## 2 In Situ Acoustic Emission (AE) Monitoring--Fundamentals
### Box 3. Comparison of accelerometer and piezoelectric AE sensor. A combination of AE sensors and triaxial accelerometers were used in the gold mines in South Africa, salt mines in Germany, and underground hard rock laboratories in Switzerland and Sweden. These AE sensors manufactured by Gesellschaft fur Materialprufung und Geophysik (GMuG) uses a piezoelectric disk of PZT ceramic, which is sensitive in the frequency range from approximately 1 kHz to approximately 200 kHz. On the other hand, the commercial triaxial piezoelectric accelerometer composed of Wilcoxon 736T has a flat frequency response between 100 Hz and 25 kHz with a sensitivity of 100 mV/g and a resonance frequency at 60 kHz. [PERSON] et al. [43] concluded, \"that the Wilcoxon accelerometers were not able to record AE events detected with the in situ AE sensors, despite the fact that AE events were present in the frequency range of the accelerometer\". Note that the in piezoelectric accelerometers the piezoelectric disk is solely used to measure the movement of the seismic mass, whereas for AE sensors the piezoelectric effect is exploited to measure stress changes. AE sensors are piezoelectric sensors that are much more sensitive in the kilohertz frequency range than a spring-mass based accelerometer. In the case of a constant acceleration, the acceleration force is in equilibrium with the restoring force of the spring deflected by \(x\) with the spring constant \(c\). \(F=m\cdot a=c\cdot x\). The measuring sensitivity \(S\) of the system results in \(S=x/a=m/c\), if \(x\) is proportional to the output voltage. Accordingly, a large mass and a low spring stiffness lead to a high measuring sensitivity. In the dynamic case, damping forces and inertial forces have to be taken into account in addition to the spring force. The essential damping force is proportional to the velocity \(\dot{x}\) and is described with the attenuation coefficient \(p\). The inertial force is proportional to the acceleration. The resulting equation describes a resonant system: \(F=m\cdot a=c\cdot x+p\cdot\dot{x}+c\cdot\ddot{x}\). Starting from a negligible damping (\(p\approx 0\)), it has a resonance frequency \(\omega_{0}=\sqrt{c/m}\). Thus, according to the above equation, the measurement sensitivity S is firmly linked to the resonance frequency \(\omega_{0}\) in the following way: \(\omega_{0}^{2}\cdot S=1\). This means that a twice as high resonance frequency must be paid for with sensitivity reduced to the factor 1/4. Such spring-mass systems show only sufficiently below their resonance frequency a sufficiently constant proportionality between the measured variable and the deflection. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Test Size/Project** & **Kxyword** & **Publications, Year** & **Network/Source-Receiver** & **Rock Type/No. of AE Events** \\  & & & **Distance \&Mode of Recording** & \\ \hline \multirow{3}{*}{\(\text{L}\)} & \multirow{3}{*}{Independently transect, Japan} & \multirow{3}{*}{Hyralative fracturing} & [PERSON] et al. [57], 1987 & 17 \(\pm\) sensors (s 10 10 kHz), & Slokesing sandstone \\  & & [PERSON] [58], 1987 & 17 \(\pm\) sensors (s 1 \(\  
\begin{table}
\begin{tabular}{l c c} \hline \hline \hline \multicolumn{1}{c}{**Test Site/Project**} & \multicolumn{1}{c}{**Kxywood**} & \multicolumn{1}{c}{**Publications, Year**} & \multicolumn{1}{c}{**Neutors/Source-Receiver**} & \multicolumn{1}{c}{**Rock Type/No. of AE Events**} \\ \hline  & & [PERSON] et al. [2012] & 8.8A represents (10.5 1361Å) and & & \\ \hline Salt mine Meekers, Germany & Cas loading & & [PERSON] et al. [2012] & 4.4S represents (10.8 10Å), & & \\ \hline Salt mine Meekers, Germany & Cas loading & & [PERSON] et al. [2015] & \(\approx\) 10 \(\mu\)s to 60 m, trigger mode with & \\ \hline Salt mine Meekers, Germany & Cas loading & & [PERSON] et al. Often real-time processing (P- and S-wave onset picking and localization) of events is implemented in trigger mode recording.