2‐D wave equation modeling and migration by a new finite difference scheme based on the Galerkin method
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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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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 it