Liquefaction Model — Mechanics-Informed Geospatial Surrogate

1. The idea¶

Practice-standard liquefaction assessments need in-situ measurements. Geospatial models don’t, but they buy that coverage by regressing liquefaction observations on proxy variables — and there are only a handful of well-mapped earthquakes per decade to learn from.

This model changes the target. Instead of learning “did the ground liquefy here,” it learns what a CPT-based triggering analysis would have said here. Training targets come from running the Idriss & Boulanger procedure Idriss & Boulanger, 2008 on ~37,000 cone penetration tests across 48 U.S. states and 19 countries; geospatial variables sampled at those same sites are the features. The mechanics live in the target, so the model inherits them rather than having to relearn them from sparse case histories — and the training set is orders of magnitude larger than any liquefaction inventory, because a CPT site doesn’t need to have experienced an earthquake to be useful. The approach builds on Geyin et al., 2022; the critique motivating it is Maurer & Sanger, 2023.

2. What it produces¶

The published product is a set of precomputed ~90 m rasters of two parameters, $A$ and $B$, that describe a site’s liquefaction response across all levels of shaking:

where $MI$ is a manifestation index — $LPI$ Iwasaki et al., 1978, $LPI_{ISH}$ Maurer et al., 2015, or $LSN$ Ballegooy et al., 2014 — and $PGA_M$ is magnitude-scaled PGA. Roughly, $A$ sets how severe the response gets and $B$ sets how quickly it gets there.

Because $A$ and $B$ are event-independent, the expensive work is already done: ~1.3 billion locations, >1 TB of geospatial input, HPC on DesignSafe and UW Hyak. At run time a user supplies a ShakeMap and evaluates the equation above — arithmetic, no ML inference, no HPC. Manifestation indices then convert to a probability of ground failure through fragility functions Geyin & Maurer, 2020, kept separate so they can be swapped as they are revised.

Two model domains ship: global (37 predictors) and New Zealand (43), each with $A$/$B$ for all three indices. Coverage is continuous except where predictions were deliberately suppressed — slopes above 5°, water, ice, permafrost. Full package sizes are 33 GB global and 85 MB for New Zealand; one index over one continent is ~1.5 GB.

3. Updating with subsurface data¶

Where the subsurface has actually been measured, the model should defer to it. $A$ and $B$ are updated by regression kriging Hengl et al., 2007: the ML prediction supplies the regression term, and the interpolated ML residual — known exactly at CPT sites, decaying to zero within ~1.2 km — supplies the correction. Predictions are scaled up or down toward what the geotechnical data says.

Each product ships with a variance classification map grading how much of the local prediction variance the ML model still owns, from no geotechnical influence to major. A user can see, per pixel, whether they are looking at a geotechnical answer or a geospatial one. Anyone holding proprietary or municipal CPT data can re-krige against the published rasters without retraining.

4. How well it works¶

Skill is scored by Brier score against the operational benchmark, Rashidian & Baise Rashidian & Baise, 2020, with significance from bootstrap confidence intervals, KS tests, and Cohen’s $d$.

Two results worth stating plainly. Updating helps — measurably, and exactly where subsurface data exists. And regionalization mostly didn’t: New Zealand has abundant CPTs and high-quality national geology, groundwater, and $V_{s30}$ layers, and its bespoke model still only matched the global one. If a region-specific model can’t clearly win there, the case for building them elsewhere is weak.

5. Where GAIA takes it¶

Groundwater depth is the model’s single most influential predictor — and it is currently frozen at its training value. Making it a run-time variable, supplied alongside shaking the way $PGA_M$ already is, is the main line of future work Sanger et al., 2025 and the direct interface to the rest of GAIA: the water table from Pillar 1 and the groundwater modeling, and with it the route by which seasonal change, drought, and sea-level rise modulate liquefaction hazard. It requires retraining with groundwater held out, not a new input slot.

Then, the model can be used in a probabilistic hazard framework, where shaking is a random variable and the water table is a random variable, and the output is a probability distribution of manifestation severity and ground failure. That is the liquefaction digital twin, and it is what the 2001–2031 Nisqually earthquake use case is built to demonstrate.

6. Products & repositories¶

Published on DesignSafe: global model maps Sanger et al., 2024, New Zealand model maps Sanger et al., 2024, and an example implementation — a Jupyter notebook and Matlab script that take a USGS ShakeMap URL and return geotiffs of the selected index and the probability of ground failure Sanger et al., 2024. Supporting CPT databases: North America Sanger et al., 2024 and Cascadia Rasanen et al., 2024.

Repositories: da-seis-groundfailure ·

Related¶

• Pillar 2 — Nowcasting Hazard Susceptibility — science framing · Liquefaction & Ground Failure — hazard page.

• Pillar 1 — Soil Reanalysis Product · Groundwater & Soil Moisture — the water table this model would consume once §6 is built.

• Data Inventory · Landslide Model · HazEvalHub.

References¶