Part of the depth step (#4) of the uncertainty arc (epic #2). A δv/v change is not a pure shear-velocity change: in partially saturated ground, filling/draining pore space changes both the shear modulus and the bulk density, so for the shear-dominated coda
δv/v ≈ ½·δμ/μ − ½·δρ/ρ,
and velocity alone cannot separate δV_S/V_S from δρ/ρ. Ignoring the density term biases the inferred velocity change — and the downstream stress — most in hydrological and cryospheric targets, where saturation swings are largest.
Deliverable (full module + demo):
- A
codameter petrophysical module (e.g. uq_density): Gassmann fluid substitution for the modulus + a porosity–saturation relation for the density; maps a saturation change → (δV_S/V_S, δρ/ρ).
- Extend the depth inversion (
uq_depth) to carry δρ/ρ as a second inverted field with its own kernel, reporting how much of the surface δv/v each field explains and propagating the porosity/fluid-modulus/saturation-path priors into the split.
- Synthetic demo on a truth-known partially saturated site; tests (mass balance, small-perturbation limit, covariance ⪰ velocity-only).
Grounds: framework text already added to the paper (§ Depth) and quarto/theory-processing-depth.qmd (§ "Partial saturation"). Refs: Gassmann (1951); Mavko, Mukerji & Dvorkin (2009); Clements & Denolle (2018); James et al. (2019).
Blocks a trustworthy effective stress (#5) in unsaturated ground.
Part of the depth step (#4) of the uncertainty arc (epic #2). A δv/v change is not a pure shear-velocity change: in partially saturated ground, filling/draining pore space changes both the shear modulus and the bulk density, so for the shear-dominated coda
δv/v ≈ ½·δμ/μ − ½·δρ/ρ,
and velocity alone cannot separate δV_S/V_S from δρ/ρ. Ignoring the density term biases the inferred velocity change — and the downstream stress — most in hydrological and cryospheric targets, where saturation swings are largest.
Deliverable (full module + demo):
codameterpetrophysical module (e.g.uq_density): Gassmann fluid substitution for the modulus + a porosity–saturation relation for the density; maps a saturation change → (δV_S/V_S, δρ/ρ).uq_depth) to carry δρ/ρ as a second inverted field with its own kernel, reporting how much of the surface δv/v each field explains and propagating the porosity/fluid-modulus/saturation-path priors into the split.Grounds: framework text already added to the paper (§ Depth) and
quarto/theory-processing-depth.qmd(§ "Partial saturation"). Refs: Gassmann (1951); Mavko, Mukerji & Dvorkin (2009); Clements & Denolle (2018); James et al. (2019).Blocks a trustworthy effective stress (#5) in unsaturated ground.