Tensor tree decomposition as a rank‐reduction method for pre‐stack interpolation
Bibliographic record
Abstract
Abstract Tensors have been proposed to represent pre‐stack seismic data, particularly for seismic data denoising and reconstruction. They naturally permit describing multi‐dimensional seismic signals that depend on time (or frequency) and source and receiver coordinates. A tensor representation aims to preserve the information embedded in the multi‐linear array in a reduced space. Such a representation is part of many algorithms for seismic data reconstruction via tensor completion methodologies. We investigate and apply one particular tensor tree representation to seismic data reconstruction. The Tensor Tree decomposition methodology permits decomposing a high‐order tensor into third‐order tensors. The technique relies on the truncated singular value decomposition, which branches the tensors into low‐dimensional tensors. As a benefit, the tensor tree allows us to reorganize the tensor into a matrix that demands the least singular values to have an optimal low‐rank approximation. We have developed an algorithm that uses the tensor tree for data reconstruction in an iterative optimization scheme and directly compared it to the parallel matrix factorization. At first, we demonstrated the proposed methodology results with five‐dimensional synthetic shot data and then moved forward with five‐dimensional field data, where we analysed it both pre and post‐stack. The tensor tree performs well in reconstructing both synthetic and field data with high fidelity, at the same level as the well‐established parallel matrix factorization.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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".