Robust time-domain full waveform inversion with normalized zero-lag cross-correlation objective function
Bibliographic record
Abstract
In full waveform inversion (FWI) with the least-squares (L2) norm, the direct amplitude matching is never perfect and the accurate estimation of the seismic source strength is not always available. In contrast, the normalized zero-lag cross-correlation objective function relaxes on the amplitude constraints and emphasizes the phase information when measuring the closeness between the simulated and observed data. This FWI method becomes insensitive to differences in amplitude. Based on this property, we investigate the effectiveness and robustness of FWI with the normalized zero-lag cross-correlation function (CFWI) against the noise and unpredictable amplitude of the data that cannot be modelled by the wavefield extrapolation operator. The effectiveness is firstly tested by noise-free data and data contaminated by Gaussian white noise. In addition, CFWI can invert the data set with incorrect source strength when compared with the L2 norm. Moreover, the data set with incorrect source signature illustrates that CFWI is slightly more insensitive to the error in source signature than the L2 norm. However, a source inversion is still needed when the source signature is severely erroneous. With non-Gaussian noise data, such as contaminated by strong ground motion noise and even by spike-type noise, CFWI provides a comparable result with that of the robust Huber norm. Numerical experiments with non-Gaussian noise also indicate that CFWI can suppress noise in data to produce clearer images when compared with the Huber norm. Besides, CFWI is free of the threshold criterion that controls the transition between the L2 and L1 norms used with the Huber and Hybrid norms and therefore free from tedious trial-and-error tests. Several numerical examples support that CFWI is an alternative and reliable inversion method. However, a numerical test with a 1-D initial model confirms that CFWI is more sensitive to the cycle-skipping problem caused by less-accurate initial velocity model than the L2 norm, which is due to the wrong matched events contributing to spurious local minima of the objective function of CFWI, but to an increase in the objective function used with the L2 norm.
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How this classification was reachedexpand
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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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; both teacher heads agree on what is shown here.
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".