## 2 In Situ Acoustic Emission (AE) Monitoring--Fundamentals  
### Comprehensive Consideration of the Scale  
An interesting analogy can be made to AE events by comparing it to earthquakes, which can be regarded as largest natural occurring emission sources. The principal mechanism does not depend on the scale: The rapid release of elastic energy by processes of crack growth or deformation within the rock generates transient pulses of elastic wave energy as AE events. In an even larger scale, the same is true for earthquakes. Similar to AE sources, seismic waves propagate through the earth, and are detected with a global network of seismometers located around the world. Therefore, most of the theory of earthquakes can be transferred to AE sources [11; 12]. Figure 1 shows the dependences between measured corner frequency \(f_{C}\), the moment magnitude \(M_{W}\), the seismic moment \(M_{0}\), and the source radius \(r_{0}\) for studies in earthquake seismology, microseismicity, in situ AE monitoring, and AE in laboratory (see more details in Box 1) [13]. In addition, in situ AE monitoring is reported from rock face monitoring e.g., on construction sites [14; 15]. The largest and thereby the longest events, namely earthquakes, are found at the lowest end of the frequency scale (Figure 1). The focal length and displacement of an earthquake can amount to more than several hundred kilometers and up to several meters, respectively. Whereas global seismology exploits frequencies less than 1 Hz, local seismology focuses on the analysis of frequencies of hundreds of Hertz or even 1000 Hz. Recordings of microseismicity in dense local (e.g., borehole) networks or underground are limited to frequencies up to a few kilohertz. In these cases pendulum-based geophones or seismometers are utilized. The corner frequency in the field of microseismic measurements ranges between 5 Hz and some hundred Hertz with magnitudes from approximately 4.0 down to \(-\)2.0. Above these frequencies, the range of in situ AE monitoring in rock begins with applications in mines. In the frequency rang of about 1 kHz up to 200 kHz accelerometersor special piezoelectric AE sensors were developed for in situ application in mines. Source-receiver distances realized depend strongly on rock type, but can reach up to 150 m in rocks with very low wave attenuation. The covered areas may have linear dimensions of up to 200 m. The expected magnitudes are in the range between \(-2.0\) and \(-5.0\). On the other hand, the highest frequencies up to several MHz are utilized in laboratory studies. These frequencies are generated by AE events in the microscopic region, for instance by microcracking of rock or dislocation movement. Only sensitive piezoelectric sensors for laboratory applications are able to measure such high frequencies. In the laboratory, the source radius may extend to some micrometers only and the displacement (Burgers vector) is to be measured in nanometers. The expected magnitude of such small AE events is below \(-6.0\)[11]. A detailed study on the theoretical limits on detection and analysis of small earthquakes in dependency on the sensitivity and frequency coverage of the monitoring network was published by [PERSON] and [PERSON] [16]. Figure 2 taken from [PERSON] et al. [17] shows the co-seismic stress drop plotted with key earthquake source parameters over the entire bandwidth of observed rupture processes, extending from large natural earthquakes to AEs in the laboratory. The source parameters were calculated from individual data sets of natural earthquakes, induced seismicity in mines and reservoirs, and volcano seismicity [18; 19; 20; 21; 22]. AE data are unpublished results from the rock-deformation laboratory in the German research Centre for Geosciences, Potsdam, (GFZ)-Section 4.2. The Madariaga [23] circular source model is assumed to calculate source radii and the lines of constant static stress drop from 0.01 MPa up to 100 MPa and \(v_{s}=3500\) m/s (see Box 1).