Pyramid

Reverse-engineering and testing Filippo Biondi's SAR Doppler tomography ideas against open SAR data, with a focus on the Giza pyramids.

This repository is both:

• a research sandbox for trying Biondi-style single-acquisition Doppler/sub-aperture tomography
• a record of what worked, what failed, and what the current physics-based limits appear to be on open Sentinel-1 data

Current status

The short version:

• we successfully ingested a real Sentinel-1A Giza SLC scene
• we reproduced several families of sub-aperture tomography pipelines
• we built an interactive slice explorer
• we tested many variants of a Biondi-like displacement/acoustic focusing approach
• we did not obtain robust, defensible subsurface imagery from open Sentinel-1 IW TOPS data

The current evidence points to a hard limit in the available geometry, not just a tuning problem.

What is in this repo

• sardt.py: baseline EM-style TomoSAR utilities
• giza_backend.py: Sentinel-1 SAFE ingestion, target localization, geometry derivation, and slice/point helpers
• biondi_core.py: Biondi-style displacement tracking, acoustic steering, and TOPS deramping experiments
• app.py: interactive Flask viewer for top-down SAR plus vertical slices
• experiments/: runnable experiments, sweeps, and feasibility checks

Main experiments

• experiments/run_sentinel1_giza_test.py First real-data Giza smoke test on Sentinel-1 IW2 VV
• experiments/run_hypothesis_loop.py EM-style tomography sweeps over measurement and inversion variants
• experiments/run_biondi_hypothesis_loop.py Biondi-style displacement/acoustic hypothesis sweeps
• experiments/run_biondi_perpixel_slice_scan.py Global slice inversion with per-pixel steering and frequency sweeps
• experiments/run_sensor_feasibility_model.py Theoretical resolution/conditioning/displacement-limit model for Sentinel-1 and illustrative COSMO-like apertures

Key results

1. Real Giza Sentinel-1 data works as an input

This is the Giza-area IW2 VV chip extracted from the Sentinel-1 scene:

That confirmed the ingestion, geolocation, swath selection, and complex-data processing path.

2. TOPS-aware preprocessing improved tracking, but not enough

We compared no deramp, simple deramp, and 2D deramp before Biondi-style tracking:

Tracking metrics improved, but the inversion still failed to produce stable depth-resolved structure.

3. Per-pixel steering still produced unstable depth peaks

The strongest remaining open-data variant used per-point steering inside the slice solver:

This was still not robust. Depth peaks moved under small parameter changes and often collapsed to the depth-range edges.

4. The feasibility math is the most important result

The theoretical model is here:

The model computes:

• aperture-limited acoustic depth resolution
• steering-matrix conditioning and PSF width
• phase-based displacement precision bounds

For the actual Sentinel-1 Giza geometry, the numbers are unfavorable:

• actual Sentinel-1 aperture span used by the model: about 11.86 km
• EM-style TomoSAR vertical resolution: about 4.62 km
• acoustic-style resolution at c = 1500 m/s, f = 500 Hz: about 215 m
• acoustic-style resolution at c = 1500 m/s, f = 1000 Hz: about 108 m

Those bounds explain why the reconstructions do not show meter-scale buried structure.

Interpretation

The most defensible current conclusion is:

• open Sentinel-1 IW TOPS data does not appear sufficient to reproduce Biondi-style subsurface imagery in a robust way
• the failure mode is not only implementation error; the geometry and conditioning look fundamentally weak for the target claim
• if the published results are reproducible, they likely depend on materially different data and/or a stronger forward model than what is inferable from the papers alone

This does not prove Biondi's results are impossible in all settings. It does show that a broad set of plausible reconstructions on open Sentinel-1 data fail, and that the theoretical bounds for this scene are poor.

Running the code

Create a Python environment with the packages already used in this repo:

python3 -m venv .venv
. .venv/bin/activate
pip install numpy matplotlib tifffile flask

Run the interactive viewer:

MPLCONFIGDIR=/tmp/mpl .venv/bin/python app.py

Then open http://127.0.0.1:5001.

Run the main feasibility model:

MPLCONFIGDIR=/tmp/mpl .venv/bin/python experiments/run_sensor_feasibility_model.py

Data

This repo does not include the multi-gigabyte raw SAR inputs.

The main Giza scene used in the experiments was:

• S1A_IW_SLC__1SDV_20160706T155618_20160706T155645_012030_012959_83DC

It can be obtained from ASF / NASA Earthdata:

• ASF datapool ZIP: https://datapool.asf.alaska.edu/SLC/SA/S1A_IW_SLC__1SDV_20160706T155618_20160706T155645_012030_012959_83DC.zip
• CMR granule search: https://cmr.earthdata.nasa.gov/search/granules.json?collection_concept_id=C1214470488-ASF&temporal=2016-07-06T00:00:00Z,2016-07-06T23:59:59Z&point=31.1342,29.9792&page_size=20

Notes for anyone trying to rerun the tests:

• you need a NASA Earthdata account
• you need to authorize the ASF application for that account
• programmatic download works most easily with a ~/.netrc entry for urs.earthdata.nasa.gov

Minimal ~/.netrc example:

machine urs.earthdata.nasa.gov
login YOUR_USERNAME
password YOUR_PASSWORD

If ASF access has not been authorized yet, log in once through:

• https://sentinel1.asf.alaska.edu/login

The public figures and JSON summaries included in this repo are enough to inspect the results, but contributors will need to obtain the original SAR product themselves for full reruns.

Open questions

• Can the Biondi papers be reverse-engineered more faithfully from public descriptions alone?
• Is the missing ingredient mostly data mode, mostly forward model, or both?
• Would spotlight/staring commercial SAR materially change the feasibility bounds?
• Is there a defensible passive-vibration interpretation here that does not overstate subsurface claims?

Contributing

Useful contributions would include:

• better derivations of the Biondi forward model from published sources
• stronger burst-domain / spotlight-domain processing
• independent checks of the feasibility math
• alternative open datasets with more favorable geometry
• skeptical reproductions and failure analyses

This repo is intended to be scientifically useful even if the answer remains negative.