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Inference-Mode Ambient Noise Tomography

This repository contains the reference implementation accompanying the GJI submission:

"Towards Inference-Mode Ambient Noise Tomography: A Framework for Phase Velocity Field Reconstruction and Uncertainty Quantification."

It provides a fully reproducible synthetic experiment (regular station geometry) demonstrating Bayesian phase velocity reconstruction using:

  • Whittle–Matérn Gaussian random field prior
  • Karhunen–Loève (KL) dimensionality reduction
  • Straight-ray line-integral forward operator
  • Maximum a posteriori (MAP) estimation (L-BFGS)
  • Full posterior sampling using NUTS
  • Posterior post-processing and uncertainty visualization

The repository supports reproducible inference-mode imaging, where geological interpretation is grounded in posterior uncertainty quantification.

1. Required Packages

The recommended way to reproduce the results is via conda:

conda env create -f environment.yml
conda activate inference-mode-ant

Main Dependencies

  • Python: 3.12
  • NumPy: < 2.0 (for PyTorch compatibility)
  • SciPy
  • Matplotlib
  • PyTorch: 2.2
  • Pyro: 1.9.1
  • scikit-image
  • ArviZ

Sanity Check

Run the following command to verify the environment:

python -c "import torch, pyro, numpy; print('Environment OK')"

2. Synthetic Field Generation

The synthetic velocity field is located in:

make_synthetic_field/

If needed, regenerate it via:

python make_synthetic_field/generate_synthetic_field.py

This produces:

synthetic_field.npy

True_field.png

The field defines two velocity levels representing geological structure.

3. Generate Synthetic Observations

Run:

python core/save_signal.py

This:

Loads the synthetic velocity field

Computes straight-ray travel times

Saves observation data to:

obs/obs_data.pickle

4. MAP Estimation (L-BFGS)

Run:

python core/MAP_estimate.py --device cpu

This computes the maximum a posteriori (MAP) estimate of the phase velocity field under:

  • Whittle–Matérn prior

  • KL parameterization

  • Straight-ray forward operator

5. Posterior Sampling (NUTS)

Run:

python core/sampling.py --device cpu

This performs full Bayesian posterior sampling using:

  • Hamiltonian Monte Carlo (NUTS)

  • Pyro backend

  • Reduced KL parameterization

Samples are saved in:

stat/

6. Posterior Post-Processing

Run:

python core/post_process.py

This generates:

  • Posterior mean field

  • Posterior standard deviation (UQ)

  • Sampling diagnostics (ESS, trace plots)

Core Components

core/line_integral.py

Implements the straight-ray forward operator used to compute travel times along station pairs.

core/prior.py

Defines the Whittle–Matérn Gaussian prior and KL expansion used to parameterize the velocity field.

These two modules form the mathematical backbone of the inference engine.

Important

All commands must be executed from the repository root:

inference-mode-ant/

Full Reproduction Pipeline

conda env create -f environment.yml
conda activate inference-mode-ant

python make_synthetic_field/generate_synthetic_field.py
python core/save_signal.py
python core/MAP_estimate.py --device cpu
python core/sampling.py --device cpu
python core/post_process.py

Output

The full pipeline produces:

  • True synthetic field
  • MAP reconstruction
  • Posterior mean
  • Posterior uncertainty maps
  • Sampling diagnostics