Intelligent Mining Software “Solutions” IMS - Model Histograms

Copyright © 2013 by William Seldon Mart and Geoff Markey. All rights reserved.

Table of Contents

INTRODUCTION

RUNNING THE HISTOGRAM MODULE

The Model Page

The Parameters Page

The Axes Page

The Data Page

The Fonts Page

The Report File Page

STATISTICS REPORTED

Histograms and Cumulative Plots

APPENDIX: USING HISTOGRAMS FOR QUICK TONNAGE CALCULATIONS

INTRODUCTION

The Histogram module performs statistical analysis on a model cell. It provides the distribution of the value of the parameter, considered with respect to the total model or a portion of the model or a specified plan file. Any stratigraphic unit type (i.e. stratigraphic units present in the seam/benches present in the model) may be used with or without weighting for thickness.

RUNNING THE HISTOGRAM MODULE

  1. Load the required model into the 3D View Pane.
  1. Select the <Model<Histograms...> menu item (Figure 1) to display the first page of the Histogram parameters wizard.

Figure 1: Selecting the Histogram menu item

The Model Page

Figure 2: Selecting stratigraphies and restrictions

  1. Select the stratigraphic units that you want to work on from the seams list (Figure 2).
  1. Restrict the range of elevations if required. The elevation is is the height above sea level (or some chosen datum) of the top of the stratigraphic unit.
  1. Restrict the range of depths if required. The depth is the distance from the surface to the roof of the stratigraphic unit.
  1. Restrict the range of stratigraphic thicknesses if required.

Data values that do not satisfy the restrictions are excluded from the plot and associated statistics.

The Parameters Page

Figure 3: Plot information

  1. Enter the name of the plot file or leave it blank if a plot file is not required. Plot files are standard EMF (Enhanced Meta Files) that can be viewed any image viewer.
  1. Select the plot type. There are five plot types available:
  • Histogram
  • Histogram (Log Scale)
  • Cumulative
  • Cumulative (Log Scale)
  • Scatter
  1. Enter the width and height of the plot. The plot will be scaled to fit the sizes specified here. The sizes refer to the actual graph only and do not include the axis labels, titles, etc. A practical minimum x-axis size is about 200mm.
  1. Select the title box option if required. If you choose not include the title box, the plot will be produced without the title box border.

The Axes Page

Figure 4: Axis parameters

  1. Select the quality required to calculate the statistics. The qualities are shown in Table 1.

Table 1: Available qualities

Data Type / Use On
Roof / Laminar Models
Floor / Laminar Models
Thickness / Laminar Models
Depth / Laminar Models
Qualities (Assays) / Laminar Models, Block Models
  1. Enter the minimum and maximum valuesfor the x-axis.
  1. Enter the increment for the x-axis. This determines the interval between tick marks. Up to a maximum of three hundred intervals can be used on each axis, (i.e. ).
  1. Enter the minimum and maximum accepted values. Only data that falls between (and including) these values are considered in the calculations.
  1. Enter the upper-cut. Data values larger than the upper-cut are reassigned the upper-cut value.
  1. If you selected a scatter plot type then the y-axis parameters are enabled.
  1. Select the quality for the y-axis.
  2. Enter the minimum and maximum values for the y-axis.
  3. Enter the increment for the y-axis. This determines the interval between tick marks.
  4. If you require a regression line then select the Show regression check box.
  1. If you require grid lines on the plot then select the x-grid and/or the y-grid check boxes.
  1. If you require a line representing the median on the histogram plot then select the Show histogram median linecheck box.

The Data Page

Figure 5: Restricting the data

Select the subset of data required for the plot. If you select Use data inside polygons then a file selection dialog box is displayed. Enter the name of a plan file in this dialog box. The plan file must contain at least one closed polygon to define the region of interest.

The Fonts Page

Figure 6: Fonts for graph elements

Select the fonts for the various graph elements. Only the font name, colour and size (in points) are currently available.

The Report File Page

Figure 7: Reporting the statistics

  1. Enter the name of the report file or leave blank if a report file is not required.
  1. Enter the header line text if required.
  1. Press <Finish> to start the calculations.

STATISTICS REPORTED

The Histogram module displays the required graph on screen and saves it to the plot file if one was specified. The statistics displayed on the graph are a subset of those used in the calculations. Consult the report file for the extra statistics (e.g. standard deviation, the number of observations and the median).

NOTE: If the number of observations is less than thirty then a simple standard deviation is used. Otherwise, the Histogram module uses a population standard deviation.

Histograms and Cumulative Plots

Standard deviations are calculated as grouped data points,i.e. the midpoint of each class interval is taken to be the datum for the calculations. However, the value added to that class interval is the thickness for the selected cell divided by the total average thickness of all cells.

Since the calculations are performed on grouped data, the reported standard deviation will be marginally different to that of the raw data. If a calculation of the raw data statistics is required, it is necessary to reduce the class intervals to the minimum possible.

Note:The maximum number of class intervals is three hundred.This procedure will still not produce completely comparable results but will reduce any possible errors to an absolute minimum.

APPENDIX: USING HISTOGRAMS FOR QUICK TONNAGE CALCULATIONS

The Histogram module provides the following benefits:

  • It presents the results of the analysis in a compact and easily readable form.
  • The shape of the distribution is immediately apparent.
  • The output is suitable for inclusion in reports without further processing.

If the analysis is weighted by thickness then the results can be used to derive the ore tonnages for each nominated step in the parameter value(s) by applying the percentage derived for that step to the total tonnage for the stratigraphic unit. This is achieved as follows:

  1. Graph the thickness of the stratigraphic unit and the qualities (weighted by stratigraphic unit thickness) of interest.
  1. Determine the mean of each of these parameters and multiply the average thickness of the seam by the mean quality derived.
  1. Multiply the result gained by the area of interest.

This procedure supplies the tonnages provided the relative density of the quality being considered is corrected by using the following equation:

Example

Average thickness of strat unit = 1.5m (from the Histogram module)

Average grade of product= 10.0% (from the Histogram module)

Area of interest= 1,000,000m2

Relative density of product= 2 tonnes / m3

Therefore the total tonnage is tonnes of product

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