Finite-difference modeling of SH-wave propagation in nonwelded contact media
Bibliographic record
Abstract
Abstract Many geological structures of interest are known to exhibit fracturing. Fracturing directly affects seismic wave propagation because, depending on its scale, fracturing may give rise to scattering and/or anisotropy. A fracture may be described mathematically as an interface in nonwelded contact (i.e., as a displacement discontinuity). This poses a difficulty for finite-difference modeling of seismic wave propagation in fractured media, because the standard heterogeneous approach assumes welded contact. In the past, this difficulty has been circumvented by incorporating nonwelded contact into the medium parameters using equivalent medium theory. We present an alternate method based on the homogeneous approach to finite differencing, whereby nonwelded contact boundary conditions are imposed explicitly. For simplicity, we develop the method in the SH-wave case. In the homogeneous approach, nonwelded contact boundary conditions are discretized by introducing auxiliary, so-called fictitious, grid points. Wavefield values at fictitious grid points are then used in the discrete equation of motion, so that the time-evolved wavefield satisfies the correct boundary conditions. Although not as general as the heterogeneous approach, the homogeneous approach has the advantage of being relatively simple and manifestly satisfying nonwelded contact boundary conditions. For fractures aligned with the numerical grid, the homogeneous and heterogeneous approaches yield identical results. In particular, in both approaches nonwelded contact results in a larger maximum stable time step size than in the welded contact case.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| 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) | 0.002 | 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".