November 2022

Energy – moment relationship

Energy and moment are two independent measures of the strength of a seismic event. Their physical meaning and how they are calculated was described in a previous blog post. Analysis of the relationship between the energy and moment of events can provide insight into seismic sources. For example, blasts or ore pass noise, falsely processed as real events, tend to have distinct zones on an energy-moment chart. In general, events with higher-than-average energy are associated with high relative stress. Energy index is a parameter used to estimate effective stress. To calculate energy index, the mean energy-moment relationship must be defined. Energy index is the log difference in energy from the mean energy-moment relationship. When comparing energy index in different software or from separate sites, it is important to note that if the energy-moment relationship is not the same, the energy index will not be consistent. The most common method of fitting a linear relationship between two variables is known as least squares regression (LSR). This method essentially minimizes the vertical (Y-axis) difference between the data points and the line of best fit. For the energy-moment case, this would be minimizing the energy difference. LSR is designed for cases where the independent variable (X-axis) is known perfectly (zero error) and the error is only associated with the dependent variable (Y-axis). This is not suitable for the energy-moment case as there is uncertainty in both the energy and moment parameters. The uncertainty in moment and the uncertainty in energy are also generally not the same scale. There are several linear regression methods that account for uncertainty in both parameters. Orthogonal regression minimizes the perpendicular difference between the data and best fit line, assuming a constant ratio between the X and Y variances. There is also a method known as weighted least squares which does not assume a correlation between the uncertainty of the two variables. A less complicated approach is to use the quantile-quantile (QQ) plot of the data. This plots the smallest energy against the smallest moment, the second smallest energy against the second smallest moment, etc. This approach has the effect of normalizing the different scale variances of each parameter. The ordinary LSR method can then be applied to the QQ data to obtain an accurate line of best fit. This is equivalent to the orthogonal regression method. The figure below shows the difference between the QQ fit and the least squares fit of the energy-moment data at the Tasmania mine. The QQ fit is a better match to the highest point density zones. The poor LSR fit is because the variance in energy is higher than the variance in moment. The distribution of the energy and moment departure indices is plotted below. Both distributions are slightly asymmetrical, likely due to the various seismic mechanisms superimposed. The wider variance in the energy index introduces a bias that has the effect of making a shallower least squares fit as it tries to minimise the vertical departure in the centre of the chart. If you are doing your own energy index calculations, or using different software, you should be aware of the method used to define the energy-moment relationship and the linear constants used. The least squares approach or chi-square regression should be avoided. The QQ based method is the approach used in mXrap and you can find the fitted linear equation in the footer of the energy-moment chart. You might see different parameters for “global” energy index and “local” energy index. This distinction comes from the different energy-moment relationships used. The global EI relationship is based on all events that pass the quality filter. The local EI relationship is based on events that pass the current base filter (volumetric, parameter ranges etc.).

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mXsync updates

For users who have upgraded to mXrap version 5.16+, you may have noticed the new mXsync button at the bottom left of all of the windows. This button allows users to open mXsync from within mXrap to apply patches and complete backups of the root folder. When this button is blinking, it signifies that you have been requested to either complete a backup or apply a patch. Users will be automatically reminded to complete a backup every four weeks. We recommend that a single device is used to manage the root folder in mXsync to prevent confusion. This device should be logged in to mXsync and would be responsible for completing all backups and applying patches. If you are planning on using a device for this purpose, please open the built in mXsync and make sure that you are logged in. To upgrade to the latest version of mXrap, please contact our support email address.

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Caving Suite updates

The Caving Suite is a set of applications that provide tools for the analysis and interpretation of cave monitoring data sources. Currently, four apps are included in the Caving Suite: Caving Sandbox, Fragmentation, Open Hole Dipping, and Caving Hydraulic Radius (see app overview and Geotechnical Engineering with mXrap seminar for more details) Over the past year, there has be numerous updates to the apps in the Caving Suite to assist with data visualisation, and analysis. Caving Sandbox: This app brings together all of your cave monitoring sources and puts them in one place, allowing complex multi-factor analysis. Changes include: General: Improved controls for manipulating and filtering data. This includes the addition of filter volumes, distance to survey filters, selection box filters, and data source-specific filters and controls. Users can now export event density isosurfaces, production columns, and production surfaces as DXFs to be used in external packages. Users can now easily export videos of the 3D View using time slicing or cumulative date filters. Production: Production columns can be displayed as either Height of cave, height of draw or bulked height. New Charts – production versus depth, individual drawpoint production timelines, daily activity. Production Column display modes Instrumentation: Alerts have been added for beacon displacement. Users can define the conditions for the alert, including the monitoring period and threshold displacement, from within the caving sandbox. A device inspection window has been added where users can easily inspect individual markers and beacons. Improved visualisation of beacons and network smart markers. This includes a 3D series for beacon flow, size by marker styles, and new charts. Added support for the auto-export of beacon positions, RSSI, and tilt readings from GeoHive directly into mXrap. If you are interested in setting this up at your site please contact us at our support email address. Standard smart markers can now be imported into the caving sandbox. Cave tracker beacon inspection window mXrap app integrations: We have started integrating data from other mXrap apps into the caving sandbox. We are working on tools to make this process easier and allow users to customise the sandbox to suit their needs. So far we have the following data sources integrated into the sandbox including 3D series, charts, and tables: Instrumentation – extensometers Instrumentation – prisms RMDA – rock mass quality Intervals Other apps that we plan on integrating with the caving sandbox includes more data sources from RMDA (e.g. structures), Damage Mapping and other instrumentation. Fragmentation: This app allows you to import your fragmentation data into an mXrap database, then visualise and analyse the data. Analysis can be conducted in conjunction with other relevant data sources (including production data). Changes include: New data import interface. Users can import either fixed/variable percentage or fixed/variable size data. Updated analysis tools: Cumulative fragmentation chart Particle size distribution chart User defined bin sizes Heat map Pie charts Mapping fragmentation to production columns Fragmentation analysis window For more information, please contact our info email.

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