Correcting an acoustic wavefield for elastic effects
Bibliographic record
Abstract
Finite-difference simulations are an important tool for studying elastic and acoustic wave propagation, but remain computationally challenging for elastic waves in three dimensions. Computations for acoustic waves are significantly simpler as they require less memory and operations per grid cell, and more significantly can be performed with coarser grids, both in space and time. In this paper, we present a procedure for correcting acoustic simulations for some of the effects of elasticity, at a cost considerably less than full elastic simulations. Two models are considered: the full elastic model and an equivalent acoustic model with the same P velocity and density. In this paper, although the basic theory is presented for anisotropic elasticity, the specific examples are for an isotropic model. The simulations are performed using the finite-difference method, but the basic method could be applied to other numerical techniques. A simulation in the acoustic model is performed and treated as an approximate solution of the wave propagation in the elastic model. As the acoustic solution is known, the error to the elastic wave equations can be calculated. If extra sources equal to this error were introduced into the elastic model, then the acoustic solution would be an exact solution of the elastic wave equations. Instead, the negative of these sources is introduced into a second acoustic simulation that is used to correct the first acoustic simulation. The corrected acoustic simulation contains some of the effects of elasticity without the full cost of an elastic simulation. It does not contain any shear waves, but amplitudes of reflected P waves are approximately corrected. We expect the corrected acoustic solution to be useful in regions of space and time around a P-wave source, but to deteriorate in some regions, for example, wider angles, and later in time, or after propagation through many interfaces. In this paper, we outline the theory of the correction method, and present results for simulations in a 2-D model with a plane interface. Reflections from a plane interface are simple enough that an analytic analysis is possible, and for plane waves, we give the correction to the acoustic reflection and transmission coefficients. Finally, finite-difference calculations for plane waves are used to confirm the analytic results. Results for wave propagation in more complicated, realistic models will be presented elsewhere.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 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) | 0.003 | 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".