Full waveform inversion using wave‐equation depth migration with tying to wells
Bibliographic record
Abstract
We examine the key concepts in full waveform inversion (FWI) and relate them to processes familiar to practicing geophysicists. For clarity, we present the central theoretical result behind FWI as a mathematical statement that a linear update to a migration velocity model is proportional to a prestack reverse-time migration of the data residual (the difference between the actual data and data predicted by the model) where the proportionality factor must be estimated. We argue that in many cases this factor will be complex-valued and frequency dependent, or in the time domain, it will be a convolutional wavelet. We find an analogy between estimation of the velocity update from the migrated section and the common process of impedance inversion, and we suggest that FWI can be viewed as a practical cycle of data modeling, migration of the data residual, and “calibration” of this migration to deduce the velocity update. The calibration step can be accomplished like a conventional impedance inversion where the migrated data residual is tied to the velocity residual (the difference between actual velocity and migration velocity) at a well. As there are a great many established algorithms for impedance inversion, so there are a plethora of possibilities for calibration. We present an extended example using the Marmousi model in which we use wave-equation migration (e.g. depth stepping) of the data residual and a simple least-squares amplitude scaling and constant phase rotation, determined at a simulated well, to calibrate the migration. We find that our approach produces a much improved velocity model in only a few iterations.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| 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".