2‐D wave equation modeling and migration by a new finite difference scheme based on the Galerkin method
Bibliographic record
Abstract
2‐D wave equation modeling and migration using a new finite difference scheme based on the Galerkin method are presented. Since it involves the semi‐descretization of the finite element method (FEM), it is also called the finite element and finite difference method (FE‐FDM). For a 2‐D acoustic wave equation, by using the semi‐discretization technique of the finite element method (FEM) in the z direction with linear elements, the original problem can be written as a coupled system of lower dimensional partial differential equations (PDEs) that depend continuously upon time and space in the x direction. The fourth‐order finite difference method (FDM) is used to solve these PDEs. The concept and principle are introduced in this paper. Compared with the explicit finite‐difference method of the same accuracy, the stability condition becomes looser and shows an advantage over the conventional FDM. An absorbing boundary condition of fourth‐order accuracy is used to prevent boundary reflections. In numerical experiments, comparison is made between a FE‐FDM numerical solution and an analytic solution of the quarter‐plane. Here, FE‐FDM is shown to be accurate in numerical computation. In addition, a constant velocity model with two irregular interfaces is simulated to obtain a poststack seismic section, which is then successfully migrated. These examples show the potential of FE‐FDM in modeling and reverse‐time migration.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| 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 | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".