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.

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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

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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.

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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