Fast Least-Squares Reverse Time Migration Via Approximating the Hessian as the Sum of Kronecker Products
Bibliographic record
Abstract
Summary Least-squares reverse time migration (LS-RTM) for complex fields imaging becomes an increasingly popular imaging method. It also enjoys some other advantages. For example, it is capable of attenuating migration artifacts, compensating the image amplitude which is distorted by geometrical spreading and unbalanced illumination, improving resolution via compressing the seismic source wavelet and it can also handle incomplete and noisy data. However, the massive computational overhead of LS-RTM poses a big challenge for modern super-computers and its computation time can easily exceed hundreds of hours. To overcome the shortcomings mentioned above, we propose a fast alternative method for LS-RTM. The new approach is formulated in the model (image) domain. The Hessian matrix is approximated via the superposition of Kronecker products which honour the block-band character of the Hessian matrix. We name the Kronecker product-based new imaging method as KLSRTM. Our numerical tests show the computation time is reduced significantly and the result of the proposed method is comparable to the output of conventional LS-RTM. Also, approximating the Hessian matrix by a superposition of Kronecker products permits for efficient exploration of tradeoff parameters for regularized LS-RTM as the computation cost for solving the KLSRTM is trivial after Kronecker factors are estimated.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| 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".