Mode-Free Wave Equation Tomography of Surface Waves via GPU-Accelerated Automatic Differentiation
Bibliographic record
Abstract
Summary Surface wave inversion traditionally relies on layered Earth assumptions and modal dispersion analysis, which can be inadequate in complex geological settings and require subjective mode identification. Full-waveform inversion (FWI), while more accurate, is computationally intensive and highly sensitive to the initial model. These limitations underscore the need for a robust, efficient, and mode-independent approach to surface wave tomography. This work presents a differentiable wave equation tomography (WET) framework implemented in PyTorch, leveraging automatic differentiation and GPU acceleration for efficient optimization. The method combines two complementary misfit strategies: cross-correlation lag minimization of dispersion spectra and full-spectrum comparison. Both are formulated to avoid mode picking and enable end-to-end differentiability. Synthetic experiments on 1D and 2D models demonstrate accurate recovery of velocity structures and dispersion characteristics, even in the presence of velocity reversals and lateral heterogeneities. The approach achieves rapid convergence within practical runtimes, offering a viable alternative to traditional surface wave analysis. This framework provides a flexible foundation for advanced seismic imaging and is readily extensible to incorporate other seismic phases, such as guided waves and reflections, for future joint inversion applications.
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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 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 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".