ifwi-pub

Reproducible synthetic examples for two companion papers by Shaowen Wang and Tariq Alkhalifah:

Accelerating High Resolution Implicit Full Waveform Inversion (Geophysics)
— the single-parameter velocity examples (Overthrust, Marmousi)

Implicit Full Waveform Inversion Imaging (GJI, 2026) — DOI 10.1093/gji/ggag277
— the joint velocity–impedance imaging (IFWIM) example (Marmousi2)

All forward/adjoint modeling runs on the sweep differentiable acoustic solver. The two single-parameter notebooks each reproduce one Geophysics experiment — three inversions on one model and the comparison figures — and the multiparameter notebook reproduces the joint $(v_p, Z)$ imaging example of the GJI paper:

Notebook	Model	Experiments
notebooks/pseudo_hessian_overthrust.ipynb	Overthrust	conventional FWI · iFWI (SIREN) · iFWI + pseudo-Hessian
notebooks/hash_encoding_marmousi.ipynb	Marmousi	conventional FWI · iFWI (SIREN) · iFWI + hash encoding
notebooks/multiparameter_marmousi2.ipynb	Marmousi2	joint $(v_p, Z)$ implicit FWI imaging (variable density, hash + multiscale)

The two single-parameter methods (which the Geophysics paper builds on) were first presented as EAGE extended abstracts, reproduced here:

• Implicit full waveform inversion with energy-weighted gradient — DOI 10.3997/2214-4609.202510069 (pseudo-Hessian / Overthrust)
• Multiresolution hash encoding for high resolution implicit full waveform inversion — DOI 10.3997/2214-4609.202510109 (hash encoding / Marmousi)

The multiparameter Marmousi2 notebook reproduces the joint velocity–impedance imaging example of the GJI paper Implicit Full Waveform Inversion Imaging (DOI 10.1093/gji/ggag277).

Method

The velocity model is reparameterized by a coordinate network and inverted through the wave equation:

vp(grid) = vp_init + std · net(coords) + mean

• Conventional FWI optimizes the grid velocity directly.
• Implicit FWI (iFWI) makes net a SIREN MLP (the paper's baseline).
• Pseudo-Hessian preconditions the velocity-grid gradient by the source/receiver illumination — g ← g / sqrt(s·r) — before back-propagating it into the network. s and r are read directly off the sweep solver (solver.source_illumination / solver.receiver_illumination), which the compiled backend fills during the backward pass. (Overthrust example.)
• Hash encoding prepends a native Instant-NGP multiresolution hash-grid encoder to the SIREN. (Marmousi example.)
• Multiparameter imaging (FWIM) inverts velocity and impedance jointly with a single shared hash + SIREN network (model_i = init_i + std_i · net(coords)[i]), driven by the variable-density AcousticVRZ solver. A band-pass multiscale schedule (3, 5, 8, all Hz) restarts the network + optimizer at each scale, baking the previous scale's model into the init. (Marmousi2 example.) Reproduction detail: the zero-phase band-pass must be a time-domain filtfilt (torchaudio, fp64) — a frequency-domain |H|² multiply leaves a coherent t=0 wrap artefact that destabilises the joint inversion.

Everything except the wave solver is implemented from scratch in src/ifwi_sweep.py: the SIREN network, the multiresolution hash encoding (pure PyTorch — not tinycudann) and the pseudo-Hessian preconditioner. The notebooks depend only on sweep plus torch / numpy / matplotlib.

Solver settings

All forward/adjoint modeling uses the compiled CUDA backend with boundary saving:

solver = PropTorch(Acoustic(spatial_order=..., device="cuda"), shape, dh, dt,
                   abcn=..., source_type=["h1"], receiver_type=["h1"], impl="c")
syn = solver(wavelet, sources, receivers, models=[vp], use_boundary_saving=True)  # 'bs' mode

Layout

src/ifwi_sweep.py     solver wiring + SIREN + hash encoding + pseudo-Hessian + VRZ restart + filters
src/models.py         Overthrust/Marmousi vp and Marmousi2 vp+impedance, true/smooth, embedded (zlib+base85)
notebooks/            pseudo_hessian_overthrust + hash_encoding_marmousi + multiparameter_marmousi2
figures/              comparison figures written by the notebooks (and cached results, gitignored)
tools/encode_models.py  regenerates src/models.py from .npy (only needed to update the models)

Installation

A CUDA GPU is required — this repo drives the solver with impl='c' (the compiled CUDA path). Install the sweep differentiable solver from PyPI:

pip install sweepx

This provides the sweep package used by the code. Full notes are in the sweep docs.

The notebooks additionally need torch numpy scipy matplotlib jupyter (all present in a sweep environment; see requirements.txt); the multiparameter notebook also uses torchaudio for the zero-phase band-pass filtfilt. No model data files are needed — the velocity models are embedded in src/models.py.

Running

With sweep installed, run the notebooks:

cd notebooks
jupyter lab            # open a notebook and run all cells

The notebooks ship with SMOKE = False (the full paper run — Overthrust 500 iterations, Marmousi 200, Marmousi2 400 = 4 scales × 100). Set SMOKE = True in the config cell for a quick reduced-iteration check (or set IFWI_EPOCHS). Inversion results are cached under figures/cache_*.npz, so re-running only re-plots (seconds) — delete the cache, or change any config value, to recompute. Observed data is generated on the fly by the same solver, so no pre-computed data is needed.

License

Released under the MIT License — see LICENSE.

Citation

If this repository is useful in your research, please cite the relevant paper(s):

Journal articles

• S. Wang and T. Alkhalifah, Implicit Full Waveform Inversion Imaging — Geophysical Journal International, 2026 — DOI 10.1093/gji/ggag277 (multiparameter IFWIM / Marmousi2)
• S. Wang and T. Alkhalifah, Accelerating High Resolution Implicit Full Waveform Inversion — Geophysics (under review) — single-parameter velocity: pseudo-Hessian + hash encoding

Conference abstracts

• S. Wang and T. Alkhalifah, Implicit full waveform inversion with energy-weighted gradient — EAGE Annual Conference & Exhibition, 2025 — DOI 10.3997/2214-4609.202510069 (pseudo-Hessian / Overthrust)
• S. Wang, M. Ravasi and T. Alkhalifah, Multiresolution hash encoding for high resolution implicit full waveform inversion — EAGE Annual Conference & Exhibition, 2025 — DOI 10.3997/2214-4609.202510109 (hash encoding / Marmousi)
• S. Wang and T. Alkhalifah, Accelerating the convergence of implicit FWI and LSRTM with a field data application — International Meeting for Applied Geoscience & Energy (IMAGE), 2025 — DOI 10.1190/image2025-4302395.1

BibTeX

@article{wang2026imaging,
  author  = {Wang, Shaowen and Alkhalifah, Tariq},
  title   = {Implicit Full Waveform Inversion Imaging},
  journal = {Geophysical Journal International},
  year    = {2026},
  doi     = {10.1093/gji/ggag277}
}

@article{wang_accelerating,
  author  = {Wang, Shaowen and Alkhalifah, Tariq},
  title   = {Accelerating High Resolution Implicit Full Waveform Inversion},
  journal = {Geophysics},
  note    = {Under review}
}

@inproceedings{wang2025energyweighted,
  author    = {Wang, Shaowen and Alkhalifah, Tariq},
  title     = {Implicit Full Waveform Inversion with Energy-Weighted Gradient},
  booktitle = {EAGE Annual Conference \& Exhibition},
  year      = {2025},
  doi       = {10.3997/2214-4609.202510069}
}

@inproceedings{wang2025hash,
  author    = {Wang, Shaowen and Ravasi, Matteo and Alkhalifah, Tariq},
  title     = {Multiresolution Hash Encoding for High Resolution Implicit Full Waveform Inversion},
  booktitle = {EAGE Annual Conference \& Exhibition},
  year      = {2025},
  doi       = {10.3997/2214-4609.202510109}
}

@inproceedings{wang2025lsrtm,
  author    = {Wang, Shaowen and Alkhalifah, Tariq},
  title     = {Accelerating the Convergence of Implicit {FWI} and {LSRTM} with a Field Data Application},
  booktitle = {International Meeting for Applied Geoscience \& Energy (IMAGE)},
  year      = {2025},
  doi       = {10.1190/image2025-4302395.1}
}