Application of multiple-point simulation of mineral deposits based on discrete wavelet transform
Bibliographic record
Abstract
Traditionally, geostatistical simulations of mineral deposits are done by using methods based on two-point spatial statistics, such as variograms.However, second-order spatial statistics are not sufficient to capture critical and common features from mineral deposits, such as connectivity of extreme values and curvilinear patterns, which in turn drive a mine production sequence.As a way to overcome these important limitations, multiple-point simulation (MPS) methods have been developed.In this thesis, a MPS method based on wavelet analysis and on pattern recognition is described in detail.The idea in wavelet analysis applied to image compression is to decompose an image in two types of information: 1) average type information of the nearby pixels, called approximate sub-band of the image; and 2) how these pixels depart from local average.Usually, the sub-band image is a sufficient representation of the whole image, and can be used for several applications instead of the whole image.The simulation method used herein works as follows: first, it scans a training image with a template to generate a pattern database; then this database has its dimension reduced by applying discrete wavelet transform, so the approximate sub-band image of the patterns are obtained; after that, the patterns are divided into classes using k-means clustering algorithm, considering the approximate sub-band image; finally, the grid is simulated by comparing the conditioning data event in each node with the classes prototypes and choosing a pattern from that class.The practical intricacies and the contributions of this approach are tested and analyzed through an application at Olympic Dam copper deposit, which is located in South Australia and is the fourth largest producer of this commodity in the world.Both material types and copper grades were simulated in this case study.The categorical training image is generated through geological interpretation, and the continuous training image is generated by using low-rank tensor completion.Olympic Dam's simulation results show that the method used herein can be applied successfully to relatively complex and large deposits.Additionally, the results suggest that care must be taken when generating the training image, since it plays a very important role in the simulation process.The resulting simulated realizations are analyzed and validated in terms of histograms, vi variograms and high-order statistics, the latter being performed by using high-order spatial cumulants.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".