Glacial isostatic adjustment on 3-D Earth models: a finite-volume formulation
Bibliographic record
Abstract
We describe and present results from a finite-volume (FV) parallel computer code for forward modelling the Maxwell viscoelastic response of a 3-D, self-gravitating, elastically compressible Earth to an arbitrary surface load. We implement a conservative, control volume discretization of the governing equations using a tetrahedral grid in Cartesian geometry and a low-order, linear interpolation. The basic starting grid honours all major radial discontinuities in the Preliminary Reference Earth Model (PREM), and the models are permitted arbitrary spatial variations in viscosity and elastic parameters. These variations may be either continuous or discontinuous at a set of grid nodes forming a 3-D surface within the (regional or global) modelling domain. In the second part of the paper, we adopt the FV methodology and a spherically symmetric Earth model to generate a suite of predictions sampling a broad class of glacial isostatic adjustment (GIA) data types (3-D crustal motions, long-wavelength gravity anomalies). These calculations, based on either a simple disc load history or a global Late Pleistocene ice load reconstruction (ICE-3G), are benchmarked against predictions generated using the traditional normal-mode approach to GIA. The detailed comparison provides a guide for future analyses (e.g. what grid resolution is required to obtain a specific accuracy?) and it indicates that discrepancies in predictions of 3-D crustal velocities less than 0.1 mm yr−1 are generally obtainable for global grids with ∼3 × 106 nodes; however, grids of higher resolution are required to predict large-amplitude (>1 cm yr−1) radial velocities in zones of peak post-glacial uplift (e.g. James bay) to the same level of absolute accuracy. We conclude the paper with a first application of the new formulation to a 3-D problem. Specifically, we consider the impact of mantle viscosity heterogeneity on predictions of present-day 3-D crustal motions in North America. In these tests, the lateral viscosity variation is constructed, with suitable scaling, from tomographic images of seismic S-wave heterogeneity, and it is characterized by approximately 2 orders of magnitude (peak-to-peak) lateral variations within the lower mantle and 1 order of magnitude variations in the bulk of the upper mantle (below the asthenosphere). We find that the introduction of 3-D viscosity structure has a profound impact on horizontal velocities; indeed, the magnitude of the perturbation (of order 1 mm yr−1) is as large as the prediction generated from the underlying (1-D) radial reference model and it far exceeds observational uncertainties currently being obtained from space-geodetic surveying. The relative impact of lateral viscosity variations on predicted radial motions is significantly smaller.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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) | 0.002 | 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 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".