L1 ⚛ L1-108 ⊙ Testnet

Interferometric SAR (InSAR) — deformation + DEM

Remote Sensing · Coherent SAR interferometry

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⬇ L1-108.md

# ⚛ L1 Principle — Interferometric SAR (InSAR) — deformation + DEM **ID:** `L1-108` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Remote Sensing — *Coherent SAR interferometry* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D deformation or DEM > **📡 Carrier:** radio_wave · **🌫 Noise:** speckle > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554198 --- ## 🧠 1. Introduction **Interferometric SAR (InSAR) — deformation + DEM** is a **nonlinear inverse problem** whose unknown lives in **2D deformation or DEM** space, within the **Coherent SAR interferometry** sub-domain of **Remote Sensing**. Measurements consist of radio-frequency electromagnetic waves via a **insar coherent interferometry** sensing mechanism. The forward operator applies, in order: L · emit · chirp operator; S · scan · platform operator; L · interferometric phase operator; L · phase unwrap operator; pixel-level spatial averaging on the detector. Observations are corrupted by multiplicative speckle from coherent imaging. Existence of the recovered 2D deformation or DEM is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 25); atmospheric_phase_screen dominates the stability cliff; baseline_error and the remaining mismatch parameters contribute higher-order bias terms. Multiplicative speckle (rayleigh amplitude / exponential intensity) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. ## ⚙ 2. Forward Model Physical chain: **x** → L · emit · chirp → S · scan · platform → L · interferometric phase → L · phase unwrap → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.phase_unwrap` `L.interferometric_phase` `S.scan.platform` `L.emit.chirp` x · η, η ~ speckle (multiplicative) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.emit.chirp` | L · emit · chirp operator | | `S.scan.platform` | S · scan · platform operator | | `L.interferometric_phase` | L · interferometric phase operator | | `L.phase_unwrap` | L · phase unwrap operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Remote Sensing | | Sub domain | Coherent SAR interferometry | | Carrier | radio_wave | | Problem class | nonlinear_inverse | | Solution space | 2D_deformation_or_DEM | | Noise model | speckle | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 4.2 | ## 📡 4. Measurement Model Existence of the recovered 2D deformation or DEM is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 25); atmospheric_phase_screen dominates the stability cliff; baseline_error and the remaining mismatch parameters contribute higher-order bias terms. Multiplicative speckle (rayleigh amplitude / exponential intensity) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `insar` · **Forward operator:** `insar_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 8192 | | W | px | 8192 | | Snr db | dB | 20 | | Pixel m | m | 3 | | Coherence | — | 0.8 | | Lambda cm | — | 5.6 | | Baseline m | m | 200 | | Baseline error | — | 0 | | Temporal decorrelation | — | 0 | | Atmospheric phase screen | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 1024 – 32768 | | W | px | 1024 – 32768 | | Snr db | dB | 0.0 – 30.0 | | Pixel m | m | 0.3 – 30 | | Coherence | — | 0.2 – 1.0 | | Lambda cm | — | 0.5 – 30 | | Baseline m | m | 50 – 2000 | | Unwrap error | — | 0.0 – 0.3 | | Baseline error | — | 0.0 – 10.0 | | Temporal decorrelation | — | 0.0 – 0.8 | | Atmospheric phase screen | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 20.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x8778d2e8e3c4dfc0da39beca833fd00fda4773f64c62efcbea3cdb4791dbf79e` - **Chain tx hash:** `0x5e83f585a47652592337dae02bef3b468965795b0c248ae0c2bc3df6d38fcd56` - **Chain block:** `41554198` --- ## File Mapping This bundle consists of: `L1-108.md`, `L1-108.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-108.md` | Source of truth — edit this | Human or LLM | | `L1-108.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-108`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-108-001 Interferometric SAR (InSAR) — deformation + DEM Mismatch-Only Spec

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📋 JSON metadata

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    "title": "Interferometric SAR (InSAR) \u2014 deformation + DEM"
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Coherent SAR interferometry",
  "title": "Interferometric SAR (InSAR) \u2014 deformation + DEM"
}

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