A Probabilistic Framework for Joint Inversion of Seismic Velocity and Attenuation

Thesis Abstract

This study addresses the persistent challenge of jointly characterizing subsurface seismic velocity (Vp) and attenuation (Q) in heterogeneous media, where independent inversions often yield biased or non-unique solutions and fail to capture the coupled physics governing wave propagation. The aim is to develop a probabilistic framework that integrates multi-parameter seismic data to produce consistent, uncertainty-quantified estimates of Vp and Q, thereby enhancing subsurface imaging for exploration and hazard assessment. Specific objectives include (i) formulating a hierarchical Bayesian model that couples velocity and attenuation via shared rock-physics priors and frequency-dependent relationships, (ii) developing a joint inversion algorithm that leverages both travel-time and amplitude/frequency-domain data, (iii) evaluating model identifiability and propagation of measurement and prior uncertainties through posterior distributions, and (iv) validating the framework with both synthetic benchmarks and field datasets from a sedimentary basin. The methodology adopts a mixed-methods, quantitative research design grounded in Bayesian inference and stochastic sampling. The population comprises seismic wave measurements from controlled-source experiments and natural seismic events across a well-characterized 3D geological model. A synthetic 3D reference model with 2,500 cells and realistic heterogeneity (Vp ranging 2.0–6.5 km/s, Qp ranging 40–350) is used to stress-test the framework, complemented by a field data corpus consisting of 150 controlled-source shots and 60,000 seismic traces collected over a 15 km by 15 km grid, with frequencies up to 80 Hz. Data collection instruments include multifrequency refraction/receiver arrays and full-waveform recording systems, with pre-processing steps incorporating delay-time picking, amplitude normalization, and spectral balancing. The probabilistic model specifies a joint likelihood for observed travel times, amplitudes, and spectral ratios, conditioned on latent fields for Vp and Q and augmented by rock-physics-informed priors that relate Vp and Q to porosity, lithology, and fluid content via established theoretical relations (e.g., Gassmann-type poroelasticity, the Khachaturyan attenuation framework). The prior distributions for Vp and Q are constructed as spatially smooth Gaussian random fields with hyperparameters estimated through hierarchical Bayesian calibration, enabling automatic adjustment of correlation lengths and variance. A Markov chain Monte Carlo (MCMC) algorithm, combining Hamiltonian Monte Carlo and adaptive Metropolis steps, is implemented to sample the joint posterior distribution, while a parallel tempering scheme mitigates multimodality. Model validation employs synthetic-to-field transfer tests, cross-validated on 20% of the field data withheld during inversion. Model comparison uses Bayes factors and predictive posterior checks, and sensitivity analyses quantify the impact of priors and noise levels on parameter recovery. For the field dataset, calibration against borehole-vetted lithology and porosity logs enables testing of rock-physics consistency and improves constraint on the Q estimates. Expected findings include robust joint posterior estimates of Vp and Q with credible intervals that reflect both data noise and model uncertainty, improved resolution in regions of velocity-attenuation coupling, and reduced non-uniqueness relative to single-parameter inversions. The study anticipates revealing systematic bias in velocity-only inversions in zones with fluids or fractures, which the probabilistic joint approach should mitigate by exploiting cross-parameter correlations. The contribution to knowledge lies in delivering a rigorously tested, scalable probabilistic joint-inversion framework that explicitly ties seismic velocity and attenuation to physical rock properties, enabling more reliable subsurface imaging and uncertainty quantification for hydrocarbon, groundwater, and geohazard applications. The work also advances methodological practice by integrating hierarchical priors, rock-physics constraints, and hybrid MCMC techniques tailored to large-scale geophysical problems. The main conclusion expected is that joint probabilistic inversion markedly improves the fidelity and interpretability of subsurface models under realistic noise and heterogeneity, compared with conventional separate-inversion strategies. The study recommends adopting the framework in mineral and hydrocarbon exploration campaigns, extending it to anisotropic and viscoelastic settings, and pursuing real-time implementation with high-performance computing to enable near real-time uncertainty-quantified updates as new data become available.