Difference between revisions of "Mining induced seismicity"
(→S-wave to P-wave Energy Ratio)
(→Magnitude – Time)
|Line 233:||Line 233:|
===== Magnitude – Time =====
===== Magnitude – Time =====
Plotting the seismic events according to their magnitude and time leads to Magnitude -Time history of seismic events. From measuring the changes in the slope of cumulative number of events line, it is possible to infer about the seismic event rate <ref name="Hudyma 2007a"> Hudyma, M, Potvin, Y and Allison, D. (2007a) Seismic monitoring of the Northparkes Lift 2 block cave - Part 1 Undercutting. Proceedings 1st International Symposium on Block and Sub-Level Caving, The Southern African Institute of Mining and Metallurgy, Cape Town, pp. 303-333.</ref>. For example in a time period in which the slope of the cumulative number of events line is relatively constant it is indicating the constant rate of seismic event, while large variations indicate the changes in the event rate which might be related to the different failure mechanisms. Figure
Plotting the seismic events according to their magnitude and time leads to Magnitude -Time history of seismic events. From measuring the changes in the slope of cumulative number of events line, it is possible to infer about the seismic event rate <ref name="Hudyma 2007a"> Hudyma, M, Potvin, Y and Allison, D. (2007a) Seismic monitoring of the Northparkes Lift 2 block cave - Part 1 Undercutting. Proceedings 1st International Symposium on Block and Sub-Level Caving, The Southern African Institute of Mining and Metallurgy, Cape Town, pp. 303-333.</ref>. For example in a time period in which the slope of the cumulative number of events line is relatively constant it is indicating the constant rate of seismic event, while large variations indicate the changes in the event rate which might be related to the different failure mechanisms. Figure shows the Magnitude-Time history plot of seismic events from a mine in Australia. The cumulative number of events is plotted on the secondary axes. This plot shows events with different magnitudes from March 2006 to February 2007. The variation in the slope of the cumulative number of events line, represents variations in seismic event rates.
[[File:Magnitude_time_history_and_cumulative_number_of_events.png|thumb|center|500px| Figure : Magnitude time history and cumulative number of events during initial blasting in a caving mine in Australia from March 2006 to February 2007 <ref name="Abolfazlzadeh"> Abolfazlzadeh, Y. (2013) Application of seismic monitoring in caving mine-case study of Telfer gold mine. Master thesis, Laurentian University, Sudbury, Ontario, Canada. </ref> ]]
===== Energy- Moment =====
===== Energy- Moment =====
Revision as of 12:22, 6 December 2014
The scope of this article covers seismic sources, monitoring and analysis methods of seismic events and mine design in the context of seismicity management in underground mines. All Underground mines experience some degree of seismicity. Damage due to seismicity has been observed in various mines around the globe. Seismic events will occur as a result of blasting, fault slip, rockbursts or any other source of rock fracture and ground movement. Reducing seismicity in mines is a major challenge of deep underground mining. To minimize and mitigate damage from dynamic ground in an underground mine; understanding, assessing and designing with consideration of seismicity, and changes in seismicity, are essential.
- 1 Why Seismic Monitoring?
- 2 Seismic Waveform Characteristics
- 3 Seismic Data Collection
- 4 Analysis of Induced Seismicity
- 4.1 Event Clusters
- 4.2 Seismic Source Mechanisms
- 4.3 Maximum Expected Magnitude
- 4.4 Gutenberg-Richter Relationship
- 4.5 Seismic Hazard Magnitude
- 5 Planning
- 6 References
Why Seismic Monitoring?
Seismic monitoring in a micro scale provides useful information about the local state and stress conditions which can be used for identifying active structures and for better understanding of the rock mass behaviour (i.e. rock mass failure and its failure mechanism). This is done by analyzing the continuous four-dimensional seismic record from a rock mass as a result of progressive mining. On the other hand, in a macro scale, microseismic monitoring can be used to determine the current state of tectonic activity ( and).
The location of seismic events provides an insight into the relation between the events and active mining area, and also the time dependent variations of this relation. Provided this information, ground control and the mine design sequences can be optimized which can help in increasing the mining safety and reducing the costs.
Seismic Waveform Characteristics
Seismic events are caused by the sudden release of energy as a result of stresses overcoming the strength of the rock, breaking it. This energy release is then propagated through the rock as pressure waves. Some waveform characteristics that are important to know for application to mines are as follows:
Compressional Waves and Shear Waves
P-waves or compressional waves can travel through air, liquid and solid. The slowest P-wave velocity is in the air which is around 330 m/s (around the speed of sound). S-waves or shear waves can only travel through solid. For example when a seismic wave attempts to travel through a volume of water, the P-wave component of the seismic wave can transmit through the body (not the surface) of the water but the S-waves (vertical and horizontal components) cannot travel through the medium. Figure 1 is representing typical waveforms of P and S-wave.
Compressional and Shear Waves Propagation Through Various Media
Table 1 shows the velocity of the P and S-waves in different mediums 
There are three general waveforms produced from a single seismic event; P-waves, S-waves and surface waves. P-waves are compressional waves, and travel at the greatest velocity, making them the first-arrival waveforms. The S-Waves are shear waves, travel at a velocity slower than the P-waves making them the second arrival waveforms. Surface waves are not significant in mining applications. Figure 2 displays a seismic form with the first-arrival P-wave and second-arrival S-wave.
Magnitude is an assessment of the energy released during a seismic event, describing the event size . Magnitude is a relative measure of a seismic event size. Majority of the magnitude scales are based on amplitudes recorded over a particular spectral band. Magnitude scales are logarithmic, so a seismic event with magnitude of 1.0 has a 10 time larger amplitude than a seismic event with magnitude of 0.0 and also approximately 30 times greater energy. Some of the commonly used magnitudes for measuring the strength of a seismic event are described in Table 2.
For mining applications, the Richter scale is used. Event magnitude is generally proportional to potential damage of a rockburst, as the magnitude increases the probability of a large rockburst increases . Table 3 displays the approximate relationship between the characteristic maximum event magnitudes with source mechanisms.
The hypocenter of a seismic event is the original location at which the seismic event has taken place. From the hypocenter, the waveform propagates outwards. The original sudden release of energy from fracturing rock, such as a fault slip or rockburst event, takes place at the hypocenter of the event. Commonly, the original seismic event will be the result of induced stresses from within the mine.
As a result of the sudden seismic event the stress, strain and particle velocity is propagated through the rock. This may alter the stress field, which may drive additional rock failure. For example, rockburst may occur in brittle rock when a sudden increase of stresses are present. Also, at the face of excavations, when the stress wave is reflected backwards, the tensile stresses of the waveform may be high enough to exceed the tensile strength of the rock, which is relatively low compared to compressive rock strength .
Static Stress Drop
For seismic events related to the fault slip, the static stress drop is defined as the average difference between the initial and final (shear) stresses.
Dynamic Stress Drop
Dynamic stress drop measures the stress release related to the failure along the strongest part of a fault. The dynamic stress drop is model dependent.
Apparent Stress is a model independent estimate of stress variation at a seismic source and is defined as the difference between the average loading stress and the average resisting stress. Apparent Stress is a seismic source parameter derived from using the following relation .
High stress regions tend to release more seismic energy while they tend not to allow as much deformation due to high clamping forces. This results in comparatively higher Apparent Stress events. Low Apparent Stress events may be due to lower stress areas, or areas that have shed load due to prior rock mass fracturing. It is possible to track the relative stress levels using seismic data . At Brunswick Mine, Simser et al.  found that it is common to see well-developed stress fracturing around openings in the massive sulphide material, particularly in sill pillar situations. The more fractured the rock mass is, the more mobile it becomes, and relatively higher seismic moments are characteristics of this seismicity (Figure 3).
Seismic events are caused by sudden failures within the rock mass which result in stress drop. The most significant seismic events should normally be associated with a stress reduction. Consequently, higher Apparent Stress seismic events usually occur in areas where the stress levels are still relatively high .
Seismic events associated with areas where significant stress occurs due to blasting (change in geometry), often have a higher than expected seismic energy, that results in a higher than normal Apparent Stress ( and ). Hudyma  also noted, in several case studies, that blasting often triggers increases in the number of high Apparent Stress events, specifically in proximity to where stress increase would be caused by the blast.
Apparent Stress Time History (ASTH) is a seismic data analysis technique, in which the daily number of events with an Apparent Stress equal or greater than a threshold in a trailing (preceding) time period. ASTH is a method for investigating variations of Apparent Stress. Apparent Stress is a potential indicator of elevated temporal seismic hazard . Figure 4 shows ASTH for a group of events where all 8 of the large events (local magnitude > 0) occur during or very close to period in which the Apparent Stress Frequency exceeds 5 events per day. In this example, Apparent Stress frequency is averaged over 7 days and the Apparent Stress threshold is 10,000 Pa .
Seismic Data Collection
Collection of seismic data includes quantified results from monitoring in conjunction with qualitative observations in the mine. Results from monitoring must be compared to visual observations underground from routine inspections, in order to calibrate and accurately assess the monitor data .
Monitoring with Instrumentation
Monitoring in mines allows for observations to be assessed numerically. Seismic monitoring systems consist of a network of geophones, which measure the acoustic waveforms, generated from rock fracture, at the locations of the individual geophones. With the digitization of the geophone monitoring systems data is automatically uploaded for engineers to access, and patterns over large time-frames can be assessed .
Instrumentation used to assess seismicity, as well as strain and deformation as a result of seismicity, includes geophone networks, extensometers and strain gauge cells. Through strain gauge cells and extensometers, the ground stress and strain can be monitored in order to access damage due to seismicity. However, there is more inherent error associated with these two instruments. The effectiveness of using geophones is dependent on the accuracy of the assumed seismic velocities and the accuracy of the acoustic waveform reading. Also accuracy is commonly within a few meters when determining hypocenter location. However, by implementing a good seismic network of geophones, more accurate results can be achieved.
Implementation of a monitoring network must be done in order to minimize error by designing the spatial formation, volume and configuration of the network. Figure 5 displays a schematic diagram of a typical seismic monitoring network for an underground mine. The spatial formation of the geophones should take in account the distance to the event hypocenter as well as the structural geometry between the hypocenter and the geophones. The configuration of geophones around the hypocenter should be at a range of distances in order to detect several waveforms from a single event. The number of sensors used determines the volume of the monitoring network. The volume of the network will vary depending on the critical structures or stopes that are assessed. Seismic sensor configuration can be uniaxial or triaxial. Triaxial configurations are able to assess event magnitude, seismic energy and seismic moment, whereas the uniaxial geophones are more accurate in locating the source hypocenter. Uniaxial sensors are better for coverage in the mine, whereas triaxial sensors are better for post-processing seismic results.
In reality, the location of the seismic event will not be known, as the location of the seismic event will vary, as a result of dynamic stresses and deformation within the mine. However, the preliminary stability design of the mine should have a valuation of the at-risk structure and stopes of the mine, and the seismic monitoring systems should be configurable to the at-risk structures. Overall, geophone monitoring networks are recommended to monitor seismicity in a mine, as they are easy to install and the network can be configured to assess the particular failure mechanisms of the mine. If fault surfaces are exposed in the excavations, evidence of fault slip (movement along the fault surface) or strain should be observed.
Geophones (4.5 vs. 15 Hz), Accelerometers and Strong Ground Motion Systems
It is necessary to have an accurate event source location. This accuracy depends on several factors such as number of sensors used, seismic system array, velocity model and etc. There are generally two types of seismic monitoring systems for recording seismic events in the mining area, geophones and accelerometers. Two types of geophones, 4.5 Hz and 15 Hz, are most the commonly used for mine seismicity monitoring. The 4.5 Hz geophones are used for recording events with larger moment magnitudes (0.5 < Mw < 3.0) while the 15 Hz geophones record smaller events (-1.5 < Mw < 1.5). Accelerometers record very small events (-1.5 < Mw < -3.0). Thus, for having a decent coverage of different seismic event magnitudes, it is necessary to have a combination of geophones and accelerometers . Each of the geophones or accelerometers can be uniaxial or triaxial. Triaxial sensors are consisted of three orthogonally mounted uniaxial sensors. The primary function of uniaxial and triaxial sensors is different as uniaxial sensors provide accurate event source location, whereas the triaxial sensors determine the seismic source parameters . Although uniaxial sensors have lower cost but for having a full record of seismic wave energy (leads to accuracy in source parameter and mechanism), more accurate S-wave recognition, and having an ideal seismic array, it is necessary to have a good balance between triaxial and uniaxial sensors. As a rule of thumb, for every 3 uniaxials, one triaxial is needed.
Table 4 represents the advantages of different kinds of sensors, geophones (uniaxial/triaxial) and accelerometers (uniaxial/triaxial).
In addition to these sensors, strong ground motions systems (SGM) are used for improving the event location and magnitude measurements for large events. Strong ground motion systems are unusually installed on the ground surface and record larger events.
Recorded seismic waveforms similar to other waveforms, have certain characteristics such as signal, amplitude, wavelength, frequency and corner frequency. The corner frequency is the characteristic frequency of a seismic event related to the duration, source radius, and the estimated wavelength of a signal  (Figure 6).
Table 5 shows the magnitude ranges of seismic events which can be recorded in a mine and their corner frequency, period, wavelength and associated source radius. It can be seen that the larger events have lower corner frequency, wave length and source radius (inverse relation).
Routine inspections of the excavation surfaces will provide information about the influence of seismic stress and seismic events. Seismicity in a mine will produce active ground, which will alter the observable surface of excavations. Overall, displacement of rock is indicative of changes in the stress field, and will provide information regarding the mine seismicity .
Proper inspection of the mine will include the excavation surfaces, exposed fault surfaces, failure of ground support, fresh loose rock and changes between these focuses before and after a large event. Stopes and drifts near to current development and production stopes should be inspected regularly. On the excavation surfaces, fresh cracks, buckling and loose rock are important to observe, as they may indicated changes in the stress field, as displayed in Figure 7. If there are exposed fault surfaces present in the mine, check if there is evidence of fault slip (movement along the fault) or strain. Joint surfaces are including in this description, as some joint surfaces may slip and become active faults due to a change of field stresses. Failure of ground support and additional loading of ground support are both indicators of changes to the stress field. Borehole breakouts, as displayed in Figure 8, can indicate the direction of the principle stress on a 2D plane, which are useful to quickly assess the change of the stress field in a particular drift.
Comparing inspection information with monitor data will allow for calibration of the data set and failure mechanisms present in the mine. Implementing regular, routine inspections are beneficial to determine a history of stability and excavation performance as development of the mine progresses.
Analysis of Induced Seismicity
Data analysis from information collected from a seismic monitoring network in a mine will determine the seismic parameters of the separate seismic event clusters in the mine. For each seismic cluster, seismic parameters are to be analyzed in order to design for mitigation of seismic damage. Common seismic parameters that will be discussed in this article are maximum expected magnitude, the Gutenberg-Richter relationship and source mechanism. Additional seismic parameters are discussed in. Understanding the seismicity hazard and failure mechanism of each event cluster indicates risks in the mine plan. The seismic hazard is assessed from the seismic likelihood and consequence which are determined form the Gutenberg-Richter relationship and the maximum expected magnitude, respectively.
To assess the seismicity in a mine, the single events must be clustered according to event location and time. There is high inherent variability in mines due to production and development blasting and equipment noise as well as from rock failure, therefore clustering of events is an important step. Seismic events will commonly cluster near in geologic discontinuances or at excavation boundaries, as displayed in Figure 9, where there are high concentrations of stresses and the difference in material properties will allow for higher changes in the stress field to occur. Commonly, individual event clusters will have different seismic sources.
Events are clustered by location of the event hypocenter as well as the time of the event. With digital monitoring, event timing is easily assessed. To determine the location of the seismic source, the differences between arrival times of the incoming waveforms to the geophone sensors are recorded, in order to find the distance of the hypocenter from at least three individual sensors with an assumed value for seismic travel velocity. Figure 10 displays the computation of a hypocenter from the arrival times of three individual sensors.
Seismic Source Mechanisms
The failure mechanism for each cluster of events may differ. To reduce complexity in the analysis, assessing the failure mechanism sources should be completed independently for each event cluster. The failure mechanism will vary between different clusters of events, due to the variation of failure mechanisms driving the seismicity, as displayed in Figure 11. Seismic source mechanisms in mines are either shear failures of geological structure, fault slip, or from tensile rockmass failure. From a variety of analysis techniques the source of the seismicity mechanism can be determined, whether it is from rockmass failure of a pillar or stope wall, or fault slip along a geological structure.
To differentiate fault slip failure mechanism from the rockmass failure mechanisms, P-waves and S-waves of events within the cluster are assessed. The ratio of seismic energy between the S-waves and P- waves indicate the type of failure mechanism for that event cluster. Dilatational, compressive or tensional, failure mechanisms, such as strain bursting (rock bursts), caving and pillar failure, produce more energy in the compression waves, P-wave. On the other hand, shear failure mechanisms, such as fault-slip on geological structure such as joints, faults and geological material boundaries. There is always more S-wave energy than P-wave energy, thus the S:P Ratio for dilatational failure is 3 -1 and the S:P Ratio for shear failure is >10. If the S:P ration of the event cluster is between these values, the failure mechanism will have both shear and dilatational failure mechanisms.
In the case of shear failure, the orientation of the fault plane, displayed as the moment tensor solution, can be determined through fault plane solutions (or also referred to as focal mechanism). The waveforms detected from a fault slip event will have either compressive or dilation polarity at the first arrival of the waveform, as displayed in Figure 12. Assessment of the waveform polarities at many seismic sensors surrounding the hypocenter will produce a moment tensor, as displayed in Figure 13. The moment tensor displays the orientation of the fault surface as well as an estimate of principal stresses present to activate the fault slip.
As previously discussed, there is more energy present in shear-waves that in pressure-waves. This is also displayed above in Table 3, where the seismic source mechanisms are generalized. Table 3 presents fault slip and shear failure mechanisms with greater energy. Ortlepp’s work also presents many other characteristics and patterns of rockbursts and seismic events with the seismic source mechanism.
Direct Waveform Techniques
When a seismic event occurs, the produced energy in the form of waves, radiate from the hypocenter to all directions. This is plotted in a lower-hemisphere stereographic projection. Interpreting the lower hemisphere projection is a tool for determining the seismic source mechanism. Two main technique which are used for defining the seismic source mechanisms, are moment tensor inversion technique and fist motion analysis.
First Motion Analysis
According to the polarity of the P-wave arrivals, the area around the epicenter can be divided into the dilatational and compressional quadrants. These quadrants are related to the initial upward and downward vertical motion on the seismograms, respectively. Generally, compressional quadrants are shaded and dilatational quadrants are left unshaded producing a P-wave first motion pattern similar to a beachball. For example, in the case of seismic event due to fault slip the area around the epicenter can be divided into 4 equal quadrants related to the dilatational (two quadrants) and compressional (two quadrants). These quadrants are separated by two perpendicular nodal planes.
Real events have a mixture of positive and negative polarities but blasts have explosional first motions (all sensors should record a positive first motion). Figure 5 represents the stereonet plots for classical Anderson faults.
So, direction of first motions depicted by seismic sensors provides information on the source mechanism.
Moment Tensor Inversion
Moment tensor is a powerful tool in defining the source parameters mathematically. Jost and Herrmann . proposed that the first order moment tensor defines the equivalent forces acting at seismic point source in a first order of approximation. The magnitude and mechanism of a seismic event can be conveniently represented by a moment tensor:
The seismic moment tensor includes double-couple forces (most earthquakes may be approximated by double-couple) and other force couples (Figure 14). Six out of the 9 components of the moment tensor are unique (moment tensor is symmetric).
Moment tensor inversion methods provide meaningful information about the mechanism of the fracture plane failure for understanding the fracturing process, geological and mining activities. Generally the seismic moment tensor can be decomposed into isotropic (the least well-resolved parameter) and deviatoric components. The decomposition of Mdeviatoric is not unique and various decompositions may lead to different interpretations. The Mdeviatoric can be decomposed into a double-couple and a compensated linear vector dipole (represents crack opening under tension). The tensors of isotropic, double-couple and CLVD sources are as follows:
Figure 15 shows the different modes of failure and their estimated radiation inferred from moment tensor inversion.
Indirect Waveform Techniques
Seismic waveform techniques or inferred seismic techniques are used for inferring seismic source mechanism and seismic hazard. The theory behind these techniques is that the most of the seismic events from one seismic source have similar seismic source mechanism and parameters. So it is important to have a large number of events to apply this methods properly .
S-wave to P-wave Energy Ratio
The ratio between the S-wave to P-wave is an indicator of seismic source mechanism . When the low ES/EP (ES/EP < 3) represents events due to strain-bursting, tensile failure, and volumetric rock mass fracturing , the high ES/EP (ES/EP > 10) is often due to shearing mechanism such as fault slip . It is necessary to note that these are approximate values and uniaxial sensors cannot be used to get meaningful ES and EP ratio.
Figure 16 shows the ES/EP distribution of the all seismic data compared to a cluster of events (black dashed line) from a mine in Australia. The median for the cluster of events is around 2 while this value is around 6.5 for all seismic records. This can be interpreted as the non-shearing failure mechanism is the dominant failure mechanism in this cluster of events .
Magnitude – Time
Plotting the seismic events according to their magnitude and time leads to Magnitude -Time history of seismic events. From measuring the changes in the slope of cumulative number of events line, it is possible to infer about the seismic event rate . For example in a time period in which the slope of the cumulative number of events line is relatively constant it is indicating the constant rate of seismic event, while large variations indicate the changes in the event rate which might be related to the different failure mechanisms. Figure 17 shows the Magnitude-Time history plot of seismic events from a mine in Australia. The cumulative number of events is plotted on the secondary axes. This plot shows events with different magnitudes from March 2006 to February 2007. The variation in the slope of the cumulative number of events line, represents variations in seismic event rates.
Seismic energy is defined as the area under the curve of the velocity spectrum of a triaxial waveform . The seismic moment is a quantity to measure the strength of a seismic event by considering the double couple, shear dislocation source model parameters . The concept behind the Energy-Moment relation is for an event with larger seismic moment we expect greater energy release. Also plotting the logarithmic value of seismic energy versus logarithmic value of seismic moment can be used as a tool to test the seismic data quality . It provides meaningful information to delineate if monitoring-related artefacts exist within the dataset or not (Figure 10).
Energy Index is defined as the ratio between the seismic energy released from a seismic event and the expected radiated seismic energy. This analysis is used to differentiate between the changes in released energy within a group of seismic events .
To simplify the displaying of seismic data and highlighting the periods which have meaningful trends in Energy Index, it is better to use a trailing-moving average trend (i.e. 30 event). The event by event Energy Index calculations and ordering them chronologically, has excessive fluctuations and does not give decent information . In conclusion, EI expresses the stress variations in a rock mass. In a time period when stress is increasing EI tends to be high and starts to fluctuate. While in a case of a major failure, stress starts to be shed and EI drops .
Cumulative Apparent Volume
Cumulative Apparent Volume is the sum of the Apparent Volume. The Apparent Volume is derived from following relation :
Cumulative Apparent Volume (CAV) is a good measure of rock mass deformation related to seismicity. Cumulative Apparent Volume is model dependent and it has been found that when the stress increases (large fluctuations in EI) there is low deformation (CAV). The EI (a measure of the relative stress) and CAV (a measure of rock mass deformation) are plotted together on a time history chart. Different case studies in South African “reef-style” gold mines show that EI drops (shedding away of stress) coincides with increase in CAV . Figure 12 is an example of events in a Western Australian mine from mid-September to early December 2002 in which a drop in Energy Index coincides with a significant increase in Cumulative Apparent Volume. Two events with magnitudes larger than Richter +1 occurred coincidentally .
Maximum Expected Magnitude
The maximum expected magnitude is a method to assess the consequence of a seismic event. The seismic moment and magnitude can only be assessed with triaxial sensors . Uniaxial sensors are unable to determine the seismic magnitude as the maximum displacement is unable to be assessed. The seismic magnitude is a measure of the ground displacement to assess the energy release and associated damage with an event, thus is a measure of consequence. The magnitude is calculated as follows:
Where A is the maximum displacement, T is duration of time and C is a correction factor for the path effects, site response and region of the seismic source. The maximum expected magnitude can be estimated by plotting the number of events of a specific magnitude to magnitude, as completed in the Gutenberg-Richter Relationship. Events of a larger magnitude occur less frequently than those of smaller magnitude, and when there is a large risk of a large seismic event there will be an increase in the number of smaller events . The intercept of the x-axis in the relationship, as displayed in the figure below, in the Gutenberg-Richter Relationship, is the estimated maximum expected magnitude.
This is related to the maximum expected magnitude estimated from the seismic source mechanism, as displayed in Table 1 .
The Gutenberg-Richter relationship is an assessment of the frequency at which seismic events of certain magnitude will occur. There is a power lase relationship between seismic event frequency and event magnitude. This relationship is as follows: .
Where M is event magnitude, N is the number of events equal or greater than the magnitude specified, and a and b are site constants, where a is data quality and b is the power law exponent. The b-factor is related to the likelihood of a seismic event occurring and is used to calculated the seismic hazard. The b-factor will vary greatly depending on the seismic source of the events, and will be individually determined for each separate cluster. Figure 10 displays the b-value analysis of two separate event clusters. Smaller b-values (<1) are indicative of fault-slip source mechanisms, and higher b-values (1.2 to 1.5) are indicative of a failure mechanism due to changes of the stress field. There is a larger probability of large magnitude events occurring when the b-value is smaller.
Seismic Hazard Magnitude
The seismic hazard is assessed for each event cluster, from the seismic likelihood and seismic consequence. The seismic likelihood is determined through the b-value of the Gutenberg-Richter relationship, and the seismic consequence is related to the maximum expected magnitude. Figure 11 displays the estimation of hazard magnitude, where the area under the Gutenberg-Richter relationship between the maximum expected magnitude and the minimum magnitude to cause damage. The minimum magnitude to cause damage is dependent on the condition of the mine excavations.
Seismicity is assessed in mines in order to reduce production delays and to improve mine safety. It is not possible to predict the location and timing of future rock bursts. However by understanding the common seismic failure mechanisms and high hazard clusters, damage can be successfully prevented and mitigated through strategic planning of the mine. Generally, damage from seismicity is driven by induced stresses from mining activity, geological structure and weakness of the rockmass . Methods to prevent and mitigate seismic damage include controlling stresses, continuous monitoring, implementing ground control and implementing re-entry time .
Controlling stresses in the rock effectively will minimize seismicity, by way of induced stresses from mining activity driving seismicity, as well as open voids. By controlling the progression of excavations, the evolution of stresses mine can be controlled, in order to reduce seismicity and mitigate damages. Changing the stope sequencing and mine layout will alter the seismicity. In areas of high risk, changing the stress field may reduce the risk for that region. This can be achieved by advancing the stopes upwards as a ‘chevron’ stope pattern (link), so that the high stresses will shed to the outside of the stopes and isolate the stresses from the excavations .
Another method to control stresses is to induce failure in specific high-risk regions. In particular, dykes and sills, which are commonly brittle rock, are prone to rockbursts and store more strain energy. By distressing and preconditioning the rock, the rock stiffness is decreased along with the ability to store strain energy, which decreases the probability of an uncontrolled brittle event. Distressing rock also allows for high stresses to be shifted elsewhere in the mines, decreasing the chances of a local rockbursting event. Blasting can also be used to trigger strain energy and strain relief. Rock burst events can be induced from blasting to induce failure in the surrounding rock, rendering it unable to retain high loads, thus decreasing the event magnitude .
As mining progresses, the stresses and seismic failure mechanisms present will evolve. In order for the seismicity changes to be observed, continuous monitoring through instrumentation and inspection should be implemented in all mine operations. Changing mitigation plans in mines is common and the monitoring network can be altered and improved as the seismicity progresses and evolves. Overall, damage prevention and mitigation is more application to mines, however smaller events will always precede a larger event in order to assist is estimating when and where a large event will occur .
Microseismics is used to assess small variation in rock from small seismic events. From observation of small events from excavation, potential failure planes can be determined. Through stress inversion, the stress field surrounding an excavation can be computed. A common issue in mines is repeated seismic loading, where some failure mechanisms will fail, but strains will continue to build causing more future failure. Microseismic monitoring can be utilized to identify failure mechanisms of repeated seismic loading .
In seismically active regions the deformation and damage that result from seismic activity effect the ground control utilized. From dynamic stress conditions of the rock and deformation, active ground support is needed. Frictional bolts, such as Split Set and Swellex, allow for movement of the excavation before the bolt reaches capacity. Support that will absorb energy should also be implemented to prevent collapse, such as Conebolts and yielding support. Pre-tensioned bolts are used in seismically active areas along with dynamic support in order to interlock the blocky rockmass and increase energy absorption. To contain falling rock, it is recommended to implement mesh or shotcrete to the excavation walls. Due to the high tensile stresses present in the seismic waveform, it is recommended to implement reinforced shotcrete with higher tensile strength than plain shotcrete .
Generally two kinds of load exist in the mining environment, static and dynamic. While in-situ stresses (i.e. weight) represent static loads, the dynamic loads can be due to large seismic events (rockburst). So, for ground support design in seismically active mines, both the static and dynamic loads should be considered . Ground supports are designed to reinforce the rock mass, hold and retain the broken rock. In the case of dynamic loading, ground support system should have the ability to carry load, accommodate large displacements and dissipate dynamic energy. Type of the support depends on the failure mechanism and the damage levels (thickness of the damage layer (Figure 13)) 
Figure 14 represent the three rockburst failure mechanisms .
Table 5 represents the different support systems according to the different load conditions in the mining area. It is important to note that the ground support design for dynamic loading is supplementary to the static ground support designs and cannot be replaced.
It worthwhile to note that the pre-tensioning of rock bolts has two different rules in under the static and dynamic loading :
Static loading: pre-tensioning increases the interlocking effect of a blocky rock mass Dynamic loading: pre-tensioning it reduces the energy absorbing capacity of rock bolts
Table 6 below show the suggested supported in the case of dynamic loading.
The scaling law proposed by Kaiser  is a simple scaled distance relationship for estimating the peak particle velocity (PPV) and a measure seismic source intesity. In which the PPV is the evelocity of a particle in the ground brought about by vibrating motion and is measured in mm/sec. The ground vibrations caused by a seismic event depend on some factors such as rock mass characteristics, confinement, distance from the source, and the direction of propagation. Kaiser et al  proposed a formula for PPV calculation:
Figure 15 shows he relation between the Richter magnitude, distance from the source and PPV .
For example experience from filed work showed that for a small blast usually the PPV is around 1-3 mm/s nearby the mining boundary .
Table 7 shows the rock mass degredation according to the different values of the PPV.
Re-entry time is dependent on the seismicity present after blasts. If the mine or specific stopes are seismicity active after blasting, personnel and equipment are unable to enter the area of risk. Before re-entry, stabilization must be ensured after blasting. In some cases, it may take 5 hours for stresses to reach equilibrium after a blast . If seismic events are occurring at times that are unrelated to blast timing, such as fault-slip events, then the re-entry protocol cannot be dependent on managing blasting alone. Re-entry is timed to be when the seismic activity returns to the normal level. An estimate for timing can be determined from the Omori Power Law.
Where N is the number of events within a time period, t is the time period following the blast, and k and p are constants related to the total number of events and decay time period, respectively.Figure 12 displays an example of seismic event decay after blasting. The decay analysis provides an assessment of the decay of seismicity within a specific time period after blasting, and can be used to design the re-entry protocol of the mine .
- Gibowics, S.J. & Kijko, A. (1994) An Introduction to Mining Seismology. Academic Press.
- Hudyma, M. R., Heal, D. and Mikula, P. (2003) Seismic monitoring in mines — old technology — new applications. Proceedings of the First Australasian Ground Control in Mining Conference. UNSW school of Mining Engineering, Sydney, pp. 201-218. Cite error: Invalid
<ref>tag; name "Hudyma" defined multiple times with different content Cite error: Invalid
<ref>tag; name "Hudyma" defined multiple times with different content Cite error: Invalid
<ref>tag; name "Hudyma" defined multiple times with different content
- McKinnon,S. (2013) Mine 469 Course Notes. Cite error: Invalid
<ref>tag; name "McKinnon" defined multiple times with different content Cite error: Invalid
<ref>tag; name "McKinnon" defined multiple times with different content Cite error: Invalid
<ref>tag; name "McKinnon" defined multiple times with different content Cite error: Invalid
<ref>tag; name "McKinnon" defined multiple times with different content
- Hudyma, M.R. (2011) Mine 5356 EL. Course Notes.
- Bourbié, T., Coussy, O., and Zinszner, B., (1987) Acoustics of Porous Media. Gulf Publishing Co.
- Havskov,J. & Ottemoller,L. (2010) Routine Data Processing in Earthquake Seismology. Springer.
- Duplancic, P. (2001) Characterization of caving mechanisms through analysis of stress and seismicity. PhD thesis, University of Western Australia, Perth, Australia, 227 pages.
- Richter, C.F. (1935) An instrumental earthquake magnitude scale. Bulletin of the Seismological Society of America, Vol. 25, pp. 1-32.
- Nuttli, O.W. (1973) Seismi wave attenuation and magnitude relations for Easter North America. J. Geophys. Res., vol. 78, pp. 876-885.
- Hanks, T.C. and Kanamori, H. (1979) A moment magnitude scale. Journal of Geophysical Research, Vol. 84, pp. 2348-2350.
- Ortlepp, W.D. (1998) Stress and How It Leads to Seismicity. ACG Workshop: Mine Seismicity and Rockburst Risk Management in Underground Mines
- Vergne, J. (2000) Hard Rock Miner’s Handbook. McIntosh Redpath Engineering.
- Brune, J.N. (1970) Tectonic stress and the spectra of seismic shear waves from earthquakes. Journal of Geophysical Research, Volume 75, pp. 4997-5009.
- Dahlen, F. A. (1974) On the ratio of P-wave to S-wave corner frequencies for shallow earthquake sources, Bull. Seismol. Soc. Am., 64, 1159 – 1180.
- Wyss, M. and Brune, J.N. (1968) Seismic moment, stress and source dimensions for earthquakes in the California-Nevada region. Journal of Geophysical Research, Vol.73, pp. 4681-4694.
- Simser, B.P., Falmagne, V., Gaudreau, D. and MacDonald, T. (2003) Seismic response to mining at the Brunswick mine. Canadian Institute of Mining and Metallurgy Annual General Meeting, Montreal, 12 p.
- Andrieux, P.P., Hudyma, M.R., O’Connor, C.P., Li, H., Cotesta, L. and Brummer, R.K. (2008) Calibration of large- scale three dimensional non-linear numerical models of underground mines using microseismic data. Proceedings 1st International FLAC/DEM Symposium – Minneapolis
- van Aswegen, G. and Butler, A.G. (1993) Applications of quantitative seismology in South African gold mines. Proceedings of Rockburst and Seismicity in Mines, (Editor: R.P. Young), A.A. Balkema, pp. 261-266
- Hudyma, M.R. (2008) Analysis and interpretation of clusters of seismic events in mines. PhD thesis, University of Western Australia, Perth, Australia.
- Hudyma, M.R. (2010) Applied mine seismology concepts and techniques. Technical notes, Laurentian University, Sudbury, Ontario, Canada Cite error: Invalid
<ref>tag; name "Hudyma_.282010.29" defined multiple times with different content Cite error: Invalid
<ref>tag; name "Hudyma_.282010.29" defined multiple times with different content
- Collins, D. and Hosseini, Z. (2013) Harnessing microseismic monitoring. Mine monitoring. Mining Magazine.
- Hudyma, M.R. (2011) Mine 5356 EL. Course Notes.
- Hedley, D.G.F. (1992) Rockburst handbook for Ontario mines. CANMET SP92-1E, 305 Pages.
- Engineering Seismology Group. (2013) 6th Microseismic symposium and workshop. Kingston, Ontario, Canada.
- Beck, D. (2002) Simplistic seismic monitoring. Informal presentation, AMC Consultants.
- Mendecki, A.J & Van Aswegen, G. (2001) Seismic Monitoring in Mines: Selected Terms and Definitions. In Proceedings of Rockbursts and Seismicity in Mines, Johannesburg, 2001. South African Institute of Mining and Metallurgy. Cite error: Invalid
<ref>tag; name "Mendecki" defined multiple times with different content Cite error: Invalid
<ref>tag; name "Mendecki" defined multiple times with different content
- McCreary, R.G., Grant, D., and Falmagne, V. (1993) Source mechanisms, three-dimensional boundary-element modelling, and underground observations at Ansil Mine. In Proceedings of Rockburst and Seismicity in Mines, Kingston, August 1993, (Editor R. P. Young). Rotterdam: A.A. Balkema, pp 227-232.
- Jost, M.L. and Herrmann, R.B. (1989) A student’s guide to and review of moment tensors. Seism. Res. Let., 60(2), pp. 37–57
- Aki, K. and Richards, P.G. (1980) Quantitative Seismology, W. H. Freeman, San Fransisco.
- Finck, F., Kurz, J.H., Grosse, C.U., and Reinhardt, H. (2003) Advances in moment tensor inversion for civil engineering. International symposium (NDT-CE 2003).
- Urbancic, T.I., Feigner, B. and Young, R.P. (1992) Influence of source region properties on scaling relations for M<0 events. Pure and Applied Geophysics, Vol. 139, No. 3/4, pp.721-739.
- Boatwright, J. and Fletcher, J.B. (1984) The partition of radiated energy between P and S waves. Bulletin of the Seismological Society of America, Vol. 74, pp. 361-376.
- Hudyma, M, Potvin, Y and Allison, D. (2007a) Seismic monitoring of the Northparkes Lift 2 block cave - Part 1 Undercutting. Proceedings 1st International Symposium on Block and Sub-Level Caving, The Southern African Institute of Mining and Metallurgy, Cape Town, pp. 303-333.
- Abolfazlzadeh, Y. (2013) Application of seismic monitoring in caving mine-case study of Telfer gold mine. Master thesis, Laurentian University, Sudbury, Ontario, Canada.
- Hudyma, M.R. (2010) Applied mine seismology concepts and techniques. Technical notes, Laurentian University, Sudbury, Ontario, Canada.
- Young, D.P. (2013) Energy variations in mining induced seismic event using Apparent Stress. Master thesis, Laurentian University, Sudbury, Ontario, Canada.
- van Aswegen, G. and Butler, A.G. (1993) Applications of quantitative seismology in South African gold mines. Proceedings of Rockburst and Seismicity in Mines, (Editor: R.P. Young), A.A. Balkema, pp. 261-266.
- Mendecki, A.J. (1997) Quantitative seismology and rockmass stability. Seismic Monitoring in Mines. (Editor: A.J Mendecki). Chapman & Hall, London, pp.178-219.
- Australian Centre for Geomechanics. (2005) MS-RAP Version 3.1 User Documentation. 237 pages.
- Snelling, P., Godin, L. & McKinnon, S. (2013) The Role of Geologic Structure and Stress in Triggering Remote Seismicity in Creighton Mine, Sudbury, Canada. International Journal of Rock Mechanics and Mining Sciences. Volume 58, 166-179.
- Kaiser, P.K., McCreath, D.R., and Tannant D.D. (1996) Canadian rockburst support handbook. Geomechanics Research Centre, Laurentian University, Sudbury, 303p.Rockburst Support Handbook, 1996.
- Bauer, A. and Calder, P,N. (1970) Open Pit and Blasting. Seminar Mining Eng. Dept. publication, Queen’s University, Kingston, Ontario, p. 3.