[ingehap]

Implements work package 5 of docs/IMPLEMENTATION_PLAN.md: the walkaway-VSP ε and δ of Lewis et al. (2016), following Leaney & Hornby (2007), and the calibration of the sonic γ with them.

What is added

• iwt.raytrace (exact qP kinematics in VTI, fluids included; Tsvankin, 2012):
  • phase velocity, vertical slowness q(p) and dq/dp, and the polarization;
  • two-point direct rays in layered VTI.
  • Rays steeper than 85° in any layer they cross are dropped. Past that point the first arrival would be a refraction, which is not modelled.
• iwt.vsp.walkaway:
  • Synthetic survey: several azimuths, source statics and noise.
  • Measurements: p, q and polarization, with their joint covariance propagated from the picks. Overlapping source windows make neighbouring p values correlated.
  • Inversion: (Vp0, Vs0, ε, δ) fitted on V(θ) and ψ(θ) with the exact Christoffel equation, or with Thomsen's weak form for comparison.
  • Error model: Gaussian priors and an effective-variance covariance, frozen within each iteration. The Laplace posterior reports a data_weight per parameter.
  • Checks: a χ² test across azimuths, and a polarization check for lateral heterogeneity.
• iwt.calibration:
  • upscale_gamma: Backus upscaling, with C66 averaged arithmetically and C44 harmonically.
  • bayes_linear: straight-line fit with an extra scatter term (type-II maximum likelihood), leave-one-out predictions and predictive bands.
• examples/wp5_walkaway.py and docs/figures/wp5_*.png cover:
  • six levels at 30–60°, inverted five ways;
  • the near-angle trade-off and the consistency checks;
  • heterogeneity inside the sub-array;
  • the calibrated ε and δ curves.
• Tests: 17 new, including a Monte Carlo check of the covariance, a coverage test, the near-angle trade-off, the weak-anisotropy bias, the Vs0 prior, both checks, and missing picks.
• README and plan updated; version 0.5.0.

Main findings (synthetic well)

• Fast stringers limit the direct arrivals to 775–1450 m of offset, which is 23–78° at the levels. This may be why the article had only about 30–60°.
• Adding polarizations halves the ε error and triples the δ precision.
  • Their cost is an errors-in-variables bias of about 0.5σ, which scales with the noise variance.
  • With polarizations, ε and δ also depend on the Vs0 prior (Grechka & Mateeva, 2007).
  • Fitting slowness only gives calibrated errors, but Vp0 then comes from its prior alone.
• Heterogeneity inside the 40 m sub-array shifts ε by up to 0.03 while χ² stays small, so the posterior σ is too small. Add a model error of about 0.01.
• The polarization check found a 5 ms/km source static at only four of six levels. That static biases the slowness-only δ by up to 0.11.
• The γ → ε calibration fits well inside 640–860 m but fails below. Below 860 m half of the true ε curve falls outside its 2σ band, because the WP4 γ bias changes with depth there.

Validation

• Python 3.13 with RuntimeWarning and DeprecationWarning as errors: 128 passed.
• Python 3.9 with numpy 1.21 and scipy 1.7: 124 passed, 1 skipped (plotting).
• pyflakes is clean, and the README quick start runs.

🤖 Generated with Claude Code

https://claude.ai/code/session_019vaUDUPicoFeQaUhfhnoYq

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Generated by Claude Code

[Copilot]

🟡 Changes recommended

Calibration leakage, uncertainty diagnostics, and kinematic boundary errors remain unresolved.

6 open findings

• Preserve input length when running window exceeds log · New
• Re-estimate scatter separately for each leave-one-out fold · New
• Treat q=0 as valid horizontal propagation endpoint · New
• Handle zero horizontal qP eigenvector at q=0 · New
• Avoid claiming full data weight for infinite posterior variance · New
• Account for correlated errors in polarization chi-square · New

What changed in this PR

Implements WP5, connecting walkaway VSP anisotropy estimates with the existing sonic calibration workflow.

Changes:

• Adds exact VTI ray tracing, walkaway measurements, inversion, and consistency checks.
• Adds gamma upscaling and Bayesian calibration to epsilon and delta.
• Adds tests, a synthetic example, documentation, and version 0.5.0.

File	Description
tests/​test_walkaway.py	Tests ray tracing and walkaway inversion.
tests/​test_calibration.py	Tests upscaling and linear calibration.
README.md	Documents WP5 usage, results, and limitations.
pyproject.toml	Updates package version.
iwt/​vsp/​walkaway.py	Implements survey processing, inversion, and checks.
iwt/​vsp/​__init__.py	Documents the walkaway module.
iwt/​raytrace.py	Adds exact qP kinematics and layered rays.
iwt/​calibration.py	Adds gamma upscaling and Bayesian regression.
iwt/​__init__.py	Exposes ray tracing and updates version.
examples/​wp5_walkaway.py	Demonstrates inversion and calibration.
docs/​IMPLEMENTATION_PLAN.md	Records WP5 completion and deviations.

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