Enabling Probabilistic Full Waveform Inversion in Multi-Observable Thermochemical Tomography through Reduced-Order Spectral Element Modeling

Multi-Observable Thermochemical Tomography (MTT) is a simulation-driven, joint probabilistic inversion framework designed to estimate the thermochemical state of the Earth’s lithosphere by integrating geophysical datasets with complementary sensitivities. By jointly inverting observables such as gravity and geoid anomalies, surface heat flow, seismic dispersion, body-wave data, and magnetotelluric responses, MTT directly estimates primary thermodynamic variables, including temperature, pressure, and bulk composition, from which all secondary physical properties are derived through internally consistent thermodynamic models. This bottom-up approach provides physically-consistent constraints on lithospheric structure across regional to prospect scales.

Within this framework, MTT offers a powerful basis for characterizing lithospheric architecture and compositional domains that are commonly examined in mineral systems studies. In particular, MTT can help delineate major crustal- and lithospheric-scale structures, identify metasomatized/altered domains, and map thermochemical contrasts that serve as lithospheric-scale proxies commonly associated with specific classes of magmatic and hydrothermal mineral systems.

Despite recent advances incorporating ray-based seismic tomography solvers (Fomin, I., Afonso, J. C., Gorbatov, A., Salajegheh, F., Dave, R., Darbyshire, F. A., et al. (2026). Multi-observable thermochemical tomography: New advances and applications to the superior and North Australian cratons. Journal of Geophysical Research: Solid Earth, 131, e2025JB031939. https://doi.org/10.1029/2025JB031939 ), the integration of full-waveform seismic solvers within the MTT framework has not yet been achieved. Full-waveform inversion (FWI) offers enhanced sensitivity to both seismic velocity and density and the potential for improved spatial resolution relative to traditional tomography approaches. However, the computational cost of FWI remains prohibitive, particularly in probabilistic or ensemble-based inversion settings required for uncertainty quantification.

This contribution presents a computational strategy aimed at reducing the cost of full wavefield simulations to enable probabilistic seismic FWI within the MTT framework. We extend reduced-order modeling (ROM) techniques to the spectral element method (SEM), which is widely used for accurate time-domain seismic wave propagation in complex geological settings. Specifically, we consider projection (Galerkin)–based ROMs in which the SEM wavefield is approximated in a low-dimensional reduced basis constructed from representative high-fidelity solutions. While ROM approaches are well established for simpler formulations, their application to SEM-based elastic wave simulations remains challenging due to the method’s high dimensionality and complex operator structure. Beyond MTT, such reductions are also relevant to SEM-based workflows that require large numbers of forward simulations, including ground motion studies and FWI with many sources at regional-to-global scales.

We develop and test a reduced-order SEM formulation using synthetic benchmark models relevant to lithospheric-scale imaging. Results demonstrate computational speed-ups of up to two orders of magnitude relative to full SEM simulations, while retaining sufficient accuracy in simulated wavefields for inversion purposes. These results represent a first proof of concept toward incorporating probabilistic FWI into multi-observable thermochemical tomography and reducing a key computational barrier to uncertainty-aware, physics-based lithospheric imaging.