A Bayesian framework with geology-informed structural priors for tomographic reconstruction and uncertainty quantification

Tomographic reconstruction involves fundamental trade-offs between resolution, data coverage and parametrization.
Conventional approaches commonly rely on regularized pixel-wise or cell-based parametrizations. These regularizations
are valuable and can themselves be geology-informed when their assumptions match the target setting. However, they
often encode structural information only indirectly through generic penalty terms and regularization weights. As a re-
sult, they can be less suited to questions in which the objective is to test a specific structural hypothesis. We develop
a Bayesian framework for tomographic reconstruction and uncertainty quantification that formulates such hypotheses
explicitly and assesses them through posterior uncertainty. As an illustrative application of the framework, we consider
ambient noise tomography. The phase velocity reconstruction is reformulated to address a targeted geological hypothe-
sis by introducing a parametrized structural prior. The prior is constructed from a Whittle–Matérn latent Gaussian field,
combined with spectral dimensional reduction via a truncated Karhunen–Loève expansion and a differentiable nonlinear
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pushforward mapping that promotes approximately piecewise-constant velocity structures. The prior parameters, includ-
ing the correlation length, smoothness, pushforward slope and velocity bounds, provide interpretable hyperparameters
related to expected lateral scale, structural regularity, transition sharpness and plausible phase-velocity contrasts. In this
formulation, the prior is used as a parametrized structural assumption informed by geological context, rather than as hard
geological knowledge. The resulting parametrization substantially reduces dimensionality, making both maximum a pos-
teriori estimation and Hamiltonian Monte Carlo sampling computationally feasible for the synthetic and observed data
sets considered here. Synthetic experiments demonstrate accurate recovery of prescribed velocity contrasts and show that
posterior uncertainty patterns reflect acquisition geometry and data coverage. Application to an ∼1000-sensor dense array
data set produces structures consistent with the imposed geology-informed prior assumptions, while providing spatially
resolved uncertainty estimates that identify regions of robust inference and remaining ambiguity. The framework offers a
proof-of-concept formulation for goal-oriented, uncertainty-aware seismic tomography when prior information supports
an explicit structural hypothesis that can be encoded through the proposed Whittle–Matérn latent-field parametrization.