Statistical Diagrams in Micromine. Definitions and Functionalities

• ●   Distribution Analysis: allows to visualise the distribution of a geological parameter or property and analyse its statistical characteristics, such as mean, variance and skewness. 
• ●   Identification of Zones of Interest: allows to detect deviations from normal data distributions, which may indicate anomalies in the concentrations of useful components or geological parameters.
• ●   Data Classification: allows to classify geological data based on their values. For example, to divide data into domains during geological and resource modelling.

Histogram (Multivariate)

• ●    Comparison of Distributions of Multiple Variables: allows to visualise the distribution of different variables or categories, helping to identify relationships, patterns, trends and correlations between them. For example, comparison of the content of several chemical elements in rock or ore samples.
• ●    Comparison of Distributions of Multiple Data Sets: highlights similarities or differences between groups, conditions, etc., e.g. comparison raw sample data, composites and/or block model to assess the resource model quality.

Box and Whisker

• ●    Comparison of Multiple Data Set Parameters: geological formations, domains, ore types by density, porosity, grain size distribution, etc.
• ●    Geochemical Data Analysis: to display variations in different elements contents in rock samples to identify distribution trends and anomalies.
• ●    Outlier Detection: could indicate unique geological features or possible errors in data collection requiring additional verification.
• ●    Evaluation of Geological Sampling Quality: the box controls that the central part of the data is reliable, while the whiskers reveal the samples beyond.

Scattergram

It is used in correlation analysis to establish relationships between different geological factors or variables.

The width of the scatter of the points can indicate the closeness of the population’s relationship.

• ●   Parameter Correlation Analysis in a Dataset: to estimate a relationship between the chemical contents or physical parameters in rock samples.
• ●   Correlation Analysis of Dataset by Specific Parameter: to identify similarities and differences between different rock types by geochemical, geophysical or other parameters.
• ●   Sample Pair Comparison: to determine the correlation of grade values in field or analytical duplicates during QA/QC analysis to identify laboratory test problems.

Q-Q Plot

If the points lie on or near the straight line, the sample data is consistent with the theoretical distribution. Deviations from the line suggest discrepancies between the sample and theoretical distributions.

• ●   Assessment of Model Fit: to compare the distribution of modelling data to the raw data and evaluate the effectiveness of the modeling approach.
• ●   Assessment of Geological Data Distribution:  to assess whether the distribution of geological data (such as rock composition, mineral concentrations, or geochemical properties) conforms to expected statistical distributions.
• ●   Identification of Outliers and Anomalies:  it  can be indicative of geological features or processes that warrant further investigation, such as ore mineralisation, geological boundaries, or measurement errors.
• ●   Comparison of Geological Data Sets:  to visually compare the distributions of geological data sets and assess their similarities or differences, which helps in geological interpretation, stratigraphic correlation, or exploration targeting.

Gaussian Anamorphosis

• ●    Geostatistics and Kriging: Transforms geological data sets (e.g., grades) that are skewed and do not follow a normal distribution, making them suitable for kriging and other geostatistical methods; applied by transforming the original data to a Gaussian distribution and then back-transforming the results

Change of Support

• ●   Geostatistics and Kriging: The shape of the distribution will converge to the Gaussian distribution as support increases, if the geological continuity of the variable is assumed, which is positive for the application of kriging.
• ●   Recoverable Resource Estimation: can provide a target for an estimated grade distribution, an indication of the degree of averaging and potentially highlight the importance of mining selectivity.

Cell Declustering

• ●   Geochemical Surveys: helps to identify true geochemical anomalies, reducing the impact of over-sampled areas by preventing bias of average concentrations.
• ●   Resource Estimation: provides more precise and unbiased resource models by ensuring that all samples are weighted are equal, relative to the area that they informand reducing the impact of over-explored areas.

Principal Component Analysis

• ●   Geological Interpretation and Modelling: helps to identify the most significant geological factors and their correlation for better understanding of the project and correct interpretation of the available geological data.
• ●   Processing of Laboratory Analysis Results: allows to identify the main components and determine their correlation with the components of interest, and classify rock and ore samples by the content of a large number of chemical elements.

Variogram Map

• ●  Geostatistics and Spatial Analysis: study of the spatial variability of geological parameters by determining the change in variance with distance for forecasting (interpolation); determination of the main directions of the data interpolation neighborhood.

Variogram

• ●  Spatial Modelling and Resource Estimation: geostatistical interpolation of geological parameters (e.g. grades) by kriging, which uses variograms to predict values by weighting surrounding sampling points.

Omnidirectional Variogram

• ●    Geostatistical Analysis: determination of the optimal influence interval (lag) and general influence zone and variation of grade populations for further creation of directional variograms.

Cross Validation

• ●   Optimizing Kriging Parameters: evaluates the performance of spatial interpolation methods and helps to select the optimal parameters for kriging, such as the search radius, variogram model, and number of data points.
• ●   Comparison and Validation of Resource Models: validates resource estimates by comparing estimated grades against known values, usually preferring to the estimate with the best cross-validation performance.

Top Cut

The following methods and diagrams are used for Top Cutting: Decile Analysis, Histogram, Cumulative Frequency, Probability Plot, Mean vs Cut, CV vs Top Cut, Relative Nugget vs Top Cut

• ●   Compliance with Reporting Standards: industry standards and reporting codes (e.g., JORC, NI 43-101) require the application of top-cut grades for transparent and fair reporting of mineral resources.
• ●   Resource Estimation Accuracy: high-grade outliers can skew the average grade, leading to overestimation of the resource; applying a top cut grade ensures a more realistic and conservative estimate.
• ●   Reducing Risks in Economic Assessment: prevents overestimation of potential revenue, positively affecting investment decisions and financial planning.
• ●   Data Normalisation in Statistical Analysis: helps to increase the reliability of statistical data analysis and obtain more stable statistical parameter estimates.
• ●   Improving Geostatistical Models: Reducing the impact of extreme values on the quality of geostatistical analysis and variographies that are sensitive to outliers.

Boundary Analysis

The Boundary Analysis works using spatial statistics of the investigated domains with equal binning of data from the contact (zero distance) at regular distance increments until the maximum distance is reached or no data is available.

• ●   Mapping of Lithological and Stratigraphic Contacts: mapping the boundaries between different rock types, such as sedimentary, igneous, and metamorphic rocks; analyzing the boundaries between different stratigraphic layers for correct correlation.
• ●   Mapping of Tectonic Structures: helps to identify boundaries created by tectonic structures, such as faults and fractures.
• ●   Mineral Resources and Reserves Estimation: delineation of mineral deposits and ore bodies for project economic potential evaluation and strategic planning; geological or structural domaining verification
• ●   Geotechnical Engineering: determination of stability limits for the design of open pits, underground mines, roads and infrastructure facilities.

Swath Plot

• ●   Geostatistical Model Validation: to compare interpolated values with raw, helping to verify the geostatistical model’s accuracy – how precisely the model reflects the real grade variations.
• ●   Trend Analysis: identifying spatial trends and patterns in topography or relief, geological properties such as grade distribution, thickness of mineralized zones, or rock types, etc.
• ●   Comparison of Different Datasets: for comparing different datasets, such as drilling results, geophysical surveys, or geochemical assays, highlighting consistencies or discrepancies between datasets.

Search Neighbourhood

• ●   Search Area Optimisation: changing the interpolation ellipse parameters and search area revaluation allows to determine the optimal search area and improves the accuracy of the estimate.
• ●   Interpolation Parameters Valuation:  checks for optimal search area parameters, such as shape (ellipsoid or sphere), size (radius and axis ratio), and orientation.

Quantitative Kriging Neighbourhood Analysis

• ●   Enhance the Precision of the Resource Model by optimizing kriging parameters – Balance between smoothing (overestimation of low values and underestimation of high values) and local accuracy.
• ●   Optimisation of Neighborhood Parameters: Evaluation different configurations of the kriging neighborhood, varying the search radius, number of sectors, and data points used in each sector.

Grade Tonnage Curve

Generally, three curves are involved: (1) graph of tonnage above cutoff grade versus cutoff grade, (2) average grade of tonnage above cutoff versus cutoff grade and (3) quantity of metal versus cutoff grade.

• ●   Cut-off Grade Analysis: determining the economically viable cut-off grade based on the relation between the average mineral grade and ore tonnage.
• ●   Mineral Resource Estimation and Reporting: estimation of the quantity and quality of resources by various cut-off grades, traditionally used for mineral resource and reserve reporting.
• ●   Economic Analysis: determining the economic viability of a mining project by analyzing the balance between ore grade and tonnage.

Multi-purpose Chart

• ●   Pit and Stope Optimisation: helps to select the optimal pit shell or stope by integrating and analysing parameters such as cash flow, present value, volume and tonnage of ore / waste rock / total, strip ratio, average grade, mining and processing cost, revenue, etc.
• ●   Life of Mine Cycle: forecasts the development of the mine, displaying capital and operating expenditure, cash flow, mined ore and waste rock tonnage, profit, etc. in one chart by period.

Ternary Diagram

• ●   Phase Analysis in Mineralogy and Petrography: triangular diagrams show phase equilibria, phase transitions and steady states and allow to identify mineral and rock types based on their phase composition or conditions.
• ●   Rock Classification Using QAPF Diagram:  this is a double ternary diagram used to classify igneous or volcanic rocks based on their mineralogical composition.  Its name refers to the classification minerals: Quartz, Alkali feldspar, Plagioclase, Feldspathoid.
• ●   Classification of Sediments and Soils by Sand, Silt and Clay Components: allows to classify soil samples into sandy loam, clay loam, silty clay, etc. by position on the triangle graph.

Gantt Chart

• ●   Exploration Project Management: helps visualize the sequence and duration of various exploration activities (drilling, sampling, laboratory tests, etc.), ensuring efficient project management and timely completion.
• ●   Scheduling and Coordination of Mining Operations: the diagram is used to visualise the sequence and duration of mining tasks and operations, ensuring their optimisation and efficient resource allocation.

Spider Graph

• ●   Geochemical Composition Analysis: to display of chemical element concentrations in rocks or ores to identify and compare geochemical features and patterns.
• ●   Mineralogical Analysis: to compare the mineralogy of different rock types, assess the degree of alteration, or identify mineral assemblages.
• ●   Physical Properties Assessment: porosity, permeability, density can be represented on a graph to compare the properties of rock or soil properties in different zones, layers, etc

Continuous Sampling

• ●    Visual Comparison of the Histogram’s Fit to the Theoretical Probability Density Function: significant deviations can indicate that the sample data does not follow the expected distribution.

Shewhart Control Chart

The centre line (reference or mean value) and control levels (based on the standard deviation) help to check the stability of the process and identify potential anomalies.

• ●    Laboratory Quality Control Using Standard Reference Materials (SRM): helps monitor the quality and stability of measurements over time, ensuring that laboratory instruments and procedures remain reliable.
• ●    Laboratory Quality Control Using Blanks helps to identify contamination and systematic errors in the process of sample preparation, crushing, etc.
• ●    Process Control in Drilling Operations: parameters such as drilling speed, pressure, and fluid composition can be monitored using control charts to ensure that drilling operations proceed smoothly and within predefined limits.

Cumulative Sum (CUSUM) Chart

This chart is an effective alternative to the Shewhart Chart but is more sensitive to detecting small deviations from the mean.

• ●   Tracking Mineral Exploration Data: Identify shifts in mineral grade for monitoring assay samples to detect small but consistent changes in the concentration.
• ●   Mine Safety Monitoring: detects small changes in environmental parameters like gas concentrations, temperature, and humidity  within mines.