On the role of tomographic resolution and uncertainty in reconstructing past mantle flow

Tomographic images play a crucial role in estimating the thermodynamic state of Earth's mantle, yet reliable quantification of their uncertainties is essential for drawing robust conclusions in geodynamics. In particular, reconstructions of past mantle flow that rely on tomographic inputs require a practical handling of the difference in spatial scales between predictions from fluid dynamics and the heterogeneities observable through seismology. This scale discrepancy can indeed already be addressed through so-called tomographic filtering as a post-processing step applied to standard forward models of mantle circulation. However, integrating such approaches technically into adjoint or inverse modeling frameworks—used in data-driven mantle flow reconstructions—remains to be thoroughly explored.

Here, we perform a fully synthetic experiment to highlight the difficulties in quantitatively linking tomographic images with geodynamic models. Specifically, we employ the Subtractive Optimally Localized Averages (SOLA) method—a linear Backus–Gilbert-type inversion technique—to image a reference mantle circulation model. The SOLA inversions are based on finite-frequency traveltime residuals derived from full-waveform numerical seismograms computed for the geodynamic reference model.

Drawing on the insights provided by this synthetic experiment, we propose a workflow for adjoint-based mantle flow reconstructions that aims to leverage the tools provided by the SOLA approach. For the tomographic component, this involves generating spatially optimized averaging kernels that characterize local resolution (i.e. the specific tomographic filter), along with rigorous uncertainty estimates for parameter averages obtained by the propagation of data errors (both being built-in features of SOLA). On the geodynamic side, one should first aim to incorporate measures of tomographic resolution directly into the misfit/cost function of the adjoint method. This step is critical because the adjoint model validation compares observed surface dynamic topography in time with its prediction from the reconstructed flow history, which is highly sensitive to the tomographic input.  Once resolution-related biases are factored in, small model ensembles should make it possible to practically account for stochastic uncertainties, eventually yielding more robust constraints on mantle flow history. We suggest that the success of a specific misfit function and the realization of model ensembles can be assessed with dedicated synthetic closed-loop experiments, prior to their actual application.

Overall, our results offer practical guidance towards a strategy that integrates the complete tomographic information, including resolution and uncertainty, into fully operational reconstructions of past mantle flow.