Image‐Domain Least‐Squares Migration Through Preconditioned Hessian
Bibliographic record
Abstract
ABSTRACT Image‐domain least‐squares migration (IDLSM), which typically employs a diagonally dominant Hessian with narrow bandwidth for the inverse problem, provides an efficient deconvolution strategy for subsurface reflectivity imaging. Conventional methods often rely on the adjoint of the Born/Kirchhoff modelling operator to compute the Hessian matrix. However, the adjoint‐derived Hessian is highly ill‐conditioned, leading to slow convergence during linear inversion and resulting in images with undesired resolution and amplitude fidelity. To overcome these limitations, this study introduces a novel IDLSM approach that integrates the state‐of‐the‐art migration operator. We derive and compute the preconditioned Hessian matrix through a Kirchhoff migration engine with source‐side and receiver‐side illumination. The preconditioned Hessian matrix exhibits identical values along its main diagonal. This illumination compensation will explicitly reduce the condition number of the Hessian matrix and significantly improve the quality of migrated images in terms of amplitude fidelity. In addition, we remove redundant source wavelets from the migrated image and the Hessian matrix. As a result, these improvements will greatly accelerate the convergence of linear inversion solvers while enhancing the resolution and amplitude fidelity of the resulting images. Experiments on synthetic and field datasets demonstrate that the proposed IDLSM method retrieves high‐fidelity reflectivity images with superior resolution and amplitude fidelity compared to conventional IDLSM techniques.
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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 | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".