Non-Euclidean Spatial Covariance for Bayesian Post-Stack Inversion and Ordinary Kriging with Hamiltonian Fast Marching
Bibliographic record
Abstract
Summary We introduce a novel workflow that integrates non-Euclidean shortest path distances (SPD) using locally varying geometric anisotropy (LVA) to define spatial covariance matrices. The resulting covariance can be used in both geophysical and geostatistical algorithms where spatial continuity is utilized. The use of LVA in proposed methodology bypasses the limitation of constant geometric anisotropy traditionally assumed in geostatistical methods; it produces a more accurate covariance and generates more geologically realistic models. The Hamiltonian Fast Marching (HFM) algorithm is more precise than other approaches to evaluate SPD, such as the Dijkstra algorithm. While robust spatial covariance estimation needs redundant measurements in any direction, in petroleum exploration only the vertical direction is sampled sufficiently. Lateral direction data scarcity is mitigated by extracting the local dips and anisotropy ratios along the major and minor continuity directions from the seismic data itself. We demonstrate the HFM method on Bayesian post-stack inversion and LVA ordinary kriging (OK) for estimating acoustic impedance. The proposed workflow is also valid for other inversion algorithms, varieties of kriging, and sequential Gaussian simulation.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".