From uncertain velocity models to ensemble-based ground motion simulations

Physics-based earthquake wave propagation and ground motion simulations rely critically on three-dimensional seismic velocity models as inputs. These models may originate from seismic tomography, empirical regional compilations, geological constraints, or hybrid modelling approaches, and are commonly treated as deterministic representations of the subsurface. However, all such velocity models are affected by substantial epistemic uncertainty arising from limited data coverage, modelling assumptions, and methodological choices, and often disagree in overlapping regions. Neglecting this uncertainty obscures how variability in Earth structure propagates into simulated wavefields and ground motion estimates, limiting the interpretability and robustness of physics-based seismic hazard assessments.

We present a probabilistic framework to account for velocity model variability in physics-based ground motion predictions. Rather than selecting a single preferred velocity model, we represent model uncertainty through the fusion of multiple, spatially overlapping velocity models using scalable Gaussian process (GP) regression. Our approach treats existing velocity models as spatially correlated observations of an underlying velocity field and infers a continuous probability distribution that captures both shared structural features and model disagreement. The GP formulation thus preserves spatial coherence across scales and provides an interpretable description of uncertainty in terms of spatial covariance, characteristic length scales, and amplitude variability. This enables the generation of ensembles of physically plausible velocity model realisations for use in wave propagation solvers, thereby producing ground motion predictions that explicitly reflect velocity model uncertainty.

Using our framework and realistic 3D seismic velocity models in a regional case study, we generate an ensemble of velocity model realisations and propagate them through physics-based earthquake simulations. We show that uncertainty in velocity structure alone can produce substantial variability in simulated wavefields and predicted ground motions, even when all other aspects of the simulation are held fixed. These results highlight the sensitivity of physics-based ground motion estimates to uncertain subsurface structure and motivate the need to explicitly incorporate velocity model uncertainty in physics-based earthquake simulations.

While demonstrated here for seismic velocity models, the framework can readily incorporate additional geophysical parameters relevant to earthquake wave propagation, such as density and attenuation. This provides a practical route for incorporating epistemic Earth model uncertainty into physics-based seismic hazard assessment.