A Nonlinear Inversion Framework for Seismic Velocity Modeling under Uncertainty

Thesis Abstract

In seismic exploration, accurately characterizing subsurface velocity structures under uncertainty remains a critical bottleneck for reliable imaging and hazard assessment, particularly in complex geological settings where heterogeneity and anisotropy influence wave propagation. This study addresses the problem of nonlinear inversion under uncertain prior information by developing a cohesive framework that combines probabilistic regularization, robust forward modeling, and data-driven parameterization to produce credible velocity models with quantified uncertainty. The aim is to create a generalizable nonlinear inversion framework that integrates physics-based forward solvers with stochastic inference to deliver velocity models and their associated confidence intervals for reliable decision-making in exploration and geohazard evaluation. Specific objectives are to (i) formulate a nonlinear inversion architecture that couples a differentiable wave equation solver with hierarchical Bayesian priors, (ii) implement a scalable sampling strategy to explore multimodal posterior distributions using Markov chain Monte Carlo with tempered transitions and variational inference for efficiency, (iii) incorporate model-reduction techniques and sparse regularization to handle high-dimensional parameter spaces while preserving salient velocity contrasts, (iv) calibrate and validate the framework on synthetic benchmarks and field data from heterogeneous sedimentary basins, and (v) assess the impact of uncertainty quantification on seismic velocity estimates and subsequent imaging workflows. Methodologically, the research adopts a mixed-methods design rooted in computational geophysics and statistical inference. The population comprises synthetic models representing layered, faulted, and anisotropic media, alongside real field datasets totaling approximately 1200 virtual seismograms and 2250 field traces collected from two complex basins with varying acquisition geometries. Data collection involves generating synthetic seismograms using a high-fidelity finite-difference solver for the 3D elastic wave equation and collating field records from publicly available and partner-company repositories, ensuring diverse source-receiver configurations. Instruments include controlled-source seismic data, ambient-noise correlations, and borehole-derived velocity logs used for validation. The core analysis employs a nonlinear inversion pipeline that integrates (i) a differentiable forward model leveraging a pseudo-spectral or finite-difference solver to produce synthetic data from proposed velocity fields, (ii) a hierarchical Bayesian framework to encode uncertainty in prior velocity distributions, anisotropy parameters, and noise models, and (iii) an efficient posterior exploration strategy combining Hamiltonian Monte Carlo with adaptive leapfrog steps and a variational autoencoder-based surrogate to reduce computational cost. Model specification includes a multi-parameter velocity field parameterization with spatially varying parameters and a sparsity-promoting prior to encourage geologically plausible contrasts. Validity and reliability are addressed through cross-validation on held-out field segments and sensitivity analyses to priors and noise assumptions. Expected findings include robust posterior velocity estimates with credible intervals that reflect both measurement noise and structural nonlinearity, improved resolution of high-contrast interfaces, and quantifiable reductions in velocity misfit compared with conventional linearized inversions. The framework is anticipated to reveal underdetermination regions where data poorly constrain velocity, guiding acquisition design. Comparative analyses will show that the proposed approach maintains stability under model misspecification and yields more reliable uncertainty bounds than standard least-squares or L2-regularized inversions. The study will demonstrate that posterior distributions are multimodal in complex basins, necessitating advanced sampling and model-reduction strategies. Contributions to knowledge encompass (i) a unified nonlinear inversion framework that explicitly propagates uncertainty from priors and data through to velocity estimates in seismic velocity modeling; (ii) demonstrable integration of hierarchical Bayesian theory with differentiable forward modeling and scalable posterior sampling in geophysics; (iii) methodological advances in combining physics-based simulation with data-driven surrogates to enable tractable uncertainty quantification for high-dimensional seismic problems; and (iv) practical implications for seismic imaging workflows where decision-making hinges on credible velocity models and their confidence intervals. The main conclusion is that incorporating probabilistic, nonlinear inversion with robust forward modeling yields velocity models whose predictive uncertainty is actionable for exploration and risk assessment. Recommendations include extending the framework to incorporate anisotropy and attenuation more comprehensively, integrating multi-physics data (gravity, magnetic, and electrical measurements) to further constrain the posterior, and developing automated guidelines for optimal data acquisition strategies based on posterior uncertainty metrics.