Seismic Waveform Inversion by Stochastic Optimization
Bibliographic record
Abstract
We explore the use of stochastic optimization methods for seismic waveform inversion. The basic principle of such methods is to randomly draw a batch of realizations of a given misfit function and goes back to the 1950s. The ultimate goal of such an approach is to dramatically reduce the computational cost involved in evaluating the misfit. Following earlier work, we introduce the stochasticity in waveform inversion problem in a rigorous way via a technique calledrandomized trace estimation. We then review theoretical results that underlie recent developments in the use of stochastic methods for waveform inversion. We present numerical experiments to illustrate the behavior of different types of stochastic optimization methods and investigate the sensitivity to the batch size and the noise level in the data. We find that it is possible to reproduce results that are qualitatively similar to the solution of the full problem with modest batch sizes, even on noisy data. Each iteration of the corresponding stochastic methods requires an order of magnitude fewer PDE solves than a comparable deterministic method applied to the full problem, which may lead to an order of magnitude speedup for waveform inversion in practice.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| 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 | 0.001 |
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".