Liquefaction Model — Geospatial GLM Surrogate

1. What the model computes (and what it does not)¶

The product is the probability and areal extent of liquefaction and its surface manifestation severity, served in three framings (§4): conditional on a ground motion, unconditional over a return period, and for a specific event. A geospatial model trades per-site borehole data for spatially continuous proxies — predicting liquefaction from PGV/PGA, $V_{s30}$, water-table depth, precipitation, and distance to water Zhu et al., 2015Zhu et al., 2017 — so it covers regions where site investigations do not exist.

What the model does not do: it does not replace site-specific CPT/SPT triggering analysis at an engineered site; it does not solve transient 3-D groundwater flow (it consumes a water-table field, §6); and it does not by itself produce ground motion — that comes from a ShakeMap (event) or the NSHM (probabilistic), §4–§5.

2. The physics — the equations we solve¶

The simplified procedure Seed & Idriss, 1971Idriss & Boulanger, 2006 compares seismic demand to soil capacity. The cyclic stress ratio (demand) is

the cyclic resistance ratio $\mathrm{CRR}$ is the capacity, and triggering is expected when the factor of safety

Surface severity is summarized by manifestation indices — the Liquefaction Potential Index Iwasaki et al., 1978 and the Liquefaction Severity Number Ballegooy et al., 2014. Two Pillar-1 state variables enter directly:

• Hydrology (water table). Pore pressure sets the effective stress $\sigma'_{v0}=\sigma_{v0}-u$, which appears in both demand (the $\sigma_{v0}/\sigma'_{v0}$ ratio in CSR) and capacity (overburden correction of $V_{s1}$). Only saturated soil below the water table can liquefy — saturation is a binary gate. A shallower water table raises demand and exposes more liquefiable column.

• Rigidity (shear-wave velocity). $V_s$ is the small-strain stiffness proxy ($G_{max}=\rho V_s^2$). It raises capacity — CRR increases with overburden-corrected $V_{s1}$ Andrus & Stokoe, 2000 — and modulates demand, because $V_{s30}$ controls site amplification of $a_{max}$. Stiffer ground resists triggering, but soft sites amplify shaking.

3. The geospatial surrogate — what is solved vs. assumed¶

Classical triggering (§2) is evaluated per soil column. The geospatial model regresses the outcome (liquefaction occurrence / manifestation) on spatially available proxies, and GAIA’s GLM uses the mechanics-informed ML surrogate of Sanger et al., 2025, which emulates physics-based triggering at national scale and in near-real time, demonstrated for the PNW in Sanger & Maurer, 2026.

The surrogate’s value is speed and coverage: it runs the conditional model everywhere, fast enough for the unconditional integral (§4) and for Earth2Studio ensembles (§7).

4. The three hazard framings¶

A GLM digital twin must serve three distinct questions, each with different ground-motion input and data/model need:

The unconditional product is the “total risk for a return period” baseline; the event-based product is the real-time nowcast for a specific rupture (e.g. a Cascadia or Nisqually scenario). All three call the same conditional surrogate — they differ only in how the ground motion is supplied and integrated.

5. Attenuation, $\kappa_0$, and the NSHM¶

High-frequency ground motion — and therefore $a_{max}$ — is controlled by attenuation, parameterized by the site spectral-decay term $\kappa_0$ Anderson & Hough, 1984. Two questions the GAIA seismic networks help answer:

• Where is $\kappa_0$ measured? From the high-frequency slope of recorded acceleration spectra ($A(f)\propto e^{-\pi\kappa f}$); the zero-distance intercept is the site $\kappa_0$. GAIA’s dense seismic/DAS data make this estimable per site.

• Can $\kappa_0$ vary in time? It is dominated by attenuation in the shallow, moisture-sensitive subsurface, so it is not strictly static — seasonal variation has been observed Händel et al., 2025Ktenidou et al., 2015. This couples to the Pillar-1 soil reanalysis (the same near-surface saturation GAIA monitors via $dv/v$).

Open integration question. The NSHM embeds a fixed reference-rock $\kappa_0$ and $V_{s30}$ site term Petersen et al., 2024; how to feed a time-varying site term ($\kappa_0(t)$, $V_s(t)$) back into the hazard input for the unconditional product (§4) is unresolved and a GAIA research target.

6. Coupling map — where the other GAIA projects plug in¶

(a) Soil reanalysis (Pillar 1, Soil Hydromechanical Memory). The water-table depth $d_{wt}(x,t)$ and saturation $S_w$ are the dynamic liquefaction controls (§2); the seismic $dv/v$ inversion also delivers a time-varying $V_s$ for both the capacity term and the site amplification. This is the direct line from the reanalysis to liquefaction susceptibility, and the route by which sea-level rise and seasonal water-table change modulate hazard (via the groundwater modeling).

(b) The landslide model (Landslide Model — Landlab Implementation). Liquefaction and landslides share the same antecedent hydromechanical state — saturation and water table — but couple it to a seismic trigger (PGA/PGV) rather than rainfall recharge. The landslide engine’s Monte-Carlo-over-uncertain-strength structure is the template the liquefaction surrogate mirrors: both are “soil state + trigger → probability of failure.”

(c) Earthquake wavefields & the NSHM. The ground-motion field comes from ShakeMap (event) or the NSHM (probabilistic, via gaia-nhsm-deagg); GAIA’s wavefield reconstruction/forecasting work is the natural source of refined, possibly time-varying, site ground motion.

7. Interoperability with Earth2Studio¶

The dynamic half of the GLM twin needs forecast forcing, routed through Earth2Studio — the same AI weather/climate stack the landslide model and Pillar 3 forecasting use:

• Climate/weather → groundwater → water table. Earth2Studio forecasts (precipitation, plus sea-level-rise and seasonal scenarios) drive the groundwater model that sets $d_{wt}$ — the dynamic liquefaction control.

• GLM surrogate as a diagnostic model. The fast mechanics-informed surrogate Sanger et al., 2025 can be wrapped with the Earth2Studio diagnostic signature for large scenario / return-period ensembles on GPU.

• Time-varying site terms. Seismic-derived $V_s(t)$ / $\kappa_0(t)$ feed the ground-motion side (§5), closing the dynamic loop.

8. Evaluation & metrics¶

As for the landslide model, separate calibration of intermediate states from validation of the prediction; full metric definitions live in HazEvalHub.

• Calibration — against the geotechnical case-history record (CPT/SPT triggering, manifestation fragility Geyin & Maurer, 2020Maurer et al., 2015) and the $V_s$ / water-table inputs.

• Validation — against observed liquefaction maps from past earthquakes (the Nisqually 2001 event is the regional target): probabilistic skill (Brier, reliability), spatial agreement (IoU) of mapped manifestation, and — for the unconditional product — consistency with return-period expectations.

9. Repositories (placeholders — for Morgan to confirm)¶

• da-seis-groundfailure — the liquefaction / ground-failure modeling repo (hydrology + seismology + geotech).

• gaia-nhsm-deagg — USGS NSHM disaggregation client feeding the unconditional integration.

• gaia-model-liquefaction (proposed) — the GLM surrogate digital twin (conditional / unconditional / event-based runners).

• gaia-vs-conus (proposed) — the parametric $V_s$-profile product Sanger & Maurer, 2025.

Proposed repositories do not exist yet — the names are placeholders for the team to create/confirm.

Related¶

• Pillar 2 — Nowcasting Hazard Susceptibility — the science framing.

• Pillar 1 — Soil Reanalysis Product · Groundwater & Soil Moisture — the soil state and water-table this model consumes.

• Liquefaction & Ground Failure — the hazard page.

• Data Inventory — every input/output with sources, resolution, and the data-prep pipeline.

• Landslide Model — the sibling model this one mirrors.

• HazEvalHub — metric definitions.

References¶