Shot-record extended model domain preconditioners for least-squares migration
Bibliographic record
Abstract
ABSTRACT We have studied the preconditioned conjugate gradient (CG) algorithm in the context of shot-record extended model domain least-squares migration. The CG algorithm is a powerful iterative technique that can solve the least-squares migration problem efficiently; however, to see the merits of least-squares migration, one needs to apply the algorithm for several iterations. Generally speaking, the convergence rate of the CG algorithm depends on the condition number of the operator. Preconditioners are a family of operators that are easy to build and invert. Proper preconditioners can cluster the eigenvalues of the original operator; hence, they reduce the condition number of the operator that one wishes to invert. Accordingly, preconditioning the operator can, in theory, improve the convergence rate of the algorithm. In least-squares migration, the diagonal scaling of the Hessian and the approximated inverse of the Hessian are proven to work well as a preconditioner. We develop and apply two types of preconditioners for the shot-record extended model domain least-squares migration problem. The first preconditioner belongs to the diagonal scaling category, and a second preconditioner is a filter-based approach, which approximates the partial Hessian operators by local convolutional filters. The goal is to increase the convergence rate of the shot-record extended model domain least-squares migration using the reformulated cost function with a preconditioned operator. Experiments with a synthetic Sigsbee model and a real data example from the Gulf of Mexico, Mississippi Canyon data set, indicate that preconditioning the linear system of the equations improves the convergence rate of the algorithm.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".