MODEL VALIDATION IN MINERAL RESOURCE ESTIMATION / M. A. Akbaba
MODEL VALIDATION IN MINERAL RESOURCE ESTIMATION
M. A. Akbaba, QP, CPG (Geology)
INTRODUCTION
Checking the accuracy of the estimated mineral resource model is crucial for the mine planning and evaluation of mining projects. In order to make mineral resource models reliable and useful, the accuracy of the models must be checked with existing data, the internal consistency of the models must be ensured, and the compatibility of the models with previous estimation and production data, if any, must be verified.
Since mineral deposits have a very complex structure, a model created based on a limited number of data cannot be completely accurate. However, it is essential that the model reflects enough reality to ensure the validity of global and local predictions. This can be achieved by using a set of validation procedures at different stages of creating a resource model.
Validating mineral resource models covers a comprehensive range of verification and cross-validation techniques, including data validation and database and model validation, and ensuring compatibility with previous estimation and production data.
1-GEOLOGICAL DATA VALIDATION
Data validation is to verify that the practices in the data collection, sampling, sample preparation and analysis process comply the Best Practices and that the data reflect reality, in order to ensure the quality and security of the data. It includes carrying out checks in the field, in the core warehouse, in places where sample preparation is made, in laboratories, comparing the data in the database with the data in the original documents, and analyzing the QAQC data.
2-DATABASE and MODEL VALIDATION
Database and model validation includes validating the database using mining software during the modeling stage, evaluating the accuracy of geological and block models and their suitability to surface and drilling data using visual comparison, swath graphs and statistical methods. This process involves identifying and eliminating critical errors, estimating the degree of smoothing in the model, and keeping their impact on extractable resources under control. Model validation also includes evaluating whether the block sizes and orientation are appropriately selected with respect to the deposit geometry, and whether the appropriate interpolation technique is used. It is also crucial to check whether the reported mineralization meets the requirement for expectation of ultimate economic extraction.
Visual Comparison
Visual Comparison is the process used to evaluate how well a mineral resource estimation model's forecasts align with sample data. This involves visually examining the model's estimation by comparing them to sample data. Similarities and differences between the mineral resource estimates made by the model and the samples (drillhole, trench, channel, etc.) are analyzed visually. This is an invaluable tool for identifying and correcting the model's errors. Visual comparison makes it easier to understand complex datasets and evaluate the model's estimation in a meaningful way. Additionally, it provides clear and effective communication to stakeholders and decision-makers about the model's results. Monitoring the model's performance visually enhances our ability to adapt to changing conditions.
Swath Plots
Swath Plots are a powerful visualization method that aids in the assessment of model performance. These plots allow us to examine how well our models are estimating by displaying the distribution of observed values against estimated values. They are particularly useful for comparing different estimation methods, such as Ordinary Kriging (OK), Inverse Distance Weighting (IDW), and Nearest Neighbor (NN).
Why are Swath Plots crucial?
Visual Insights: Swath Plots provide a clear and intuitive way to assess the agreement between our model's estimations and the composite data. By visually comparing the observed and estimated values for different estimation methods, we can identify trends, discrepancies, and outliers.
Model Calibration: These plots help us fine-tune our models by revealing if there are systematic biases or errors in our estimations and which estimation method produces the best results. Understanding Bias: Swath Plots allow us to investigate the degree of bias in estimation results.
Smoothing Effects: Swath Plots also provide insights into the smoothing effect on the resulting estimation. The degree of over smoothing can be interpreted by comparing it with local estimation techniques (NN: Nearest Neighbor or IDW: Inverse Distance Weighting).
Swath Plots, when used to compare various estimation methods, help us make informed decisions and contribute to the success of our projects.
Basic Statistical Comparisons
Output Should Resemble Input Averages: The average grades (quality) in your resource model should closely resemble the average grades in your input de-clustered data.
Accurate Representation of Grades: Your resource model should accurately represent the distribution of grades in your samples. There must be accord between the estimation of statistical parameters such as mean, mode, median and others and the input data. The estimate variance must be lower than the samples. This accuracy is fundamental in building confidence in your estimates.
Domain-Based Comparison: It's important to compare different estimation techniques on a domain-by-domain basis. Each geological domain may have unique characteristics and assessing them separately allows for a more refined understanding of estimation performance.
Histogram Shape Consistency: The shape of the resulting histograms in each domain should be similar to the original data histograms, with some degree of smoothing and normalization. Deviations in histogram shapes can indicate potential issues in the estimation process.
Comparison with Alternative Estimation Methods
Mineral resource estimations must rely on accurate and reliable data. Model validation processes are crucial to ensure this reliability.
Nearest Neighbor Analysis and IDW² Estimations
Nearest neighbor analysis indicates fewer tons and higher grades (less contained metal) per block, as this method does not utilize averaging techniques to estimate block grades. The IDW² estimation is closer to kriging as it employs a distance-weighted average. However, it lacks the ability to account for anisotropy and the nugget effect. Additionally, IDW² cannot de-cluster input data. The use of the kriging algorithm provides a reliable estimate by clustering data and weighting samples based on a variogram.
Conclusion: Reliability of Kriging
The kriging algorithm offers a reliable estimation by clustering data and weighting samples based on a variogram. Comparisons with alternative estimation methods can verify whether kriging estimations show an overall bias.
Geologic Interpretation and Modeling Controls
Deterministic Geological Modeling: Precision and Accuracy Interpreting geological variables in cross-sections and plan maps forms the basis of deterministic geological modeling. This process focuses on precision and accuracy, aiming to obtain models that are consistent and reliable with the data. It should be remembered that the construction of the model cannot be done solely at the desk; the interpretation of the exploration geologist should be taken into account.
Progress with Data and General Geological Knowledge Data related to the type of deposit and general geological knowledge are foundational in the modeling process. However, it's crucial to integrate this information with possible theories of mineralization and experiences gained from similar deposits.
Shape with Technical Details: Digital Terrain Models and Wireframes In the modeling process, technical details like digital terrain models and wireframes help define geological variables more effectively. However, the use of these techniques should be approached carefully, with thorough data verification.
Create Consistent 3D Models with Various Sections Starting with drill hole data and sections, create 3D models that are consistent across different sections. Continuous attention to consistency and accuracy is essential, considering the density of available data.
Boundary Analysis Controls
Boundary Analyses: Boundary analyses are of great importance for our mineral resource model to successfully reflect grade profiles in areas near contact zones. This involves verifying contact profiles in accordance with the conditions applied during the estimation process.
Solution-Focused Approach: At this critical stage, our comparisons, where we generate contact profiles from the resource model, evaluate the accuracy of unit grades. Specifically, we examine whether the grade behavior in areas near contact points is accurately represented.
1-Hard Boundaries:
Hard boundaries are points where specific geological units are clearly separated. These boundaries often rely on distinct geological features, types of mineralization, or lithological differences. The analysis of hard boundaries assesses clear transitions between specific units and the geological processes influencing these transitions.
2-Soft Boundaries:
Soft boundaries are points where the transition between geological units is less distinct, often utilizing gradients. These boundaries may rely on gradients derived from geochemical, geophysical, or other data types, indicating an uncertain transition between specific units. The analysis of soft boundaries involves determining transitions based on gradients and assessing the reliability of these transitions.
Geological Model Construction: Boundary analyses ensure the integration of hard and soft boundaries into the geological model.
Controls of The Block Model Geometry
In the geometric control of block models, the size of the blocks, the extent of the model, its alignment with the geological model, and its compatibility during resource estimation and model validation processes are crucial. Let's elaborate on the considerations you should keep in mind:
1-Control of Block Model Extents:
✔️ Ensure it covers the entire drilling area.
✔️Consider updated topographies (post-production topographies if available).
✔️Examine the open-pit optimization area.
2-Comparison of Block Models with Solid Models: (Mineralization, lithology, alteration, geometallurgy, redox, structural elements)
✔️Verify the variable codings assigned to the blocks.
✔️Check for volume compatibility.
3-Control of Block Sizes:
✔️ Confirm compatibility with drill hole data spacing.
✔️Check alignment with optimization and mining parameters.
4-Subblocks:
✔️If subblocks are used, ensure that values are assigned to subblocks rather than predicting from the main block.
5-Rotation Control:
✔️Verify the alignment of block model rotation with the main orientation of mineralization.
6-Discretization: The impact of the chosen block discretization parameters on interpolation needs to be controlled.
✔️These controls are vital to ensure data integrity and reliability during the model validation process.
Kriging Variance
Data Configuration and Kriging Variance: Critical Link in Model Validation
Insufficient data configuration can increase kriging variance in mineral resource estimates. However, this variance provides a relative measure of the data coverage surrounding the blocks. This situation can serve as a significant guide in the mineral resource classification process.
Relationship Between Insufficient Data and Variance
Deficiencies in data configuration, incorrect selection of search ellipsoids and discretization, composite selection used in interpolation, can increase the uncertainty of the estimate and thus kriging variance. However, this variance also indicates the distribution of data points surrounding the blocks. High kriging variance may signal a lack of data around specific blocks, which should be considered during the classification of resources.
The Impact on Classification Mineral Resource Estimation
Kriging variance provides valuable guidance in the mineral resource classification process. Regions with high variance may require additional data collection or modeling improvements to deal with uncertainty. This allows for a more accurate classification of resources.
Cross Validation
Validation methods play a crucial role in achieving reliable and accurate results in the process of mineral resource estimation. At this stage, cross-validation methods offer an effective strategy for identifying the optimal variogram model in grade prediction.
Cross-validation is a method used to test the accuracy of variogram models employed in mineral resource estimation. This method evaluates variogram models tested on the remaining samples using a set extracted from the sample database. This allows multiple strategies and models to be tested to select the most suitable model.
This cross-validation method is a critical tool to understand the performance of variogram models used in mineral resource estimation and to identify modeling errors. It is also useful for understanding geostatistical analysis results and identifying potential issues in numerical computations.
The major disadvantage of this application lies in whether or not the samples closest to the point of re-prediction are neglected during cross-validation. Variogram models are often insensitive to small changes, leading to misleading or very similar error statistics. In such cases, model selection and performance evaluation can become challenging. Given this disadvantage, it is essential to carefully apply the cross-validation method and interpret the results. Additionally, considering alternative methods and validation strategies is important in light of this drawback.
These controls are vital for ensuring data integrity and reliability during the model validation process.
3-RECONCILIATION
Reconciliation refers to verifying the completed resource model against production data and revising our understanding of the deposit if necessary. In this context, comparison with previous resource estimates may also allow to increase the model's compatibility with reality.
1-Geological data obtained during the prospecting phase is the first step in creating a comprehensible conceptual model of the deposit. As the process advances, each piece of data, observation, and discovery will enhance the geological model, making this process more sophisticated. Each finding contributes to establishing a more robust foundation for the geological model.
2-When sufficient research is conducted during the exploration phase, the process moves on to the mineral resource estimation aimed at predicting the tonnage, tenor, contained metal, and recovery values of the deposit. These mineral resource models, taking into account transformative factors and optimization parameters through economic and technical assessments, create mineral reserve estimation models within the planned mine boundaries.
3- Long-term models obtained from exploration drilling not only predict the future cash flows of the project but also play a decisive role in project profitability.
4- Short-term models created with data collected from blast holes, in-mine grade-control drillholes, benches, and underground grade-control sampling shed light on production. They contribute to the formulation of mining plans, enable quick decision-making to increase project profitability, and set goals for predicting risks in advance. However, these predictions are possible only with accurate estimations of tonnage, quality, and the correct prediction of the contained metal in mining operations, which is a complex process involving many factors.
5- Grade control model is used for daily production planning and typically includes ore control polygons or cuts derived from the short-range model. This model usually represents the mineable portion of the short-range model, considering the Selective Mining Unit (SMU); in surface operations, ore control polygons define excavation boundaries in the field.
6- Success of this process is achievable through a reconciliation optimization model properly organized in accordance with best practices. The reconciliation factor, defined by Parker in 2012 and further developed by Rossi and Deutsch in 2013, provides a monitoring mechanism by comparing the predicted values for each model with actual production data. This reconciliation system is designed to identify the difference between the estimated values throughout the mining value chain and the real production data.
These controls are vital to ensure data integrity and reliability during the model validation process.
SUM UP
Validating mineral resource models covers a comprehensive range of verification and cross-validation techniques, including data validation and database and model validation, and ensuring compatibility with previous estimation and production data.
-Protocols
Reading the protocols prepared to carry out exploration activities within the framework of best practices will guide our understanding of field procedures and other research.
-Fields Procedures
Data validation is to verify that the practices in the data collection, sampling, sample preparation and analysis process comply the Best Practices and that the data reflect reality, to ensure the quality and security of the data. It includes carrying out checks in the field, in the core warehouse, in places where sample preparation is made, in laboratories, comparing the data in the database with the data in the original documents, and analyzing the QAQC data.
-Database & Model
This validation includes validating the database using mining software during the modeling stage, evaluating the accuracy of geological and block models and their suitability to surface and drilling data using visual comparison, swath graphs and statistical methods. This process involves identifying and eliminating critical errors, estimating the degree of smoothing in the model, and keeping their impact on extractable resources under control. Model validation also includes evaluating whether the block sizes and orientation are appropriately selected with respect to the deposit geometry, and whether the appropriate interpolation technique is used. It is also crucial to check whether the reported mineralization meets the requirements for expectation of ultimate economic extraction.
-Reconciliation
Refers to verifying the completed resource model against production data and revising our understanding of the deposit if necessary. In this context, comparison with previous resource estimates may also allow to increase the model's compatibility with reality.
Finally, validation also includes checking the extent to which resource classification reflects the quality of data, the detail and reliability of the modeling (whether the size and orientation of the search ellipsoid are appropriately determined according to the variability of the estimated deposit parameters, whether correct predictions are made, etc.).
REFERENCES
Rossi & Deutsch (2014); Mineral Resource Estimation. Isaaks, Srivastava (1989), Applied Geostatistics.
Davis BM (1987); Uses and abuses of cross-validation in geostatistics.
Clark I (1986); The art of cross-validation in geostatistical applications.
Reconciliation Section Defined by Parker in 2012 and further developed by Rossi and Deutsch in 2013
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