Implementation of efficient low-storage techniques for 3-D seismic simulation using the curved grid finite-difference method
Bibliographic record
Abstract
SUMMARY High-resolution 3-D seismic simulation imposes severe demands for computational memory, making low-storage seismic simulation particularly important. Due to its high-efficiency and low-storage, the half-precision floating-point 16-bit format (FP16) is widely used in heterogeneous computing platforms, such as Sunway series supercomputers and graphics processing unit (GPU) computing platforms. Furthermore, the low-storage Runge–Kutta (LSRK) technique requires lower memory resources compared with the classical Runge–Kutta. Therefore, FP16 and LSRK provide the possibility for low-storage seismic simulation. However, the orders of magnitude of the physical quantities (velocity, stress and Lamé constants) in the elastic wave equations are influenced by the P-wave and S-wave velocities and the densities of the elastic media. This results in a huge order of magnitude difference between the stored velocity and stress values, which exceed the range of the stored values of FP16. In this paper, we introduce three dimensionless constants, Cv, Cs and Cp, into elastic wave equations, and new elastic wave equations are derived. The three constants, Cv, Cs and Cp, keep the orders of magnitude of the velocity and stress at a similar level in the new elastic wave equations. Thus, the stored values of these variables in new equations remain within the range of the stored values of FP16. In addition, we introduce the use of the LSRK due to its low-storage characteristic. In this paper, based on the FP16 and LSRK low-storage techniques, we develop 3 optimized multi-GPU solvers for seismic simulation using the curved grid finite-difference method (CGFDM). Moreover, we perform a series of seismic simulations to verify the accuracy, stability, and validity of the optimized solver coupled with the two techniques. The verifications indicate that through maintaining the calculation accuracy, the computational efficiency of the solver is significantly optimized, and the memory usage is remarkably reduced. In particular, under the best conditions, the memory usage can be reduced to nearly 1/3 that of the original CGFDM solver.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".