Mechanical analysis of viscoelastic models for Earth media
Bibliographic record
Abstract
SUMMARY Linear and non-linear viscoelastic (VE) models such as the standard linear solid (SLS) and the generalized SLS (GSLS) are broadly used to represent the anelasticity of materials and Earth's media. However, although the VE approach is often satisfactory for any given observation, the inferred physical causes of anelasticity may be significantly misrepresented by this paradigm, and its predictions may be wrong or inaccurate in other cases. This problem is particularly important in heterogeneous media, including most cases of interest for seismology. For example, in homogenous media, VE and mechanics-based models predict identical quality-factor Q(f) and phase velocity c(f) spectra, but in heterogenous media, these models yield different time-stepping equations and interactions with material–property boundaries. The commonly used VE algorithms for modelling seismic waves rely on postulated convolutional integrals in time, whereas physically, models of rock rheologies should still be based on spatial interactions. To understand how VE models relate to mechanics, it is instructive to consider which physical properties of the medium are constrained reliably and which of them remain unconstrained by a pair of Q(f) and c(f) spectra, that is by VE properties. Despite its popular association with ‘attenuation,’ the peak value of Q−1(f) is actually a purely elastic property representing the existence of two (for SLS) or multiple (for GSLS) elastic moduli. These moduli are analogous to the drained and undrained moduli in poroelasticity or isothermal and adiabatic moduli in thermodynamics. By virtue of the Kramers–Krönig relations, the peak Q−1 is related to the total velocity dispersion, which is also caused by the difference between elastic moduli. By contrast, true anelasticity-related physical properties like viscosity are represented not by Q−1 values but by the frequencies of Q−1(f) peaks in the data. However, these frequencies also depend on multiple material properties that are not recognized or arbitrarily selected in the SLS and GSLS models. Inertial, body-force friction and the corresponding boundary effects are also ignored in VE models, which may again be improper for layered media. Thus, for physically accurate interpretation of laboratory experiments and numerical modelling of seismic waves, first-principle equations of mechanics should be used instead of VE models.
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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) | 0.002 | 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 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".