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.
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 email@example.com 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.
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 GR 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 GR statistical model. In other words, given a certain GR 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 GR 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 GR model will always give a lower hazard result than the original GR, 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.
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.
mXrap supports the following survey formats to be used in 3D views:
- DXF (AutoCAD .dxf)
- DTM / STR (Surpac .dtm/.str)
- PNT (.pnt)
- INP (Map3D Geometry .inp files)
Regarding DXF files, this is a complicated format that AutoCAD often updates with new specifications. Our importer will always be behind the latest updates and therefore incompatible with loading in the very newest DXF formats. When exporting your survey files, you should have compatibility options for older formats. Look for ASCII DXF options R14 or 2000, these will work in mXrap, otherwise it needs a bit of trial and error initially. Binary DXF files are not supported. The other option is to use the Teigha File Converter. It is free to download and use to convert DWG and DXF files into other formats.
Some things you see in mXrap are properties of the software, while other things are properties of the root folder.
We often use the software Excel as an analogy. Excel has many built-in capabilities with endless possibilities for creating specific calculations. The software has powerful capabilities, but without a user constructing the spreadsheet, the power and value are not fully utilised. An Excel user can set up a spreadsheet which, with the required inputs, will provide you with results. This user can then provide you with that spreadsheet, which you can then use to perform the same calculations with other inputs.
mXrap is like the software Excel that provides the basic tools and the applications are like spreadsheets that can be used to perform specific tasks. Anybody with enough understanding of the software can build their own app which can be shared with others.
For example, when you make a chart in Excel, the “add chart function” is a property of Excel. What’s in the chart, what’s on each axis, what colour are the lines etc are properties of the spreadsheet.
mXrap is the same, there is an “Add Chart” function. Every chart in mXrap uses the same tool, but the application configures what’s actually displayed in the chart.
mXrap software level changes are things that affect the “Add Chart” function itself. For example the current mXrap charts only plot data on four axes; top, bottom, left and right. If we were to add more possible axes, like a secondary left axis, this would require a change to the software. It isn’t related to the root folder. Another example is the image capturing tool. This is a feature of every chart, 3D view and table at the software level.
If you want an updated Hazard Assessment application, this is like getting an updated spreadsheet. The root folder is essentially a library of data and applications, like a folder full of different spreadsheets and their associated data.
To summarise, if it seems like its a common feature across many areas in mXrap, its probably a property of the mXrap software. If it seems to be something related to a specific app or chart etc, it’s probably a setting in the root folder.
Updating the mXrap software is easy, just download the installer from the website.
Updating the root folder is what we use mXsync for and it’s actually more complicated to manage the root folder than the software. A bit like trying to manage a lot of interconnected spreadsheets. We normally rely on sites to request root updates. If you read about a feature on the blog or watch a training video that seems different to your current version. You probably need a root update. It’s a fairly quick process, we just need a brief connection with teamviewer / webex or goto meeting to perform the update. Contact us at firstname.lastname@example.org.