Tutorial 13: Bayesian AVO Inversion

Tutorial 13: Bayesian AVO Inversion#

Note

This tutorial is available as a Python script examples/13_bayes_avo_inversion.py and an interactive Jupyter notebook examples/notebooks/13_bayes_avo_inversion.ipynb.

Perform Bayesian AVO inversion using all four samplers (SVGD, HMC, NUTS, LDS) and learn the InverseProblem framework that bridges deterministic and Bayesian solvers.

What You Will Learn#

  • Use InverseProblem with create_inverter() for deterministic inversion

  • Use InverseProblem with as_posterior() for Bayesian inference

  • Set up AVO forward modeling through rock physics and Shuey reflectivity

  • Run Bayesian inversion with four samplers: SVGD, HMC, NUTS, LDS

  • Compare posterior mean, uncertainty, and convergence across samplers

Key Concepts#

InverseProblem provides a unified interface: define the forward model and observed data once, then switch between deterministic optimization (create_inverter()) and Bayesian sampling (as_posterior()).

Bayesian AVO inversion recovers a posterior distribution over elastic properties from pre-stack seismic data, quantifying uncertainty in the inversion result.

The tutorial proceeds in two parts. Part 1 demonstrates a deterministic inversion using the InverseProblem framework to obtain a point estimate of the elastic properties. Part 2 converts the same problem to a Bayesian formulation and runs all four samplers, comparing the posterior distributions and uncertainty estimates they produce.

Code#

from geobrain.core import InverseProblem
from geobrain.bayes import Posterior, SVGD, HMC, NUTS, LDS

# InverseProblem framework
problem = InverseProblem(forward_fn=forward, observed=d_obs, noise_std=0.01)
inverter = problem.create_inverter(initial_model=m0)   # deterministic
posterior = problem.as_posterior(log_prior=log_prior)    # Bayesian

# Run samplers
svgd = SVGD(target=posterior, lr=1e-4)
result = svgd.run(n_samples=50, n_steps=500)

Results#

The deterministic inversion provides a point estimate of the elastic properties, establishing a baseline before moving to Bayesian inference.

../_images/13_part1_demo.png

Fig. 71 Deterministic AVO inversion with InverseProblem framework.#

The four Bayesian samplers – SVGD, HMC, NUTS, and LDS – each produce a posterior distribution over elastic properties. Comparing them reveals differences in posterior mean, credible intervals, and sampling efficiency.

../_images/13_bayesian_avo_comparison.png

Fig. 72 Bayesian AVO inversion: posterior comparison across four samplers.#

Full Example#

See examples/13_bayes_avo_inversion.py.

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