Endmember modelling of detrital zircon petrochronology data via multivariate Tucker-1 tensor decomposition
Bibliographic record
Abstract
Detrital petrochronology is a powerful method of characterizing sediment and potentially sediment sources. The recently developed Tucker-1 decomposition method holds promise of using detrital petrochronology to identify both sediment-source characteristics and the proportions in which sources are present in sink samples even when sediment sources are unknown or unavailable for sampling. However, the correlation between endmember characteristics and lithological sources or proportions and sedimentary processes has not been established. Herein we present a case study of the recently developed Tucker-1 decomposition method to a multivariate geochemical data set from detrital zircons in till samples collected above the Cu-bearing Guichon Creek Batholith (GCB) in southern British Columbia, Canada. Data include a suite of eleven variables, including age, Ce anomaly, CeN/NdN, DyN/YbN, ΔFMQ, Eu anomaly, ΣHREE/ΣMREE, Hf, Th/U, Ti temperature, and YbN/GdN, from 12 samples from collected at a range of distances in the down ice-flow direction from the GCB.We demonstrate that endmember modelling using the Tucker-1 decomposition method successfully deconvolves the multivariate data sets into two endmembers in which the geochemical distributions are consistent with derivation from either non-oxidized and relatively anhydrous (i.e., low ore potential, Source 1) or oxidized and hydrous (i.e., potential ore bodies, Source 2) igneous rocks. Furthermore, we demonstrate that the proportions of the Source 2 endmember decrease with increasing distance from the ore bodies, as expected due to downstream zircon mixing and dilution.Finally, we attribute each of the zircon grains to either the Source 1 or 2 endmember based on maximization of the likelihood that their measured multivariate geochemistry was drawn from one or the other of the learned multivariate endmembers. We compared these grain attributions to the results of an independent Classification and Regression Tree (CART) analysis designed to characterize zircon grains as either “fertile” or “barren” with respect to copper based on their geochemistry. We find that there is ~80% overlap between the source attributions based on the CART analysis and the grain-source identification based on the Tucker-1 decomposition.We conclude that the novel Tucker-1 decomposition approach provides a flexible, precise, and accurate method of characterizing multivariate sediment sources even when those sources are unknown. It thus provides a basis for future petrochronological interpretations with applied and pure geoscience applications. All of the analyses presented herein can be freely accessed through a web application (https://dzgrainalyzer.eoas.ubc.ca/) or open-source Julia code (https://github.com/MPF-Optimization-Laboratory/MatrixTensorFactor.jl).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".