28 March 2020

New hazard charts in General Analysis

Two new charts have been added to the General Analysis application related to assessing hazard with the frequency-magnitude relationship. The new charts plot various hazard parameters over time, or, by time of day:                 Charts / Time Series / Hazard over Time                 Charts / Diurnal / Diurnal Hazard The following parameters can be plotted in each chart (maximum two at a time): Mmin – The magnitude of completeness. The magnitude, above which the dataset is complete. b-value – The slope of the Gutenberg-Richter distribution, describes how the frequency of events scales with magnitude. N at Mref – The number of events (N) above the reference magnitude (Mref, user defined). Note for reference magnitudes less than Mmin, N will not reflect the actual number of events in the database, since it is based on the Gutenberg Richter distribution, assuming a complete dataset. Hazard Probability – The probability of an event exceeding the design magnitude (user defined) within one year. Hazard Magnitude – The magnitude that, to a certain reliability (user defined), won’t be exceeded within one year. Hazard magnitude is essentially the inverse of hazard probability. Each chart is generated by breaking up the data into bins and fitting the Gutenberg-Richter distribution. The bin width can be set in the control panel. Since there can be a lot of variability in the data and fitting procedures, there are also controls to smooth the results, with a user defined bandwidth. The figure below is an example of the Diurnal Hazard chart, showing how the b-value varies based on the time-of-day. The b-value drops from around 1.3 to 0.7 during shift change. This represents a large difference in hazard, which is highly sensitive to b-value (illustrated in previous post). Note that the hazard calculations assume a constant b-value within the analysis volume. This can result in an underestimated hazard (explained in the Hazard Iso’s blog post). For more accurate results, use the hazard assessment application, where the volume is discretised and the probabilities are integrated together from the small scale, to the larger scale. If you would like to arrange a root upgrade to get these charts, let us know at our support email address.

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Background filters in the hazard app

The new background filters have been added to the Hazard Assessment application. The time of day filter can be used to see the effect of removing events during blasting/shift change on the hazard results. You can either view the results in raw or normalised form. The hazard calculations do normalisation for the event rate calcs anyway, to represent hazard in yearly terms. If your analysis period is six months, the number of events is doubled to represent a year’s worth of events. When applying the time-of-day filter though, the actual analysis period is less than six months, because several hours per day have been removed. Without normalisation, the hazard should always drop when applying the time-of-day filter, because you are removing events, and nothing else changes (i.e. still using 6 months). If normalisation is turned on, the time period that has been removed is accounted for in the hazard calculations. The results then represent accurately the state of the hazard during the relevant times of day. Normalisation also applies to the short-term responses filter, where events can be removed based on a time and distance from a blast or significant event. In this case the normalisation is a bit more complicated. With the time-of-day filter, the effective analysis period is the same for the whole grid. In this case however, there will be an uneven distribution of space and time removed from the analysis. So, each individual cell has its own effective analysis period, based on how many triggers (and responses) are nearby. The idea is still the same though, without normalisation, the hazard will drop due to the removal of events without adjusting the analysis period. With normalisation turned on, the results will represent the hazard state outside of short-term response regions. A new chart has been added to the Hazard Assessment app that shows the effect of different short-term response filtering on hazard. The chart works in a similar way as the Track Volumes over Time chart, by computing the hazard over and over again, automatically changing variables with each run. The chart and associated control panel can be found in the Hazard Assessment / Hazard ISO’s window, under the Response Analysis menu. To generate the chart, you need to specify a maximum response time, a time delta, and response distances (up to 6). The hazard will be calculated for each response distance and for each response time from zero to the maximum (at delta intervals). The hazard recorded is the probability of exceeding the design magnitude within the chosen grid, which is the value displayed in the footer of the 3D ISO view. It can take some time to calculate, depending on how many iterations you specify. The video below shows the chart being generated for response times up to 72 hours and response distances of 50, 100 and 150 m.

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