max}\)) of the AE signal (it is somewhat reflecting the vibration velocity of the elastic wave [13]), as follows:  
\[M=\log(A_{max}/A_{0})+M_{0} \tag{1}\]  
where \(A_{0}\) is the threshold for detection, and \(M_{0}\) is a constant (approximately \(-10\), in our system) for converting the obtained value to a magnitude that is roughly comparable with the magnitude of an earthquake. Normally, \(M_{0}\) = 0 is used, and Equation (1) yields a relative magnitude that can be used for calculation of seismic \(b\)-values in the Gutenberg-Richter magnitude-frequency relation. \[\log N=a-bM \tag{2}\]  
where \(N\) is the number of events of magnitude \(M\) or greater, and \(a\) and \(b\) are constants. In order to investigate the temporal evolution of the \(b\)-value, we calculated \(b\)-values using both the maximum likelihood method for a running window of an equal number of events (\(n\)) with a running step of \(n/4\) events (75% overlap). The approximate standard error of the \(b\)-value estimation is \(b/\sqrt{N}\). A larger window size results in smoother evolution of the \(b\)-value. In the present study, \(n\) = 1000 was used for a long-term view, while \(n\) = 250 was used to explore \(b\)-value variation for each stick-slip event. We performed this analysis using various values of \(n\) and found that \(n\) = 250 was a good choice for exploring the details of \(b\)-value evolution with sufficiently small errors. Due to attenuation, some small events could be recorded by only one peak detector close to the AE hypocenter. As a result, the number of events counted by two detectors could be different. However, we confirmed that the two datasets yielded consistent results for the temporal variation of the \(b\)-value [7]. Waveform data were recorded for the purposes of hypocenter determination and source mechanism solution, which require clear first motion at more than four sensors.