Linearized inverse scattering of teleseismic waves for anisotropic crust and mantle structure: 1. Theory
Bibliographic record
Abstract
In this study we examine the recovery of vertically varying anisotropic crust and upper mantle structure using converted teleseismic waves recorded on three‐component seismograms from individual broadband stations. Our analysis is cast in terms of inverse scattering theory for a one‐dimensional medium and begins with a derivation of the plane wave Green's function for a homogeneous medium exhibiting arbitrary elastic anisotropy. This Green's function is employed within the single‐scattering approximation to derive formulae that relate the amplitude of the scattered wave in time to perturbations in material properties at corresponding depths. Inclusion of seismograms from multiple events representing a range of azimuths and incident angles leads to the construction of a linear system of equations that is readily solved using singular value decomposition. A useful by‐product of this “amplitude‐versus‐slowness” approach is the identification of simple and compact expressions for linearized reflection and conversion coefficients in anisotropic media that are accurate for small contrasts at near‐vertical angles of incidence. We demonstrate the accuracy of the linearized P‐to‐S transmission coefficient for an idealized upper mantle model. In a companion paper we will examine the application of this approach to field data recorded at stations of the Canadian National Seismograph Network.
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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 | 0.001 | 0.001 |
| 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) | 0.001 | 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".