Damage Mapping application

As part of the ACG’s Ground Support Guidelines for Rockburst Prone Conditions research project, we have developed an application for damage mapping. It is a web-based application design for use with a tablet. This allows users to do their damage mapping offline while underground on the tablet, then when the tablet is connected to the network, the information is synced with our server and pulled into mXrap (making it a single pass process). Each damage mapping instance is stored as a separate report. Within each level plan, mine development is segmented into short lengths (approximately 5m) called ‘Tracks’. Information is stored on each of these tracks, to allow the history of each underground location to be monitored. Tracks in damage mapping web application. Tracks shown in orange are selected for use in the current report Data collected for each track includes: Location co-ordinates Location name Corrosion Water Excavation height/span Rock Mass Characteristics Installed Ground Support Falls of Ground Photos Assigning ground support in web application In addition to this information, damage data is also collected with more detail at each point on the profile (backs, shoulder, walls and floor). Damage information is captured in terms of both broad damage scales (i.e. rock and support damage scales) and detailed observations of individual support element damage. In addition to damage data, information on locations which have not been damaged can also be captured. Damage data on different points on the profile of the drive (web application) The application focuses on damage mapping for rockburst occurrences, however will soon be expanded to cater for routine damage mapping, with a site specific configuration allowing mines to choose which information to capture for day-to-day damage mapping. Once the damage data has been synced into mXrap, the mXrap app is used for visualisation and analysis. The basic viewer window operates in a similar manner to the general analysis 3D view. Users can view and filter their damage locations and colour them by different parameters. Seismic events, blasts etc. can be seen and filtered simultaneously. 3D view showing damage locations coloured by Support Damage Scale (mXrap application) The user can also select individual tracks/points and see the more detailed damage data that was entered. Points on profile showing damage (mXrap application) This includes photos, which allows users to easily organise their photos so that they can look at photos from a specific location underground over time. Photo viewing window in mXrap application

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What do the hazard iso’s mean?

The Iso View in the Hazard Assessment application expresses the seismic hazard in two ways. The current yearly hazard within the chosen grid volume. This is shown in the footer of the 3D view, as the probability of an event exceeding the design magnitude. The spatial distribution of the hazard. This is highlighted by the hazard isosurfaces. In the case below, the design magnitude is set as ML2. The corresponding hazard isosurfaces for ML2 can be interpreted as the most likely location for that event to occur. The ML rating essentially delineates the areas of the mine from lowest to highest hazard. The volume bounded by the ML2 isosurface indicates the ML rating is above ML2. Note that the colours in the legend are slightly different than the isosurfaces’ apparent colour in the 3D view. This is due to transparency effects and viewing multiple transparent surfaces on top of one another. It is important to note that while the data period can change (6 months in the example above), the hazard calculations are all referring to the yearly hazard. This is a simple matter of normalisation. E.g. if you record 100 events in an area in six months, this area is assigned an activity rate of 200 events per year. The use of yearly hazard is to help interpretation. Reducing the time period used in the definition reduces the probabilistic hazard and this can be misleading. For example, let’s say you give your mine manager a report every day and it says that based on recent data, the probability that we will experience an event in the next 24 hours over ML2 is 0.77%. You do this every day for a year and each day, the mine manager looks at the number and thinks, “Hmm, 0.77%, that’s pretty small, risk is pretty low”. A daily hazard of 0.77% is the same as the yearly hazard in the example above. 1 – (1 – 0.0077)365 = 94% The mine manager may interpret the risk more accurately when presented with the same hazard but expressed for a hazard period that is more intuitive. The current yearly hazard displayed in the footer of the 3D view applies to the entire volume of the chosen grid. We also compute the yearly hazard in the VTM table in General Analysis. So, you might reasonably assume that if you specify a volume in General Analysis the same as the grid volume in the Hazard app, the two numbers should match. In fact, while the probability of exceeding ML2 is 94% in the example above, the same volume and time period in the VTM table gives 86%. This is because the two calculation methods are quite different. To compute hazard, the main inputs are the seismic activity rate, and the b-value (Mmin and MUL are also required). In the VTM table, a single b-value and activity rate is computed for events within the volume, and the seismic hazard is computed directly. In cases where the b-value does not vary significantly within the volume, this is a reasonable approach. However, in most cases, the b-value varies in space, and this approach tends to underestimate the seismic hazard. This is illustrated in the figure below. You can represent the full volume with its activity rate and b-value to compute the probabilistic hazard, like in the VTM table. In the Hazard app, the variations in activity rate and b-values are calculated on a regular grid through space (in sub-volumes). While the event search radius for each grid point may exceed the grid cell spacing, the activity rate is normalised and the b-value is assigned to represent the seismicity for the specific grid cell volume. The probability of exceeding the design magnitude within each sub-volume can then be calculated. Then the probabilistic hazard for the full volume can be calculated by integrating together all of the sub-probabilities. ML Rating – Technical Meaning As mentioned already, the yearly seismic hazard is expressed as the probability of exceeding the design magnitude. An alternate definition of hazard, is to use a design reliability rather than a design magnitude. I.e. the hazard can be expressed as the magnitude that, to the design reliability, will not be exceeded. We use a reliability of 85%. The ML rating is the design magnitude that would have a probability of exceedance of 15%. An ML rating is assigned to each grid point to compute the isosurfaces. On the surface of the ML2 iso for example, the ML rating refers to the magnitude that, to a reliability of 85%, would not be exceeded within the standard volume given one year’s seismicity. The standard volume we use is that of a sphere of 50m radius.

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What are minodes?

Minodes are what we use in multiple places in mXrap if we want to assign information to development. They are just point locations, dotted along your development, in roughly 5m intervals. Things like ground support and PPV hazard are really only relevant for development locations, so minodes are our way of denoting these places. Minodes are also used to calculate the span of the excavation at that point. The tunnel length is also used in the Hazard Assessment app. Minodes are not generated automatically for new development. The minode calculations use an older generation of code that can’t be used in the current mXrap. So, we need to generate the minodes for you periodically as you add more development. Minodes can be created from floor strings but 3D development surveys work best, the same formats you use for mXrap.   Minode Update Procedure  Add your most recent 3D development surveys to the #Data folder in your root. Include all surveys where you want to show minodes, even if minodes are already there. Run a default backup of your root folder in mXsync. If you are unsure how to do that, review the “Intro and Default Backup” video on the mXsync page.  Send an email to our support email address and ask us to update your minodes. Please confirm that you have updated your surveys, run a backup in mXsync, and indicate which surveys are for minode generation. It can take some time depending on other work, so please indicate if it is especially urgent. We will generate your new minodes and merge all previous information from the old minodes. We will let you know when it’s done via email. Your new minodes will be sent as a patch in mXsync back to you. All you need to do is apply the update. See the “Apply patch” video on the mXsync page. Review your new minodes (in the Hazard Assessment app for example) and confirm they are as expected. Then run another default backup in mXsync if you are happy. Contact support if there are any problems.

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Seismic source parameters – quick guide

As mentioned in the last blog post, energy and moment are independently calculated based on the displacement and velocity spectra of the recorded waveforms. Another spectral parameter is the corner frequency. The figure on the left shows the corner frequency (f0) on theoretical displacement, velocity and acceleration spectra. The calculation of corner frequency relies on fitting a reliable source model to the observed spectra. Many commonly used source parameters are derived from Energy, Moment and Corner Frequency. Below is a quick guide to these parameters, illustrated with an Energy-Moment chart that has events coloured by the relevant parameter. The corner frequency is indicative of the dimensions of the source (source radius in the case of a circular fault). This is a physical relationship easily demonstrated. In the linked video, you can see and hear the decrease in frequency as the length of the ruler is increased. Another example is the change in frequency resulting from changing the length of vibrating guitar strings. For the same physical reasons, larger seismic events tend to have lower frequencies. The radius of the seismic source is calculated from f0. In theory, the source volume can be calculated based on the Moment and source radius. In practice however, “Apparent” volume is more commonly used to approximate the source volume. The source volume is proportional to the cube of source radius, therefore any errors in the source radius parameter (or corner frequency) are amplified. The method of calculating Apparent Volume is more stable, based on Energy and Moment.

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Seismic energy and moment

You know that energy and moment are parameters to describe seismic events. But what exactly is their physical meaning for a seismic event source and how are they calculated? Moment and energy are both separate (but related) measures of the strength of a seismic event. A similar example is a car engine, the performance is described with two separate (but related) measures: power (hp or kW) and torque (Nm). In a simplified piston and crankshaft arrangement, the torque is the twisting force exerted by the force of the piston on the lever arm (crankshaft). Power relates to the rate at which work is done and how fast the torque is applied (torque x RPM). So, moment, energy and power are all related measures of the system performance. You might have heard that energy and moment are independent source parameters. This is to distinguish them from derived parameters (parameters that are calculated from energy, moment, corner frequency etc). They are independently calculated but they are not unrelated to one another. Moment is related to the displacement (strain) of the source. Energy is related to the speed at which the displacement happens. In general, higher stress conditions lead to higher rates of displacement and therefore higher energy relative to moment. What does Moment physically mean? So, you know that moment is a force applied to a lever arm. You might be wondering, where is the lever arm for a seismic source? In the context of seismic sources, moment is a force couple. Two equal and opposite forces, with a notional distance between them, forms a definite moment. Let’s look at a force couple applied to a small crack. The images below are displacement results from a simple Phase2 model of a small horizontal and vertical crack. The arrows indicate the direction of the displacement. Notice that the displacement pattern is essentially the same for both force couples. This is why, when you do an inversion from the observed waves trying to model the source, the solution comes down to a double-couple. There is no way to distinguish between the two possible solutions. The displacement field caused by a dislocation on a plane is fundamentally equivalent to that produced by a double-couple. For a homogeneous and isotropic medium, the moment of a seismic event caused by the shear fracture on a plane is: M = G x D x A Where, G = Shear stiffness of the rock D = Average displacement A = Area of slip How is Moment calculated? We are rarely in a position to be able to measure the area of slip or the amount of displacement. In practice, moment is calculated from seismic waveforms, usually in the far-field (outside the source volume). The Brune model is used to relate the characteristics of the seismic source to the characteristics of the recorded waveform. The model is based on a circular disc (penny) shaped dislocation surface where a tangential stress drop is applied instantaneously, resulting in a shear wave propogating perpendicular to the fault surface. To compute Moment, a Fourier transform is required to convert the displacement waveform from the time domain to the frequency domain. The frequency content is also referred to as the spectrum of the signal. Moment is proportional to the spectral level (Ω0); the plateau of the displacement spectrum at lower frequencies. The spectra for each sensor must be corrected for geometric attenuation and decay and the Brune model must be fitted to the signal. Moment can then be computed as: M0 = 4πρV3Ω0R Where: ρ = rock density V = the sonic velocity in rock R = the distance to the source In theory, the Brune model is only applicable to the S-wave but in practice, the same method is used for the P-wave. The final Moment for a seismic event is the average of the S-wave and P-wave moment. M0 = (Mp + Ms)/2 What does Energy physically mean? While seismic moment is a better description of the intensity of a seismic event within the near-field, seismic energy is a better description of the potential damage outside the source volume. The energy source parameter does not represent the total work done during the event, rather the energy that is radiated away from the source. The elastic energy radiated by a seismic event is only a fraction of the total work done by the source. How is Energy calculated? Similarly to moment, energy is calculated in the frequency domain, except energy uses the velocity spectrum rather than displacement. The radiated energy is proportional to the velocity-squared spectrum integrated across the full frequency domain. The total energy for a seismic event is the sum of the P-wave and S-wave energy. E = Ep + Es Conclusions The calculations for seismic energy and moment are complex and there are several assumptions and sources of error such as: Error associated with integrating recorded wave to displacement in the time domain Assumptions associated with the Brune source model Error associated with fitting the Brune model to the displacement and velocity spectra, including when bandwidth limitations of seismic systems result in a poorly constrained fit Error associated with the calculation of source location (R)

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Download a root in mXsync

Did you know you can download root folders from mXsync? We have uploaded root folders for Tasmania and Big Bell mines. These sites have closed and the data has been made available for research. Have a look at the ‘Download a component‘ training video for a guide to downloading these roots onto your computer. The data can be handy for research projects or just for curiosity’s sake. You may even want to download the Xgames root…. for work purposes of course.

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Track seismic hazard over Time (per volume)

We have added some new features to the Hazard Assessment app to calculate the minode hazard for filter volumes. This works just like the current minode calculations, where you can select minodes and compute the probability, P, of exceeding your design magnitude, within R of any selected minodes. The volume hazard refers to the seismic hazard for minodes within the filter volume. The same backdate, backrange, Mdesign and R parameters apply as the existing tools. Another tool has been added to track the volume hazard over time. Essentially this repeats the volume hazard calculations, stepping the backdate through time and plotting the hazard per volume. Refer to the ‘Track Volume Hazard‘ training video for a walkthrough of the new tools in the hazard app. We will need to upgrade your root before you can use the new tools. If you would like us to upgrade, drop an email to our support email address. Root upgrades are fairly quick but you will need to give us access via TeamViewer, Webex or similar.

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Seismic hazard – sensitivity to b-value

Probabilistic seismic hazard calculations are dependent on the number of events (N) and the b-value. But which has more effect on the hazard result? The chart below shows how seismic hazard varies with b-value for N = 1,000, N = 10,000 and N = 100,000. The seismic hazard in the chart below can be considered in the following way. For a given time span and volume, if N events have been recorded, what is the probability that one of those events was above Mdesign? In this case Mdesign = ML2. Seismic hazard increases with increasing N and decreasing b-value. Note on the chart, N = 1,000 and b = 0.9 gives the same seismic hazard as N = 10,000 and b = 1.2 (approx.). In other words an increase of 0.3 in b means you need 10 times more events for an equivalent hazard. So, seismic hazard is very sensitive to the b-value of the area. This is important to consider when looking at daily activity rates. In some areas, 100 events may represent a very different hazard to 100 events in another area if the b-value varies. Another point of interest in the chart is that for areas with b-values above 2, even very high event numbers represent low hazard.

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What on Earth is MUL?

Yes, this is a frequently asked question…. MUL or MUpper-Limit refers to the truncating magnitude of the Gutenberg-Richter distribution. We used to refer to this as Mmax in the Hazard Assessment app and on the frequency-magnitude chart but we found there was confusion caused by Mmax being used to describe multiple things. Hopefully if we refer to MUL or the upper-limit magnitude, this will clear up the terminology a little. A quick review on the terminology that concerns the frequency-magnitude chart and the Gutenberg-Richter distribution: Mmin – The magnitude of completeness, the dataset is considered complete above this magnitude (property of the data). b-value – The slope of the Gutenberg-Richter distribution, describes how the frequency of events scales with magnitude (property of the statistical model). Xmax – The largest magnitude event in the dataset (property of the data). a/b – The magnitude at N = 1 of the Gutenberg-Richter distribution (property of the model, maximum likelihood, see previous blog post). max(m,n) – This is the probability density function, given n events, of the largest event in that n events. This is a property of the Gutenberg-Richter statistical model. In other words, given a certain Gutenberg-Richter model, if you record N events, what is the largest event? This is not a single number but a likelihood distribution. The maximum likelihood of the largest event is the a/b value. MUL – The upper-limit magnitude of the max(m,n) distribution. It is an estimate only and a property of the statistical model. The truncating magnitude has slightly different meanings in mining seismology and crustal seismology. MUL is usually referred to as Mmax in crustal seismology literature and is generally considered constant for a particular area. In mining seismology MUL generally increases over time given the gradual increase in mining dimensions and loading of the rock mass. For this reason the definition is slightly modified in mining seismology to be the upper limit of the next largest event. Why do we need an upper-limit or truncating magnitude? The truncated Gutenberg-Richter distribution, rather than the open-ended distribution, is the most common frequency-magnitude relationship used in mine seismology. If there is no upper limit given to the Gutenberg-Richter distribution, then to evaluate the total energy of events in the relevant time period, the energy tends to infinity as the relationship is integrated above Mmin. This is clearly unrealistic. We know there is a physical limit to possible magnitudes since the size of large earthquakes is related to the slip area of the fault and the physical size of faults is limited. Earthquakes on Earth above magnitude 10 (Richter) are essentially impossible given the size of known faults and a magnitude above 12 represents a fault area larger than the Earth itself! So it is safe to say that MUL for a particular mine is going to be less than Richter Magnitude 10. The question is how much less is reasonable given the significantly reduced physical dimensions in mining. How do we estimate MUL? An empirical method of estimating MUL can be taken using a dataset compiled by McGarr et al. (2002) of large events and the largest dimension of the human activity associated with them. The figure on the right comes from Wesseloo (2018) who added a few extra points to the dataset from Australian and Canadian mines. The range applicable to mining indicates rough dimensions between 500 and 5,000m. Aside from the empirical approach, there are also statistical approaches to estimating MUL. These generally take the form: MUL ≈ Xmax + Δ There are a number of different methods for calculating the Δ value. Many of these methods are described by Kijko and Singh (2011). Most of these have been implemented in the Hazard Assessment app along with the associated uncertainty of each method as described by Lasocki and Urban (2011). It is better to over-estimate MUL than to under-estimate it. In terms of probabilistic seismic hazard calculations, the truncated Gutenberg-Richter model will always give a lower hazard result than the original Gutenberg-Richter, for magnitudes approaching MUL. For magnitudes well below MUL, the seismic hazard calculations are the same. In the Hazard Assessment app, we take the maximum of each MUL + σ estimate from multiple methods. These statistical approaches assume the recorded magnitudes of large events are reliable. Moment is under-recorded for large events if there are no low-frequency sensors installed. The figure to the left comes from Morkel and Wesseloo (2017) showing the effect on the frequency-magnitude relationship, given certain sensor bandwidth limitations. In cases like this it is best to override the MUL as it is likely to be under-estimated with statistical methods. Conclusion While it is important to understand what MUL is and how it effects seismic hazard calculations, it is not something to use for design purposes or to communicate seismic hazard. It is just one part of how seismic hazard is defined. By definition, the probability of an event exceeding MUL is zero, so it isn’t a great measure of seismic hazard. If you have any questions regarding this topic, or something to add, feel free to leave a comment or send an email to support.

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Training video programme

We started making training videos about 12 months ago and feedback has been quite positive. At the last AGM, a suggestion came for a training programme aimed at new users to mXrap. The training videos are currently stored by app but a specific programme would help new users with a logical order for progressing through the training content. We have made a new page for the Training Programme under the Training tab. The programme is structured in several user levels, from a basic introduction to General Analysis, moving through all the apps and finally to advanced app building tutorials. There are a few links to relevant blog posts and papers that will help users understand some of the analysis concepts. There are also exercise questions in each section for users to complete using their own data.

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