Bibliographic record
Abstract
ABSTRACT Least squares migration uses the assumption that, if we have an operator that can create data from a reflectivity function, the optimal image will predict the actual recorded data with minimum square error. For this assumption to be true, it is also required that: (a) the prediction operator must be error‐free, (b) model elements not seen by the operator should be constrained by other means and (c) data weakly predicted by the operator should make limited contribution to the solution. Under these conditions, least squares migration has the advantage over simple migration of being able to remove interference between different model components. Least squares migration does that by de‐convolving or inverting the so‐called Hessian operator. The Hessian is the cascade of forward modelling and migration; for each image point, it computes the effects of interference from other image points (point‐spread function) given the actual recording geometry and the subsurface velocity model. Because the Hessian contains illumination information (along its diagonal), and information about the model cross‐correlation produced by non‐orthogonality of basis functions, its inversion produces illumination compensation and increases resolution. In addition, sampling deficiencies in the recording geometry map to the Hessian (both diagonal and non‐diagonal elements), so least squares migration has the potential to remove sampling artefacts as well. These (illumination compensation, resolution and mitigating recording deficiencies) are the three main goals of least squares migration, although the first one can be achieved by cheaper techniques. To invert the Hessian, least squares migration relies on the residual errors during iterations. Iterative algorithms, like conjugate gradient and others, use the residuals to calculate the direction and amplitudes (gradient and step size) of the necessary corrections to the reflectivity function or model. Failure of conditions (a), (b) or (c) leads the inversion to calculate incorrect model updates, which translate to noise in the final image. In this paper, we will discuss these conditions for Kirchhoff migration and reverse time migration.
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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".