3D frequency-domain finite-difference viscoelastic-wave modeling using weighted average 27-point operators with optimal coefficients
Bibliographic record
Abstract
ABSTRACT Experimental data suggest that the viscoelastic behavior of rocks is more easily and accurately described in the frequency domain than in the time domain, supporting the idea of simulating seismic wave propagation in the frequency domain. We evaluated weighted-averaged 27-point finite-difference operators for 3D viscoelastic wave modeling in the frequency domain. Within the proposed framework, we developed general equations for normalized phase velocities that can be used with arbitrary finite-difference operators. Three sets of weighting coefficients for second-order central finite-difference operators that minimize the numerical dispersion for up to five grid points per wavelength were found using a damped least-squares (LS) criterion as well as a global optimization scheme based on l1- and l2-norm criteria. The three sets produced very similar dispersion curves, and improvement provided by global optimization appeared marginal in this respect. We also evaluated a discrete form for the heterogeneous formulation of the 3D viscoelastic equations with a perfectly match layer (PML). Heuristic performance assessment of frequency-dependent PML absorption coefficients provided a simple rule giving good results for eight PMLs at all frequencies. The proposed formalism was implemented with a massively parallel direct solver. Modeling results were compared with an analytic solution and a time-domain finite-difference code, and they gave good agreement when using LS and l2-norm optimal coefficients. On the other hand, l1-norm coefficients produced noisy results, indicating that minimizing the difference between analytic and numerical phase velocities, although necessary, is not a sufficient condition to guarantee low-numerical noise. Finally, analysis of the computational resources required to factorize the impedance matrix revealed that the memory complexity of the factorization is O(292N4) for an N3 grid, compared to O(30N4) for the viscoacoustic case.
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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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".